CryptoCurrency_Capstone-12-8-17.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cryptocurrency Prediction Analysis & Buying Actions\n",
    "***\n",
    "\n",
    "**Disclaimer:** I am not a financial institution nor do I represent one. All that is provided here is educational material: Do not take this information as professional investment advice. \n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing Necessary Python Libraries\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import os\n",
    "import glob\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "import seaborn as sns\n",
    "from sklearn import cross_validation\n",
    "from sklearn.linear_model import LinearRegression, Ridge\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Collecting Files & Converting to DataFrames\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#1)Finding .csv files to load and converting to dataframes\n",
    "\n",
    "##b)defining our file directory to pick up files of interest\n",
    "file_path = \"C:\\\\Users\\\\Mike\\\\PythonScripts\\\\Data_New\\\\\"\n",
    "\n",
    "##c)using 'glob' function to pick up all .csv files, returning a list\n",
    "csv_files = glob.glob(file_path + \"*.csv\")\n",
    "#print(csv_files)\n",
    "\n",
    "##d)looping through list of files stored in 'c)' and converting to dataframes\n",
    "data_files_df = []  #initializing list to store dataframes converted from file paths stored in 'csv_files'\n",
    "\n",
    "for file in csv_files:\n",
    "    data = pd.read_csv(file, parse_dates=[0], index_col=0, usecols = [0,4]) #1st column is used as index for each dataframe\n",
    "    data_files_df.append(data)\n",
    "\n",
    "#print(data_files_df)\n",
    "\n",
    "##e)unpacking dataframes stored in 'data_files_df' list in part d)\n",
    "bitcoin_df, ethereum_df, litecoin_df, zcash_df = data_files_df\n",
    "\n",
    "##f) renaming columns of each dataframe so we can easily tell which cryptocurrency we are working on\n",
    "bitcoin_df.rename(columns = {\"Close\":\"VALUE_BC\"}, inplace=True)  \n",
    "ethereum_df.rename(columns = {\"Close\":\"VALUE_ET\"}, inplace=True)   \n",
    "litecoin_df.rename(columns = {\"Close\":\"VALUE_LC\"}, inplace=True) \n",
    "zcash_df.rename(columns = {\"Close\":\"VALUE_ZC\"}, inplace=True)  \n",
    "\n",
    "# print(bitcoin_df)\n",
    "# print(ethereum_df)\n",
    "# print(litecoin_df)\n",
    "# print(zcash_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Joining all Files into Single DataFrame\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            VALUE_BC  VALUE_ET  VALUE_LC  VALUE_ZC\n",
      "Date                                              \n",
      "2013-04-28    134.21       NaN      4.35       NaN\n",
      "2013-04-29    144.54       NaN      4.38       NaN\n",
      "2013-04-30    139.00       NaN      4.30       NaN\n",
      "2013-05-01    116.99       NaN      3.80       NaN\n",
      "2013-05-02    105.21       NaN      3.37       NaN\n",
      "2013-05-03     97.75       NaN      3.04       NaN\n",
      "2013-05-04    112.50       NaN      3.48       NaN\n",
      "2013-05-05    115.91       NaN      3.59       NaN\n",
      "2013-05-06    112.30       NaN      3.37       NaN\n",
      "2013-05-07    111.50       NaN      3.33       NaN\n",
      "2013-05-08    113.57       NaN      3.41       NaN\n",
      "2013-05-09    112.67       NaN      3.42       NaN\n",
      "2013-05-10    117.20       NaN      3.44       NaN\n",
      "2013-05-11    115.24       NaN      3.35       NaN\n",
      "2013-05-12    115.00       NaN      3.27       NaN\n",
      "2013-05-13    117.98       NaN      3.28       NaN\n",
      "2013-05-14    111.50       NaN      2.82       NaN\n",
      "2013-05-15    114.22       NaN      2.94       NaN\n",
      "2013-05-16    118.76       NaN      2.92       NaN\n",
      "2013-05-17    123.02       NaN      3.19       NaN\n",
      "2013-05-18    123.50       NaN      3.29       NaN\n",
      "2013-05-19    121.99       NaN      3.30       NaN\n",
      "2013-05-20    122.00       NaN      3.18       NaN\n",
      "2013-05-21    122.88       NaN      3.09       NaN\n",
      "2013-05-22    123.89       NaN      3.12       NaN\n",
      "2013-05-23    126.70       NaN      3.18       NaN\n",
      "2013-05-24    133.20       NaN      3.18       NaN\n",
      "2013-05-25    131.98       NaN      3.12       NaN\n",
      "2013-05-26    133.48       NaN      3.25       NaN\n",
      "2013-05-27    129.75       NaN      3.10       NaN\n",
      "...              ...       ...       ...       ...\n",
      "2017-10-30   6130.53    307.75     56.39    241.22\n",
      "2017-10-31   6468.40    305.88     55.75    233.01\n",
      "2017-11-01   6767.31    291.69     53.18    222.41\n",
      "2017-11-02   7078.50    287.43     54.74    218.16\n",
      "2017-11-03   7207.76    305.71     56.18    232.63\n",
      "2017-11-04   7379.95    300.47     55.04    230.39\n",
      "2017-11-05   7407.41    296.26     54.75    225.35\n",
      "2017-11-06   7022.76    298.89     55.17    228.69\n",
      "2017-11-07   7144.38    294.66     61.30    240.87\n",
      "2017-11-08   7459.69    309.07     62.57    250.60\n",
      "2017-11-09   7143.58    320.88     64.27    262.00\n",
      "2017-11-10   6618.14    299.25     59.26    237.88\n",
      "2017-11-11   6357.60    314.68     62.30    253.60\n",
      "2017-11-12   5950.07    307.91     59.01    288.67\n",
      "2017-11-13   6559.49    316.72     61.40    265.45\n",
      "2017-11-14   6635.75    337.63     62.68    271.44\n",
      "2017-11-15   7315.54    333.36     63.82    290.56\n",
      "2017-11-16   7871.69    330.92     71.06    294.91\n",
      "2017-11-17   7708.99    332.39     67.57    291.19\n",
      "2017-11-18   7790.15    347.61     69.64    298.15\n",
      "2017-11-19   8036.49    354.39     71.59    299.33\n",
      "2017-11-20   8200.64    366.73     72.25    302.17\n",
      "2017-11-21   8071.26    360.40     70.03    290.64\n",
      "2017-11-22   8253.55    380.65     71.89    319.73\n",
      "2017-11-23   8038.77    410.17     73.22    311.55\n",
      "2017-11-24   8253.69    474.91     77.97    346.36\n",
      "2017-11-25   8790.92    466.28     88.82    344.70\n",
      "2017-11-26   9330.55    471.33     85.93    340.14\n",
      "2017-11-27   9818.35    480.36     91.60    347.51\n",
      "2017-11-28  10058.80    472.90     96.03    371.24\n",
      "\n",
      "[1676 rows x 4 columns]\n"
     ]
    }
   ],
   "source": [
    "#3) Performing an outer join on dataframes with pd.concat to pair up data on same dates, making one big dataframe\n",
    "\n",
    "df = pd.concat([bitcoin_df, ethereum_df, litecoin_df, zcash_df], axis = 1) #axis = 1, means stacking as columns\n",
    "# print(\"\\n This is a joined dataframe holding values of all cryptocurrencies:\\n\")\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting  Values of Each Cryptocurrency Overtime\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea33e3cd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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d9UoppVqrxu0lJnJvWOjWKbbF+9CgopRSCvA1f+2tqaTERzaSOzgNKkoppQCo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\nVuBTklZlq2AbyBCjLmAF8K2IuBY4AdyfsYotl2k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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea3356b7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qZ9tysKzR9Cpt/vKf0NBQCgoK9Auxg4wxFBQUEBra/hlOlVKda2NuCcOTIuql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\nKs455+rGk4pzzrm68aTinHOubv4fSSXWRGUgFRAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea33e87c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea33e87978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xcXFcf/31xMTEUFBQwIYNG7jooovo27cvo0aN4vjx4wDs37+f4cOH07t3b/r0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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea356a96d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#4) Plotting dataframe to get a picture of cryptocurrencies value over time\n",
    "\n",
    "##a) plotting all cryptocurrencies on one plot\n",
    "plt.figure()\n",
    "df.plot()\n",
    "\n",
    "plt.title(\"Cryptocurrency Value vs. Time (2013 - Present)\")\n",
    "plt.xlabel(\"Dates\"), plt.ylabel(\"Value ($)\")\n",
    "plt.legend((\"Bitcoin\", \"Ethereum\", \"Litecoin\", \"Zcash\"), loc = 'upper left')\n",
    "\n",
    "###b) making sublplots of each crypto \n",
    "#plt.figure()\n",
    "#df.plot(subplots=True, layout=(2,2), sharex=False) #-1 can be used to calculate  number of rows given number columns you want (viceversa)\n",
    "\n",
    "##c) plotting all cryptocurrenices from 2016 onward (most action)\n",
    "df.loc[\"2016\":, :].plot() #partial string selection and logscaleY axis\n",
    "\n",
    "plt.title(\"Cryptocurrency Value vs. Time (2016 - Present)\")\n",
    "plt.legend((\"Bitcoin\", \"Ethereum\", \"Litecoin\", \"Zcash\"), loc = 'upper left') #adjusting labels of legend and location for easy read\n",
    "plt.xlabel(\"Dates\"), plt.ylabel(\"Value ($)\")\n",
    "\n",
    "##d) Logscale plot from 2016 onward\n",
    "plt.figure()\n",
    "df.loc[\"2016\":, :].plot(logy=True) #partial string selection and logscaleY axis\n",
    "\n",
    "plt.title(\"Cryptocurrency Value vs. Time - Logscale (2016 - Present)\")\n",
    "plt.legend((\"Bitcoin\", \"Ethereum\", \"Litecoin\", \"Zcash\"), loc = 'upper left') #adjusting labels of legend and location for easy read\n",
    "plt.xlabel(\"Dates\"), plt.ylabel(\"Value ($)\")\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Investigating Correlations Between Cryptocurrencies\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The correlation matrix from 2013 - present is:\n",
      "\n",
      "           VALUE_BC  VALUE_ET  VALUE_LC  VALUE_ZC\n",
      "VALUE_BC  1.000000  0.913293  0.913882  0.317703\n",
      "VALUE_ET  0.913293  1.000000  0.967474  0.418377\n",
      "VALUE_LC  0.913882  0.967474  1.000000  0.371804\n",
      "VALUE_ZC  0.317703  0.418377  0.371804  1.000000\n",
      "\n",
      "The correlation matrix from 2017 - present is:\n",
      "\n",
      "           VALUE_BC  VALUE_ET  VALUE_LC  VALUE_ZC\n",
      "VALUE_BC  1.000000  0.836879  0.887066  0.717885\n",
      "VALUE_ET  0.836879  1.000000  0.937040  0.957959\n",
      "VALUE_LC  0.887066  0.937040  1.000000  0.849409\n",
      "VALUE_ZC  0.717885  0.957959  0.849409  1.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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CNDOzKmnWFXYWcDzpwV5/BcZHxE2SXgNcDFzVbAfv1iWrHGR/dEMc0NMhWD/0wODX9nQI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\npZxYzMyspf4/LObi20ddlxkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea37075ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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36myypZRNDpMlfY90uloAx5EG8M3MrA1ExARgQlXZ6YXp64Draqx3B9Cp26aUTSzHAV8D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\nzMysqZxYzMysqf4/cOTx1zA28dcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea356f7b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#4-1) Investigating correlation, if any, between cryptos -- all data\n",
    "\n",
    "#a) plotting a scatter_matrix\n",
    "# plt.figure()\n",
    "# pd.plotting.scatter_matrix(df, diagonal=\"kde\")\n",
    "\n",
    "#b) plotting heatmap of \n",
    "plt.figure()\n",
    "\n",
    "xlabel = [\"Bitcoin\", \"Ethereum\", \"Litecoin\", \"Zcash\"]\n",
    "ylabel = [\"Bitcoin\", \"Ethereum\", \"Litecoin\", \"Zcash\"]\n",
    "sns.heatmap(df.corr(method='pearson'), cmap='tab20', xticklabels = xlabel, yticklabels = ylabel)\n",
    "plt.title(\"Correlation Heatmap (2013 - Present)\")\n",
    "plt.tight_layout()\n",
    "print(\"\\nThe correlation matrix from 2013 - present is:\\n\\n\", df.corr(method='pearson'))\n",
    "\n",
    "#4-2) Investigation correlation from 2017 onward\n",
    "\n",
    "#a) plotting a scatter matrix from 2017 onward\n",
    "# plt.figure() \n",
    "# pd.plotting.scatter_matrix(df.loc[\"2017\":, :], diagonal=\"kde\")\n",
    "\n",
    "#b) plotting a heatmap from 2017 onward\n",
    "plt.figure()\n",
    "sns.heatmap(df.loc[\"2017\":, :].corr(method='pearson'), cmap=\"tab20\", xticklabels = xlabel, yticklabels = ylabel)\n",
    "plt.title(\"Correlation Heatmap (2017 - Present)\")\n",
    "print(\"\\nThe correlation matrix from 2017 - present is:\\n\\n\", df.loc[\"2017\":, :].corr(method='pearson'))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Wrangling: Extracting Cryptocurrency Values from DataFrame\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['VALUE_BC', 'VALUE_ET', 'VALUE_LC', 'VALUE_ZC'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "#5) Extracting individual columns from combined dataframe as numpy arrays to faciliate \n",
    "#   matrix Reshaping for later making predictions with sklearn\n",
    "\n",
    "#a) finding number of columns in combined dataframe, df\n",
    "columns_in_df = len(df.columns) #counts number of columns in dataframe\n",
    "print(df.columns)\n",
    "\n",
    "#b) extracting each column from combined dataframe seperately using a for loop\n",
    "df_column_values = [] #initializing empty list to store numpy arrays of extracted dataframe columns\n",
    "\n",
    "for column in range(0,columns_in_df):\n",
    "    extracted_column_values = df.iloc[:, column].values # extracts columns from dataframe as an array\n",
    "    \n",
    "    #checking if extracted array has nan's\n",
    "    if np.sum(np.isnan(extracted_column_values)) > 0: #checking number of nans present in array\n",
    "        extracted_column_values = extracted_column_values[~np.isnan(extracted_column_values)] #filtering array to return all values that aren't nan's\n",
    "        \n",
    "    else:\n",
    "        extracted_column_values #There are no nan's in array, just give me the original array\n",
    "    \n",
    "    df_column_values.append(extracted_column_values) #append array to a list\n",
    "\n",
    "#print(df_column_values)\n",
    "\n",
    "#c)unpacking extracted column arrays stored in 'df_column_values'  list\n",
    "\n",
    "bc_values_np, et_values_np, lc_values_np, zc_values_np = df_column_values\n",
    "\n",
    "#d) printing each extracted column as an array with nan's removed\n",
    "# print(\"\\n These is the extracted Bitcoin array with nan's removed:\\n\\n\",bc_values_np)\n",
    "# print(\"\\n These is the extracted Ethereum array with nan's removed:\\n\\n\",et_values_np)\n",
    "# print(\"\\n These is the extracted Litecoin array with nan's removed:\\n\\n\",lc_values_np)\n",
    "# print(\"\\n These is the extracted Zcash array with nan's removed:\\n\\n\",zc_values_np)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Wrangling: Creating Function to Reshape Value Arrays\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#6) Writing a function to reshape data into square matrix based on the number\n",
    "#   of days we would like to use to make a future prediction\n",
    "\n",
    "def reshape_array(array, number_of_days=9): #default argument must precede non-default argument \n",
    "    \"\"\"Given a number of days, as integer, the function will reshape matrix\n",
    "    so that it is square and fill missing values with the median value of dataset\"\"\"\n",
    "    \n",
    "    length_of_array = len(array)\n",
    "      \n",
    "    if length_of_array % number_of_days != 0: #if there is a remainder, we need to make matrix square\n",
    "       \n",
    "        #a)finding number of rows we need to make matrix square\n",
    "        req_num_rows_sq = math.ceil(length_of_array/number_of_days) \n",
    "        \n",
    "        #b)finding total number or elements are in new square matrix\n",
    "        new_size_of_sq = req_num_rows_sq * number_of_days\n",
    "        \n",
    "        #c)finding number of elements we need to add in to make matrix square\n",
    "        num_elements_to_add = new_size_of_sq - length_of_array\n",
    "        \n",
    "        #c-1) calculating median values of array for two cases: 1) when nan's are present 2)no Nans\n",
    "        \n",
    "        if(np.isnan(array).sum()>0): #Checks if nan's are present in array. isnan() returns boolean array. When a 'nan' is present a 'True' is returned.\n",
    "            \n",
    "            median = np.nanmedian(array) #if nan's are present, we will find median without nan's\n",
    "        \n",
    "        else:#no nan's are present, typical approach to find median\n",
    "            median = np.median(array)\n",
    "        \n",
    "        #d)adding elements to matrix to make square\n",
    "        values_for_square_array = [] #this is a list - initialiazing array to store new values to add to 'array' to make square\n",
    "       \n",
    "        for element in range(num_elements_to_add): # looping around the exact number of times we need to make matrix square(i.e., the number of empty slots we need to fill to make square)\n",
    "            value_to_add = median #adding median value of 'array' to empty slots in square matrix\n",
    "            values_for_square_array.append(value_to_add) #adds median value to empty list\n",
    "        \n",
    "        #e)Now out of for loop and converting list of values in 'values_for_square_array' to a numpy array\n",
    "        values_for_square_array_np = np.array(values_for_square_array)\n",
    "        \n",
    "        #f)Adding new values to end of original array to make it a square array\n",
    "        array_sq = np.append(array, values_for_square_array_np)\n",
    "        \n",
    "        #g)Finally, reshaping this newly squared array\n",
    "        X = array_sq.reshape(req_num_rows_sq, number_of_days)\n",
    "        \n",
    "        #h)Flattening reshaped matrix to a 1-d array\n",
    "        X_flat = np.ndarray.flatten(X)\n",
    "   \n",
    "    else:#array is already square, so just need to reshape 1-d array\n",
    "        \n",
    "        #a) Determing number of rows of already square matrix\n",
    "        rows = int(length_of_array/number_of_days)\n",
    "       \n",
    "        #b) Reshaping array to a square matrix\n",
    "        X = array.reshape(rows, number_of_days)\n",
    "        \n",
    "        #c) Flattening reshaped matrix to a 1-d array\n",
    "        X_flat = np.ndarray.flatten(X)\n",
    "    \n",
    "    return((X, X_flat)) #returns tuple of two variables\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calling 'Reshape' Function  to Reshape Value Arrays\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bitcoin Array Reshaped:\n",
      " [[   134.21    144.54    139.   ...,    112.5     115.91    112.3 ]\n",
      " [   111.5     113.57    112.67 ...,    117.98    111.5     114.22]\n",
      " [   118.76    123.02    123.5  ...,    123.89    126.7     133.2 ]\n",
      " ..., \n",
      " [  7143.58   6618.14   6357.6  ...,   7315.54   7871.69   7708.99]\n",
      " [  7790.15   8036.49   8200.64 ...,   8253.69   8790.92   9330.55]\n",
      " [  9818.35  10058.8     455.67 ...,    455.67    455.67    455.67]] \n",
      "\n",
      "\n",
      "Bitcoin Array Reshaped & Flattened:\n",
      " [ 134.21  144.54  139.   ...,  455.67  455.67  455.67] \n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#7) Calling 'reshape_array()\" to reshape the arrays of each cryptocurrency into\n",
    "#   a square matrix with a default of 5 columns (number of days we will use to predictions).  \n",
    "#   A flattend 1-d array  of the reshaped matrix is also returned. \n",
    "#   The arrays being fed into function come from step 5 of program. \n",
    "    \n",
    "bc_values_np_sq, bc_values_np_sq_flat = reshape_array(bc_values_np) \n",
    "et_values_np_sq, et_values_np_sq_flat = reshape_array(et_values_np)\n",
    "lc_values_np_sq, lc_values_np_sq_flat = reshape_array(lc_values_np)\n",
    "zc_values_np_sq, zc_values_np_sq_flat = reshape_array(zc_values_np)\n",
    "\n",
    "#print(\"\\n Calling reshape_arrray function to reshape numpy arrays of cryptocurrencies:\\n\" )  \n",
    "\n",
    "print(\"Bitcoin Array Reshaped:\\n\", bc_values_np_sq, \"\\n\\n\")\n",
    "print(\"Bitcoin Array Reshaped & Flattened:\\n\", bc_values_np_sq_flat, \"\\n\\n\")\n",
    "\n",
    "# print(\"Ethereum Array Reshaped:\\n\", et_values_np_sq, \"\\n\\n\")\n",
    "# print(\"Ethereum Array Reshaped & Flattened:\\n\", et_values_np_sq_flat, \"\\n\\n\")   \n",
    "\n",
    "# print(\"Litecoin Array Reshaped:\\n\", lc_values_np_sq, \"\\n\\n\")\n",
    "# print(\"Litecoin Array Reshaped & Flattened:\\n\", lc_values_np_sq_flat, \"\\n\\n\")\n",
    "\n",
    "# print(\"Zcash Array Reshaped:\\n\", zc_values_np_sq, \"\\n\\n\")\n",
    "# print(\"Zcash Array Reshaped & Flattened:\\n\", zc_values_np_sq_flat, \"\\n\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Wrangling: Creating Function to Split into Testing & Training Data -- Single Model\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#8) Write function to split test and train data\n",
    "\n",
    "def split_test_train(feature_matrix, feature_matrix_flat, train_split_pct = .70):\n",
    "    \"\"\" Given a reshaped and flat feature matrix, this function splits\n",
    "        matrices into test and train data for a single model\"\"\"\n",
    "        \n",
    "    #a) Finding number of rows and cols in feature matrix\n",
    "    feature_matrix_shape = feature_matrix.shape\n",
    "    \n",
    "    #a-1) Unpacking rows and columns\n",
    "    rows, columns = feature_matrix_shape\n",
    "    \n",
    "    #b) Determing number of rows to use for training and testing\n",
    "    fm_rows_used = math.ceil(rows * train_split_pct) #rounds up to nearest integer\n",
    "    \n",
    "    fm_rows_leftover = rows - fm_rows_used\n",
    "    \n",
    "    #c) Splitting feature matrix into Xtrain and Xtest\n",
    "    Xtrain = feature_matrix[: fm_rows_used]\n",
    "    Xtest = feature_matrix[fm_rows_used : rows-1] #last row is omitted becuase wont have any future data to compare to.\n",
    "    \n",
    "    #d) Extracting every 5th day value from flattened feature matrix with loop\n",
    "    pred_value_originals = [] #initialize empty list\n",
    "    \n",
    "    for value in range(columns, len(feature_matrix_flat), columns):\n",
    "        pred_value_originals.append(feature_matrix_flat[value])\n",
    "        \n",
    "    #converting list to a numpy array\n",
    "    pred_value_originals_np = np.array(pred_value_originals)\n",
    "    \n",
    "    #e) Splitting Ytrain and Ytest\n",
    "    Ytrain = pred_value_originals_np[: fm_rows_used]\n",
    "    Ytest = pred_value_originals_np[fm_rows_used : rows -1] #last row is omitted becuase wont have any future data to compare to.\n",
    "    \n",
    "    #f) Returning variables for future use\n",
    "    return((Xtrain, Xtest, Ytrain, Ytest))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calling Fuction to Split Data into Testing & Training Samples\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#9) Using split_test_train() function to split data into testing and training data\n",
    "\n",
    "#a) splitting bitcoin data\n",
    "Xtrain_bc, Xtest_bc, Ytrain_bc, Ytest_bc = split_test_train(bc_values_np_sq, bc_values_np_sq_flat)\n",
    "\n",
    "#print(\"\\n Split test and train data for Bitcoin:\\n\")\n",
    "#    \n",
    "#print(\"\\nThis is Xtrain for Bitcoin:\\n\\n\", Xtrain_bc)\n",
    "#print(\"\\nThis is Xtest for Bitcoin:\\n\\n\", Xtest_bc)    \n",
    "#print(\"\\nThis is Ytrain for Bitcoin:\\n\\n\", Ytrain_bc)    \n",
    "#print(\"\\nThis is Ytest for Bitcoin:\\n\\n\", Ytest_bc)    \n",
    "\n",
    "#b) splitting ethereum data \n",
    "Xtrain_et, Xtest_et, Ytrain_et, Ytest_et = split_test_train(et_values_np_sq, et_values_np_sq_flat)    \n",
    "\n",
    "#print(\"\\n Split test and train data for Ethereum:\\n\")\n",
    "    \n",
    "#print(\"\\nThis is Xtrain for Ethereum:\\n\", Xtrain_et)\n",
    "#print(\"\\nThis is Xtest for Ethereum:\\n\\n\", Xtest_et)    \n",
    "#print(\"\\nThis is Ytrain for Ethereum:\\n\\n\", Ytrain_et)    \n",
    "#print(\"\\nThis is Ytest for Ethereum:\\n\\n\", Ytest_et)\n",
    "\n",
    "#c) splitting litecoin data\n",
    "Xtrain_lc, Xtest_lc, Ytrain_lc, Ytest_lc = split_test_train(lc_values_np_sq, lc_values_np_sq_flat)\n",
    "\n",
    "#d) splitting zcash data\n",
    "Xtrain_zc, Xtest_zc, Ytrain_zc, Ytest_zc = split_test_train(zc_values_np_sq, zc_values_np_sq_flat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating Function to Train Model, Cross Validate & Make Predictions\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#11) Write a function to train a specific machine learing model and make predictions\n",
    "def clf_train_predict(model, Xtrain, Xtest, Ytrain, param_tune = False, param_candidates=0):\n",
    "    \"\"\"This function allows you to specify whether you have parameters to tune. If you do have parameters to tune\n",
    "        the parameters can be passed into function as a dictionary. GridSearchCV will be called to determine \n",
    "        optimal tuning parameter. Regardless if you have parameters to tune, your specified machine learing \n",
    "        algorithm will be trained, and used the trained to make predictions using Xtest.\"\"\"\n",
    "    \n",
    "    param_grid = param_candidates #parameter grid to be used in grid search if 'param_tune=True'\n",
    "    \n",
    "    if param_tune == False:\n",
    "        #a) Training our model\n",
    "        clf = model.fit(Xtrain, Ytrain)\n",
    "    \n",
    "        #b) Finding length (number of rows) of Xtest\n",
    "        len_xtest = len(Xtest)\n",
    "    \n",
    "        #c) Making predictions using trained model and Xtest using loop\n",
    "    \n",
    "        pred_values = [] #initializing empty list to stroe predictions\n",
    "    \n",
    "        for fm_row in range(0, len_xtest):\n",
    "            pred_value = clf.predict(Xtest[[fm_row]])[0] # each row is passed to trained model to make prediction. Double brackets get rid of deprecation warning and [0] extracts value from array. \n",
    "            pred_values.append(pred_value)\n",
    "    \n",
    "        #d) Converting list to a numpy array\n",
    "        pred_values_np = np.array(pred_values)\n",
    "    \n",
    "        #e) Returning predictions\n",
    "        return(pred_values_np)\n",
    "    \n",
    "    else:\n",
    "        \n",
    "        #a) Instantiate model\n",
    "        clf = model\n",
    "        \n",
    "        #b) Call GridSearch\n",
    "        clf_cv = GridSearchCV(clf, param_grid,cv=3, n_jobs=-1)\n",
    "        \n",
    "        #c) Train model with results from GridSearchCV\n",
    "        clf_cv.fit(Xtrain, Ytrain)\n",
    "        \n",
    "        #d) Finding length (number of rows) of Xtest\n",
    "        len_xtest = len(Xtest)\n",
    "    \n",
    "        #e) Making predictions using trained model and Xtest using loop\n",
    "    \n",
    "        pred_values = [] #initializing empty list to stroe predictions\n",
    "    \n",
    "        for fm_row in range(0, len_xtest):\n",
    "            pred_value = clf_cv.predict(Xtest[[fm_row]])[0] # each row is passed to trained model to make prediction. Double brackets get rid of deprecation warning and [0] extracts value from array. \n",
    "            pred_values.append(pred_value)\n",
    "    \n",
    "        #d) Converting list to a numpy array\n",
    "        pred_values_np = np.array(pred_values)\n",
    "    \n",
    "        #e) Returning predictions\n",
    "        return(pred_values_np, clf_cv.best_params_)\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calling Function to Train Model & Make Predictions\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "These are the bitcoin predictions:\n",
      "\n",
      " [  649.10899952   559.87495771   565.25982444   583.62194524   571.17212515\n",
      "   598.72225315   608.21320276   607.18143209   616.10338237   646.09887626\n",
      "   689.54692677   720.57093373   700.69169423   762.98920816   756.10288989\n",
      "   774.01930947   790.62729958  1003.1239601    928.17196118   788.94687226\n",
      "   860.83752863  1026.8696435    983.1837273   1100.89825547  1250.77700339\n",
      "  1059.6925516   1038.46931306   960.39626462  1221.45951895  1170.34098331\n",
      "  1273.50102432  1529.19703313  1728.90567556  2028.93166961  2157.36640364\n",
      "  2890.68913791  2605.17075047  2446.09824033  2552.3658778   2200.47446135\n",
      "  2775.77189208  2735.29376965  3483.24822185  4242.80680798  4465.53968698\n",
      "  4547.37081204  3774.56924678  3838.7457343   4423.74870269  5643.41606412\n",
      "  5887.9116464   5955.64247895  7550.41495965  7792.29073074  9516.08634867]\n",
      "\n",
      "These are the Ethereum predictions:\n",
      "\n",
      " [  51.74747515   45.19278378   49.85658995   60.9635629    96.29581595\n",
      "   92.43368538  175.5485176   178.94758023  394.39462377  343.83323099\n",
      "  372.3714855   234.22873588  170.33695667  185.71281502  211.94806325\n",
      "  305.49083772  336.12925419  389.21077311  242.36553605  287.65237571\n",
      "  287.5262736   313.20105748  337.51011924  288.02841604  271.98189689\n",
      "  283.34128356  377.39563136]\n",
      "\n",
      "These are the litecoin predictions:\n",
      "\n",
      " [  4.00261189   3.62716757   3.55656644   4.02888488   3.84561583\n",
      "   3.83184018   3.83255762   3.9163518    3.87684464   3.98591888\n",
      "   4.07142278   3.81372926   3.92969998   4.00206146   3.95694598\n",
      "   3.48762582   3.68220657   5.34148362   3.74816868   4.03462704\n",
      "   3.7941252    4.11031724   3.79251604   3.84220399   3.84578444\n",
      "   3.81332599   3.9815345    4.27603766  11.02438639  10.21566404\n",
      "  15.62066884  22.71007221  25.90122998  23.21860343  18.90065703\n",
      "  27.74622164  52.04186137  37.73514792  54.77851557  41.25353547\n",
      "  43.16439326  43.54653559  47.63025759  45.09045918  69.0828575\n",
      "  92.83831381  40.23682367  48.48016076  50.32884899  63.52051542\n",
      "  54.5481773   57.54598596  66.90806602  69.7238307   88.85639133]\n",
      "\n",
      "These are the litecoin predictions:\n",
      "\n",
      " [ 245.23056089  233.29604013  293.73988674  199.72065747  163.9047641\n",
      "  242.81392701  253.69081191  246.72456832  211.39532316  223.61563412\n",
      "  246.91363855  312.19998882]\n",
      "\n",
      "These are the bitcoin predictions with Ridge:\n",
      "\n",
      " [  649.85266938   559.38352025   565.85674312   584.03467618   571.76267401\n",
      "   601.61289066   608.42421307   607.71607773   616.66350632   646.49597102\n",
      "   688.33115865   718.56163355   701.41148517   762.71239065   755.79908262\n",
      "   774.05177141   791.21290255  1001.09961983   934.01967456   789.75154352\n",
      "   866.57128867  1024.19896973   986.02554905  1098.89405806  1247.31821896\n",
      "  1070.17865097  1032.31329748   966.09998335  1218.19736647  1171.72217358\n",
      "  1269.17928345  1525.21525307  1743.92209902  2036.70598216  2152.65066226\n",
      "  2884.13312083  2581.8744778   2462.39115962  2555.72884939  2206.57873119\n",
      "  2812.18147151  2754.63150109  3495.34162141  4255.08821482  4472.07480131\n",
      "  4550.12246999  3721.40402397  3830.86805947  4434.17516961  5599.36266153\n",
      "  5899.5255263   5983.31357619  7547.14186651  7794.52012069  9464.33774473]\n",
      "Best Parameter(s): {'alpha': 2352}\n",
      "\n",
      "These are the Ethereum predictions with Ridge:\n",
      "\n",
      " [  51.50930545   43.69034521   49.53765708   58.31111211   95.3961759\n",
      "   91.75927293  177.54351517  210.42651155  337.41414845  359.49140605\n",
      "  321.18288751  251.09616561  180.08627071  202.34229581  219.39215333\n",
      "  299.0555532   316.59025612  377.64837789  292.64965418  284.70374097\n",
      "  294.56753179  304.28054671  334.58629812  294.83468888  287.09073168\n",
      "  305.99259423  362.19777838]\n",
      "Best Parameter(s): {'alpha': 25}\n",
      "\n",
      "These are the Litecoin predictions with Ridge:\n",
      "\n",
      " [  4.00559127   3.63510094   3.6044182    4.00028257   3.85954187\n",
      "   3.89768322   3.85587411   3.93178048   3.89362188   4.00612498\n",
      "   4.06577322   3.89068001   3.90705702   4.02800747   3.95945147   3.54185\n",
      "   3.70187268   5.15313142   3.95518043   3.99764383   3.82989854\n",
      "   4.15454556   3.82823076   3.86273517   3.86051552   3.82727967\n",
      "   4.10017556   4.25179451  11.05208798  10.38453356  15.04662083\n",
      "  20.99942314  28.29269657  24.3065976   19.77266885  28.5785916\n",
      "  47.43691379  39.13738522  53.2883344   42.01681192  44.17503345\n",
      "  42.67490852  47.44679753  44.67729616  65.74025209  88.01676188\n",
      "  41.65739395  48.22574821  51.67536319  59.66485431  55.53130889\n",
      "  56.83549471  64.44519077  69.37407621  87.41252018]\n",
      "Best Parameter(s): {'alpha': 24}\n",
      "\n",
      "These are the Zcash predictions with Ridge:\n",
      "\n",
      " [ 239.66806452  238.70380293  288.80327326  210.08544872  169.8663977\n",
      "  237.9370251   250.15035628  242.75741251  210.21398476  226.51618699\n",
      "  247.36224313  308.17533912]\n",
      "Best Parameter(s): {'alpha': 1190}\n"
     ]
    }
   ],
   "source": [
    "#12) Using clf_train_predict() to make predictions \n",
    "\n",
    "##Linear Regression\n",
    "#a) making predictions for bitcoin \n",
    "pred_bitcoin_lreg = clf_train_predict(LinearRegression(),Xtrain_bc, Xtest_bc, Ytrain_bc)\n",
    "\n",
    "print(\"\\nThese are the bitcoin predictions:\\n\\n\", pred_bitcoin_lreg)\n",
    "\n",
    "#b) making predictions for ethereum\n",
    "pred_ethereum_lreg = clf_train_predict(LinearRegression(),Xtrain_et, Xtest_et, Ytrain_et)\n",
    "\n",
    "print(\"\\nThese are the Ethereum predictions:\\n\\n\", pred_ethereum_lreg)\n",
    "\n",
    "#c) making predictions for litecoin\n",
    "pred_litecoin_lreg = clf_train_predict(LinearRegression(),Xtrain_lc, Xtest_lc, Ytrain_lc)\n",
    "\n",
    "print(\"\\nThese are the litecoin predictions:\\n\\n\", pred_litecoin_lreg)\n",
    "\n",
    "#d) making predictins for zcash\n",
    "pred_zcash_lreg = clf_train_predict(LinearRegression(),Xtrain_zc, Xtest_zc, Ytrain_zc)\n",
    "\n",
    "print(\"\\nThese are the litecoin predictions:\\n\\n\", pred_zcash_lreg)\n",
    "\n",
    "#______________________\n",
    "#Ridge Regression  -- Addressing possible overfitting with regularization\n",
    "#a) Bitcoin\n",
    "pred_bitcoin_ridge, bitcoin_ridge_best_param = clf_train_predict(Ridge(),Xtrain_bc, Xtest_bc, Ytrain_bc, param_tune=True, param_candidates={'alpha': np.arange(1,5000)})\n",
    "\n",
    "print(\"\\nThese are the bitcoin predictions with Ridge:\\n\\n\", pred_bitcoin_ridge)\n",
    "print(\"Best Parameter(s):\",bitcoin_ridge_best_param)\n",
    "\n",
    "#b) Ethereum\n",
    "pred_ethereum_ridge, ethereum_ridge_best_param = clf_train_predict(Ridge(),Xtrain_et, Xtest_et, Ytrain_et, param_tune=True, param_candidates={'alpha': np.arange(1,5000)})\n",
    "print(\"\\nThese are the Ethereum predictions with Ridge:\\n\\n\", pred_ethereum_ridge)\n",
    "print(\"Best Parameter(s):\",ethereum_ridge_best_param)\n",
    "\n",
    "#c) Litecoin\n",
    "pred_litecoin_ridge, litecoin_ridge_best_param = clf_train_predict(Ridge(),Xtrain_lc, Xtest_lc, Ytrain_lc, param_tune=True, param_candidates={'alpha': np.arange(1,5000)})\n",
    "print(\"\\nThese are the Litecoin predictions with Ridge:\\n\\n\", pred_litecoin_ridge)\n",
    "print(\"Best Parameter(s):\",litecoin_ridge_best_param)\n",
    "\n",
    "#d) Zcash\n",
    "pred_zcash_ridge, zcash_ridge_best_param  = clf_train_predict(Ridge(),Xtrain_zc, Xtest_zc, Ytrain_zc, param_tune=True, param_candidates={'alpha': np.arange(1,5000)})\n",
    "print(\"\\nThese are the Zcash predictions with Ridge:\\n\\n\", pred_zcash_ridge)\n",
    "print(\"Best Parameter(s):\",zcash_ridge_best_param)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating Function to Plot Predictions Against Original Values\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#13) Creating a function to plot prediction and original values\n",
    "\n",
    "def plot_pred(Xtest, Ytest, pred_array, crypto_name, model_used):\n",
    "    \"\"\"This function will plot original and predicted values of a cryptocurrency.\"\"\"\n",
    "    #a) Creating array of sequential numbers with same length as Ytest\n",
    "    pred_days = np.arange(0,len(Ytest))\n",
    "\n",
    "    #b) Making plot\n",
    "    plt.figure()#allow you to plot seperate instances. It opens a new figure \n",
    "    plt.plot(pred_days, Ytest) #plotting original values\n",
    "    plt.plot(pred_days, pred_array, marker ='.', markersize = 7,color='red', alpha=.5)\n",
    "    \n",
    "    #c) Adding labels to plot\n",
    "    plt.title(\"{} 1 Day Predictions Using {} Days of Historical Data\\n\".format(crypto_name,len(Xtest[0])))\n",
    "    plt.xlabel(\"Prediction Day\")\n",
    "    plt.ylabel(\"Value ($)\")\n",
    "    plt.legend((\"Original\", \"Predicted - \" + model_used), loc = \"best\") #making legend with labels specified\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calling Function to Plot Predictions against Original Values\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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TJ08SHx9PeHi4s8NRqt5cZZBEZVnB1KO8UsaY2caYwcaYwW3bnjmyMT8/n6CgIE1O6rwg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\n8bFQlulGmNlJiN7UgeED3J6UkzQWqAY2kcHxhlt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea351d10b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TeOv+aQy2RQDw/26YQHbGKFa+v5qGY118EPIAm3NPsiP/JNdGNxI4OMOr8z1g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\n3+8jq4Y/4WFtXB2KUsqNaPJxZ1evkn7wR7IaNad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9M75drko+BtggIgb4mzEmCmhgjEkD\nMMakiUhgSTuKyDhgHEDz5s3Ld/aQEGps24Fn5xBOHzvJVq8gcv4eS4dvdtGqvi8tmtajcWgHqgW3\nsSejspYKzsuzd6OkpcHp09hOnSIrOZWCbdsoyMwi1VTnckBD7h/ch8YvPF2+eJV7uXavr3i38F26\nds/nRsWXUjDGMGDAgJtukMfExJS4FlB5GGP43e9+x/jx46/b/u67797yHDabrag1NGTIEP70pz/d\n8flLWvrBGMOYMWN44403rit77Ngx3nrrLXbv3k3t2rWJjIy8bkmI0pahAPs9nxdffJGvvvqKZ555\nhqSkJAoLCwkICCjxOpTlxmtUUqwA+/fv55///CcffPABK1euZOHChfz9739n69atrFu3jtdff524\nuLgyz1X8GhT/WTliDlBXJZ/exphUK8FsFJHb/kKLlaiiwD6xaLnOHhGBHxAWHw8hY2natRf/+jGT\nTTHHWXbgEE0T0+gQs5lONb+jVX1fmgU3w6tNa8jIgGPHoG5daNwY2+l0zp1MI/3iFTIu5pGcJ8QZ\nX075BNDUP5SIC/uQhg14oK4HNfv3Lleoyg1Vq+aSe3+9evVi0qRJHDlyhDZt2pCbm0tKSgrt27fn\n2LFjJCUl0bp161JHb0VERDB//nymTZuGzWbj0qVL1KxZk+zs7KIyDz30EK+88gqjR4/Gz8+PU6dO\n4enpyU9/+lMiIyN5+eWXKSgo4Ouvv74pQXl4eNzxB/ftiIiI4LHHHmP69OkEBgZy9uxZsrOzuXjx\nIr6+vvj7+5Oens63335Lv3797ujYw4YNY8mSJSxZsoTx48cTFBTEqlWrGD58OMYYDhw4QNeuXenV\nqxdffvklI0aMYMWKFXccq6+vL9WrV+eXv/wlrVu3JjIyksLCQk6ePEn//v3p06cPy5YtIycn57rj\nPfDAA6xYsYKnn36apUuX0qdPn/L8CMvFJcnHGJNqPWaIyGqgJ5AuIo2sVk8jIMNhAdzwx90S+HVg\nTX7dtxUXLvfh/w5nsin+NGv3JlLndAqttqQy5Mt/0TntCHh7c/VSLjHNO/LPeu045VObDN/aXGpR\nj1atGtG5iT99m/rTpXEtWsTsoNqhQxX2v1elHKl+/fosXryYUaNGFXUHzZw5k7Zt2xIVFcWgQYOo\nV68effr0Kbq3UNx7773HuHHj+Pjjj/Hw8GD+/PmEh4fTu3dvOnXqxMCBA5kzZw6HDh0iPDwcAD8/\nPz777DO6d+/OiBEjCA0NpUWLFvTt27dcdRg0aBCe1qwg4eHhTJo06Zb7hISEMHPmTB588EEKCwvx\n9PTkgw8+oFevXnTr1o2OHTvSqlWrou7IO/XHP/6RJ598kueff56lS5cyYcIEZs6cSX5+PiNHjqRr\n1668++67PPXUU/z1r39l0KBBpS5bUVqsPj4+PPvss0UjFt944w1sNhtPPfUUFy5cwBjD9OnTCbih\nF2fu3LmMHTuWOXPmFA04cBanL6kgIr5ANWNMtvV8I/AnIALIKjbgoI4x5qWyjuXoJRXybYVEJ59j\n06F0Av72AQ2PJXDR2xcfY+Ny62BSnh5H56a16NwkgFb1fKlWrWK6JlTVci8vqaCcIzc3Fx8fH0SE\nFStWsHz5ctauXevqsG7pXltSoQGw2upbvA9YZoxZLyK7gZUi8hxwAhhexjGcwtOjGuGt6xLeui54\nDSU76mMKavnjn3eJamMGwQD9EqhS6u7t2bOHyZMnY4whICCAhQsXujokh3N68jHGHAW6lrA9C3vr\np3KKiKAmVOhNYKWUAvsIxP3797s6DKeqTEOtKzcX3QRWVYMxpsJGjClVGdztLRudXkcpB/P29iYr\nK8shw1WVcgVjDFlZWXh7e5f7GNryUcrBmjZtSkpKCpmZma4ORakK4+3tTdOmTcu9vyYfpRzM09Oz\n6BvqSik77XZTSinldJp8lFJKOZ0mH6WUUk7n9BkOKpKIZALH7+IQ9YAztyxVNWnd3Y+71hvct+6u\nqHcLY0z9WxW6p5PP3RKR6NuZBqIq0rq7X93dtd7gvnWvzPXWbjellFJOp8lHKaWU07l78rl5OUb3\noXV3P+5ab3Dfulfaerv1PR+llFKu4e4tH6WUUi6gyUcppZTTuW3yEZGHReRHETlirZzqNkQkWUQO\nikiMiDhuKVgXE5GFIpIhIrHFttURkY0ikmg91nZljI5SSt1niMgp67rHiMgjrozREUSkmYh8JyKH\nRCRORKZa26v0dS+j3pX2mrvlPR8R8QAOAwOAFGA3MMoYE+/SwJxERJKBMGNMlf7SnYj8FMgBPjHG\ndLK2/QU4W2y59trGmP9xZZyOUErdZwA5xpi3XBmbI4lII6CRMWaviNQE9gBDgUiq8HUvo96/opJe\nc3dt+fQEjhhjjhpjrgIrgMdcHJOqYMaYrcDZGzY/Biyxni/B/gda5ZRS9yrPGJNmjNlrPc8GDgFN\nqOLXvYx6V1rumnyaACeLvU6hkl+oCmaADSKyR0TGuToYJ2tgjEkD+x8sEOjieJxtsogcsLrlqlTX\n041EpCXQDdiFG133G+oNlfSau2vyKWk9Y3fqf+xtjOkODAQmWV00quqbD7QGQoE04K+uDcdxRMQP\n+BKYZoy56Op4nKWEelfaa+6uyScFaFbsdVMg1UWxOJ0xJtV6zABWY++GdBfpVv/4tX7yDBfH4zTG\nmHRjjM0YUwgsoIpedxHxxP4BvNQY85W1ucpf95LqXZmvubsmn91AsIgEiUh1YCSwzsUxOYWI+Fo3\nJBERX+BBILbsvaqUdcAY6/kYYK0LY3Gqax++lsepgtddRAT4GDhkjHm72FtV+rqXVu/KfM3dcrQb\ngDXk8F3AA1hojJnl4pCcQkRaYW/tgH0Z9WVVte4ishzoh31a+XTgVWANsBJoDpwAhhtjqtyN+VLq\n3g9794sBkoHx1+6DVBUi0gf4N3AQKLQ2/y/2+x9V9rqXUe9RVNJr7rbJRymllOu4a7ebUkopF9Lk\no5RSyuk0+SillHI6TT5KKaWcTpOPUkopp9Pko9yWiNismX5jRWSViNS4i2P1E5FvrOdDypopXUQC\nRGRisdeNReSL8p77hmNvsWZrPyAiCSLyvogEVMSxlapImnyUO7tsjAm1Zn2+CrxQ/E2xu+O/EWPM\nOmPM7DKKBAATi5VPNcY8cafnKcNoY0wXoAuQRxX7QqWqGjT5KGX3b6CNiLS01kSZB+wFmonIgyKy\nQ0T2Wi0kPyhaEypBRLYBw64dSEQiReR963kDEVktIvutfw8As4HWVqtrjnXOWKu8t4gsEvt6S/tE\npH+xY34lIuutNWn+cqsKWTO2vwQ0F5Gu1nHWWBPKxl2bVFZEnhORd4rF/7yIvF3yUZWqGJp8lNsT\nkfuwT7J60NrUDvs6ON2AS8AfgF9Yk7FGA/8lIt7Y58p6FOgLNCzl8HOB/zPGdAW6A3HAy0CS1er6\n7xvKTwIwxnTG/u30Jda5wP5N9RFAZ2CEiDTjFowxNmA/0N7aNNYY0wMIA6aISF3sS4oMseYGA3gW\nWHSrYyt1NzT5KHfmIyIx2BPKCexzYwEcN8bstJ73AkKA762yY4AW2D/MjxljEo19mpDPSjnHz7HP\nLIw1weOFW8TUB/jUKp8AHAfaWu9tMsZcMMZcAeKtOG5H8Vncp4jIfmAn9sl1g40xl4DNwGARaQ94\nGmMOlnAcpSrMfa4OQCkXumyMCS2+wT4/I5eKbwI2GmNG3VDu2nxZFa2k5T6uySv23MZt/P1aq/Z2\nBg6JSD/gF0C40Y/JAgAAASFJREFUMSZXRLYA11pVH2GfCywBbfUoJ9CWj1Jl2wn0FpE2ACJSQ0Ta\nYv+QDhKR1la5UaXsvwmYYO3rISK1gGygZinltwKjrfJtsU+E+WN5Are60d4AThpjDgD+wDkr8bTH\n3qoDwBizC3tL6ElgeXnOp9Sd0OSjVBmMMZlAJLBcRA5gT0btra6vccDfrQEHx0s5xFSgv4gcBPYA\nHY0xWdi78WJFZM4N5ecBHlb5z4FIY0wed2apFWss4Mt/lohfD9xnvfe6VZfiVgLfG2PO3eH5lLpj\nOqu1UgoA63tK7xhjNrk6FlX1actHKTdnfen1MPZ7YJp4lFNoy0cppZTTactHKaWU02nyUUop5XSa\nfJRSSjmdJh+llFJOp8lHKaWU0/0/q4SRjccjAuUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea351d1898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SYhs1NMwp9aKgZIyh4kA20VHh0EI9bCAFsvguHjgNGAEkA5HAD5tZtdl3oTHm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\nMsYYEzP+H8TdBe+Aq7TcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea33ebb4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NfLg+Tk13OHIEasyDsDkkppwr7+4oEqICeP6WUezKLOAn7+ykxmbGCA2N88am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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea33889128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pVaG0PQfwdHcjNNo1Z+WaoJRSSlUo+8Ahgn08kciGn2IOmqCUUkpVIj/5CD5h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\nwPhpI2vXpjGQl0deQSFF3h6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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea338141d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5eM027i7dxYpzpjPk2qs7rIa84p6bCAgJ5p3fraKmrtHD0bZv/T83ENJcz+Lr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\nd8mKefPmERUVRc+ePbHZbAwePJgPPviAOXPm8MMPP2CxWPD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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea33a18b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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825qVO51OsrOz9R9adWrGGLKzs3F2oSEPuoV6Sek3b+7iic+PWX93gdJSSk4J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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea33868860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pZxZja8G4QVT092dXhYsx87WDvbllFFfU2tW815TrY4ezbNYIXlqfzkfbD3db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\nxvik/wPRF6uxK9QapgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea3387b0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#14) Plotting orginal and predicted values using plot_pred() \n",
    "\n",
    "#a) Plotting Bitcoin predictions\n",
    "plot_pred(Xtest_bc, Ytest_bc, pred_bitcoin_lreg, \"Bitcoin\", \"Linear Regression\")\n",
    "\n",
    "#b) Plotting Ethereum predictions\n",
    "plot_pred(Xtest_et, Ytest_et, pred_ethereum_lreg, \"Ethereum\", \"Linear Regression\")\n",
    "\n",
    "#c) Plotting Litecoin predictions\n",
    "plot_pred(Xtest_lc, Ytest_lc, pred_litecoin_lreg, \"Litecoin\", \"Linear Regression\")\n",
    "\n",
    "#d) Plotting Litecoin predictions\n",
    "plot_pred(Xtest_zc, Ytest_zc, pred_zcash_lreg, \"Zcash\", \"Linear Regression\")\n",
    "\n",
    "##_________________________\n",
    "##Ridge Regression\n",
    "\n",
    "#a) Plotting Bitcoin\n",
    "plot_pred(Xtest_bc, Ytest_bc, pred_bitcoin_ridge, \"Bitcoin\", \"Ridge Regression\")\n",
    "\n",
    "#b) Plottting Ethereum \n",
    "plot_pred(Xtest_et, Ytest_et, pred_ethereum_ridge, \"Ethereum\", \"Ridge Regression\")\n",
    "\n",
    "#c) Plotting Litecoin\n",
    "plot_pred(Xtest_lc, Ytest_lc, pred_litecoin_ridge, \"Litecoin\", \"Ridge Regression\")\n",
    "\n",
    "#d) Plotting Zcash\n",
    "plot_pred(Xtest_zc, Ytest_zc, pred_zcash_ridge, \"Zcash\", \"Ridge Regression\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating Function to Combine Original and Predicted Values Along with Trading Action\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#15) Writing a function to combine original and predicted values of cryptocurrency\n",
    "\n",
    "def pred_compare_df(orig_val_array, pred_val_array):\n",
    "    \"\"\" Combines arrays of original and prediction values into a dataframe,\n",
    "        and determines if you should buy or hold the cryptocurrency for longterm investment. \n",
    "        It also tells us if we were mislead by our predictions.\"\"\"\n",
    "        \n",
    "    #a) Creating a dictionary to define columns that should hold data\n",
    "    dict_pred = {\"Original_Value\": orig_val_array, \"Predicted_Value\": pred_val_array}\n",
    "    \n",
    "    #b) Converting dictionary to dataframe\n",
    "    df_pred = pd.DataFrame(dict_pred)\n",
    "    \n",
    "    #c) Printing statement to identify dataframe\n",
    "    #title_df = print(\"\\nThis is a combined dataframe for {}:\\n\".format(crypto_name))\n",
    "    \n",
    "    #d) Calculating percent change between predicted and original value and assigning to a column in this df   \n",
    "    df_pred[\"% Error\"] = (df_pred[\"Predicted_Value\"] - df_pred[\"Original_Value\"]) / df_pred[\"Original_Value\"] *100\n",
    "    \n",
    "    #e) Determining if you should by or hold \n",
    "\n",
    "    #1)determining difference between consecutive rows (essentially calculating slope) in a predicted values column\n",
    "    df_pred[\"Action_Pred\"] =np.where(df_pred[\"Predicted_Value\"].diff()<0, \"Buy\", \"Hold\")\n",
    "   \n",
    "    #2)determining difference between consecutive rows (essentially calculating slope) in  orignal values column\n",
    "    df_pred[\"Action_Orig\"] =np.where(df_pred[\"Original_Value\"].diff()<0, \"Buy\", \"Hold\")\n",
    "   \n",
    "    #3)determining if we were mislead by our predictions (if our pred tells us to 'buy' and original values suggest a 'hold', we will have been mislead. The reverse holds as well)\n",
    "    df_pred[\"Mislead\"] = np.where(df_pred[\"Action_Pred\"].values!=df_pred[\"Action_Orig\"].values, \"Yes\", \"No\")\n",
    "    \n",
    "    #) Returning Variables\n",
    "    return df_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calling Function to Prepare DataFrame & Determine Successes of Trading Action \n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "This is a combined df of Bitcoin:\n",
      "\n",
      "     Original_Value  Predicted_Value    % Error Action_Pred Action_Orig Mislead\n",
      "0           656.99       649.109000  -1.199562        Hold        Hold      No\n",
      "1           592.69       559.874958  -5.536628         Buy         Buy      No\n",
      "2           577.44       565.259824  -2.109340        Hold         Buy     Yes\n",
      "3           577.76       583.621945   1.014599        Hold        Hold      No\n",
      "4           598.21       571.172125  -4.519797         Buy        Hold     Yes\n",
      "5           608.24       598.722253  -1.564801        Hold        Hold      No\n",
      "6           597.15       608.213203   1.852667        Hold         Buy     Yes\n",
      "7           609.74       607.181432  -0.419616         Buy        Hold     Yes\n",
      "8           616.75       616.103382  -0.104843        Hold        Hold      No\n",
      "9           637.96       646.098876   1.275766        Hold        Hold      No\n",
      "10          688.31       689.546927   0.179705        Hold        Hold      No\n",
      "11          703.42       720.570934   2.438221        Hold        Hold      No\n",
      "12          705.02       700.691694  -0.613927         Buy        Hold     Yes\n",
      "13          744.59       762.989208   2.471052        Hold        Hold      No\n",
      "14          777.94       756.102890  -2.807043         Buy        Hold     Yes\n",
      "15          769.73       774.019309   0.557249        Hold         Buy     Yes\n",
      "16          800.88       790.627300  -1.280179        Hold        Hold      No\n",
      "17          973.50      1003.123960   3.043036        Hold        Hold      No\n",
      "18          908.59       928.171961   2.155203         Buy         Buy      No\n",
      "19          831.53       788.946872  -5.121057         Buy         Buy      No\n",
      "20          901.54       860.837529  -4.514772        Hold        Hold      No\n",
      "21         1029.91      1026.869643  -0.295206        Hold        Hold      No\n",
      "22          999.18       983.183727  -1.600940         Buy         Buy      No\n",
      "23         1115.30      1100.898255  -1.291289        Hold        Hold      No\n",
      "24         1251.01      1250.777003  -0.018625        Hold        Hold      No\n",
      "25         1175.83      1059.692552  -9.877061         Buy         Buy      No\n",
      "26         1054.23      1038.469313  -1.494995         Buy         Buy      No\n",
      "27         1039.97       960.396265  -7.651541         Buy         Buy      No\n",
      "28         1176.90      1221.459519   3.786177        Hold        Hold      No\n",
      "29         1182.94      1170.340983  -1.065060         Buy        Hold     Yes\n",
      "30         1265.49      1273.501024   0.633037        Hold        Hold      No\n",
      "31         1537.67      1529.197033  -0.551026        Hold        Hold      No\n",
      "32         1804.91      1728.905676  -4.210976        Hold        Hold      No\n",
      "33         2173.40      2028.931670  -6.647112        Hold        Hold      No\n",
      "34         2286.41      2157.366404  -5.643939        Hold        Hold      No\n",
      "35         2823.81      2890.689138   2.368401        Hold        Hold      No\n",
      "36         2548.29      2605.170750   2.232114         Buy         Buy      No\n",
      "37         2552.45      2446.098240  -4.166654         Buy        Hold     Yes\n",
      "38         2608.56      2552.365878  -2.154220        Hold        Hold      No\n",
      "39         1998.86      2200.474461  10.086472         Buy         Buy      No\n",
      "40         2754.86      2775.771892   0.759091        Hold        Hold      No\n",
      "41         2710.67      2735.293770   0.908402         Buy         Buy      No\n",
      "42         3650.62      3483.248222  -4.584749        Hold        Hold      No\n",
      "43         4087.66      4242.806808   3.795492        Hold        Hold      No\n",
      "44         4579.02      4465.539687  -2.478266        Hold        Hold      No\n",
      "45         4599.88      4547.370812  -1.141534        Hold        Hold      No\n",
      "46         3625.04      3774.569247   4.124899         Buy         Buy      No\n",
      "47         3926.07      3838.745734  -2.224216        Hold        Hold      No\n",
      "48         4229.36      4423.748703   4.596173        Hold        Hold      No\n",
      "49         5647.21      5643.416064  -0.067182        Hold        Hold      No\n",
      "50         6008.42      5887.911646  -2.005658        Hold        Hold      No\n",
      "51         6468.40      5955.642479  -7.927115        Hold        Hold      No\n",
      "52         7143.58      7550.414960   5.695113        Hold        Hold      No\n",
      "53         7790.15      7792.290731   0.027480        Hold        Hold      No\n",
      "54         9818.35      9516.086349  -3.078559        Hold        Hold      No\n",
      "\n",
      "This is a combined df of Ethereum:\n",
      "\n",
      "     Original_Value  Predicted_Value    % Error Action_Pred Action_Orig Mislead\n",
      "0            50.70        51.747475   2.066026        Hold        Hold      No\n",
      "1            43.44        45.192784   4.034953         Buy         Buy      No\n",
      "2            48.31        49.856590   3.201387        Hold        Hold      No\n",
      "3            70.16        60.963563 -13.107807        Hold        Hold      No\n",
      "4            94.01        96.295816   2.431460        Hold        Hold      No\n",
      "5            89.44        92.433685   3.347144         Buy         Buy      No\n",
      "6           174.45       175.548518   0.629703        Hold        Hold      No\n",
      "7           224.38       178.947580 -20.247981        Hold        Hold      No\n",
      "8           401.49       394.394624  -1.767261        Hold        Hold      No\n",
      "9           336.87       343.833231   2.067038         Buy         Buy      No\n",
      "10          294.92       372.371485  26.261863        Hold         Buy     Yes\n",
      "11          242.14       234.228736  -3.267227         Buy         Buy      No\n",
      "12          234.39       170.336957 -27.327550         Buy         Buy      No\n",
      "13          204.32       185.712815  -9.106884        Hold         Buy     Yes\n",
      "14          256.51       211.948063 -17.372397        Hold        Hold      No\n",
      "15          300.10       305.490838   1.796347        Hold        Hold      No\n",
      "16          317.52       336.129254   5.860813        Hold        Hold      No\n",
      "17          387.74       389.210773   0.379319        Hold        Hold      No\n",
      "18          288.75       242.365536 -16.063884         Buy         Buy      No\n",
      "19          282.80       287.652376   1.715833        Hold         Buy     Yes\n",
      "20          299.15       287.526274  -3.885585         Buy        Hold     Yes\n",
      "21          311.12       313.201057   0.668892        Hold        Hold      No\n",
      "22          333.38       337.510119   1.238862        Hold        Hold      No\n",
      "23          297.93       288.028416  -3.323460         Buy         Buy      No\n",
      "24          305.71       271.981897 -11.032712         Buy        Hold     Yes\n",
      "25          307.91       283.341284  -7.979188        Hold        Hold      No\n",
      "26          360.40       377.395631   4.715769        Hold        Hold      No\n",
      "\n",
      "This is a combined df of Litecoin:\n",
      "\n",
      "     Original_Value  Predicted_Value    % Error Action_Pred Action_Orig Mislead\n",
      "0             4.08         4.002612  -1.896767        Hold        Hold      No\n",
      "1             3.78         3.627168  -4.043186         Buy         Buy      No\n",
      "2             3.64         3.556566  -2.292131         Buy         Buy      No\n",
      "3             3.80         4.028885   6.023286        Hold        Hold      No\n",
      "4             3.89         3.845616  -1.140981         Buy        Hold     Yes\n",
      "5             3.82         3.831840   0.309952         Buy         Buy      No\n",
      "6             3.84         3.832558  -0.193812        Hold        Hold      No\n",
      "7             3.84         3.916352   1.988328        Hold        Hold      No\n",
      "8             3.82         3.876845   1.488080         Buy         Buy      No\n",
      "9             3.84         3.985919   3.799971        Hold        Hold      No\n",
      "10            4.02         4.071423   1.279174        Hold        Hold      No\n",
      "11            3.87         3.813729  -1.454024         Buy         Buy      No\n",
      "12            3.88         3.929700   1.280927        Hold        Hold      No\n",
      "13            3.93         4.002061   1.833625        Hold        Hold      No\n",
      "14            3.95         3.956946   0.175848         Buy        Hold     Yes\n",
      "15            3.64         3.487626  -4.186104         Buy         Buy      No\n",
      "16            3.66         3.682207   0.606737        Hold        Hold      No\n",
      "17            4.56         5.341484  17.137799        Hold        Hold      No\n",
      "18            3.96         3.748169  -5.349276         Buy         Buy      No\n",
      "19            3.90         4.034627   3.451975        Hold         Buy     Yes\n",
      "20            3.71         3.794125   2.267525         Buy         Buy      No\n",
      "21            4.08         4.110317   0.743070        Hold        Hold      No\n",
      "22            3.76         3.792516   0.864788         Buy         Buy      No\n",
      "23            3.78         3.842204   1.645608        Hold        Hold      No\n",
      "24            3.92         3.845784  -1.893254        Hold        Hold      No\n",
      "25            3.80         3.813326   0.350684         Buy         Buy      No\n",
      "26            4.03         3.981534  -1.202618        Hold        Hold      No\n",
      "27            4.19         4.276038   2.053405        Hold        Hold      No\n",
      "28            9.37        11.024386  17.656205        Hold        Hold      No\n",
      "29           10.71        10.215664  -4.615649         Buy        Hold     Yes\n",
      "30           15.21        15.620669   2.699992        Hold        Hold      No\n",
      "31           23.39        22.710072  -2.906917        Hold        Hold      No\n",
      "32           28.91        25.901230 -10.407368        Hold        Hold      No\n",
      "33           25.38        23.218603  -8.516141         Buy         Buy      No\n",
      "34           25.30        18.900657 -25.293846         Buy         Buy      No\n",
      "35           29.68        27.746222  -6.515426        Hold        Hold      No\n",
      "36           46.04        52.041861  13.036189        Hold        Hold      No\n",
      "37           40.54        37.735148  -6.918727         Buy         Buy      No\n",
      "38           51.13        54.778516   7.135763        Hold        Hold      No\n",
      "39           38.92        41.253535   5.995723         Buy         Buy      No\n",
      "40           44.41        43.164393  -2.804789        Hold        Hold      No\n",
      "41           42.13        43.546536   3.362297        Hold         Buy     Yes\n",
      "42           47.10        47.630258   1.125812        Hold        Hold      No\n",
      "43           46.23        45.090459  -2.464938         Buy         Buy      No\n",
      "44           63.17        69.082858   9.360230        Hold        Hold      No\n",
      "45           78.48        92.838314  18.295507        Hold        Hold      No\n",
      "46           48.26        40.236824 -16.624899         Buy         Buy      No\n",
      "47           51.58        48.480161  -6.009770        Hold        Hold      No\n",
      "48           51.40        50.328849  -2.083951        Hold         Buy     Yes\n",
      "49           59.43        63.520515   6.882913        Hold        Hold      No\n",
      "50           56.81        54.548177  -3.981381         Buy         Buy      No\n",
      "51           55.75        57.545986   3.221499        Hold         Buy     Yes\n",
      "52           64.27        66.908066   4.104662        Hold        Hold      No\n",
      "53           69.64        69.723831   0.120377        Hold        Hold      No\n",
      "54           91.60        88.856391  -2.995206        Hold        Hold      No\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "This is a combined df of Zcash:\n",
      "\n",
      "     Original_Value  Predicted_Value    % Error Action_Pred Action_Orig Mislead\n",
      "0           214.31       245.230561  14.427960        Hold        Hold      No\n",
      "1           227.71       233.296040   2.453138         Buy        Hold     Yes\n",
      "2           283.29       293.739887   3.688759        Hold        Hold      No\n",
      "3           213.79       199.720657  -6.580917         Buy         Buy      No\n",
      "4           193.16       163.904764 -15.145597         Buy         Buy      No\n",
      "5           285.36       242.813927 -14.909613        Hold        Hold      No\n",
      "6           257.61       253.690812  -1.521365        Hold         Buy     Yes\n",
      "7           232.63       246.724568   6.058792         Buy         Buy      No\n",
      "8           216.04       211.395323  -2.149915         Buy         Buy      No\n",
      "9           218.16       223.615634   2.500749        Hold        Hold      No\n",
      "10          253.60       246.913639  -2.636578        Hold        Hold      No\n",
      "11          302.17       312.199989   3.319320        Hold        Hold      No\n",
      "\n",
      "This is a combined df of Bitcoin with Ridge Regression:\n",
      "\n",
      "     Original_Value  Predicted_Value    % Error Action_Pred Action_Orig Mislead\n",
      "0           656.99       649.852669  -1.086368        Hold        Hold      No\n",
      "1           592.69       559.383520  -5.619545         Buy         Buy      No\n",
      "2           577.44       565.856743  -2.005967        Hold         Buy     Yes\n",
      "3           577.76       584.034676   1.086035        Hold        Hold      No\n",
      "4           598.21       571.762674  -4.421077         Buy        Hold     Yes\n",
      "5           608.24       601.612891  -1.089555        Hold        Hold      No\n",
      "6           597.15       608.424213   1.888004        Hold         Buy     Yes\n",
      "7           609.74       607.716078  -0.331932         Buy        Hold     Yes\n",
      "8           616.75       616.663506  -0.014024        Hold        Hold      No\n",
      "9           637.96       646.495971   1.338010        Hold        Hold      No\n",
      "10          688.31       688.331159   0.003074        Hold        Hold      No\n",
      "11          703.42       718.561634   2.152574        Hold        Hold      No\n",
      "12          705.02       701.411485  -0.511832         Buy        Hold     Yes\n",
      "13          744.59       762.712391   2.433875        Hold        Hold      No\n",
      "14          777.94       755.799083  -2.846096         Buy        Hold     Yes\n",
      "15          769.73       774.051771   0.561466        Hold         Buy     Yes\n",
      "16          800.88       791.212903  -1.207059        Hold        Hold      No\n",
      "17          973.50      1001.099620   2.835092        Hold        Hold      No\n",
      "18          908.59       934.019675   2.798806         Buy         Buy      No\n",
      "19          831.53       789.751544  -5.024287         Buy         Buy      No\n",
      "20          901.54       866.571289  -3.878775        Hold        Hold      No\n",
      "21         1029.91      1024.198970  -0.554517        Hold        Hold      No\n",
      "22          999.18       986.025549  -1.316525         Buy         Buy      No\n",
      "23         1115.30      1098.894058  -1.470989        Hold        Hold      No\n",
      "24         1251.01      1247.318219  -0.295104        Hold        Hold      No\n",
      "25         1175.83      1070.178651  -8.985257         Buy         Buy      No\n",
      "26         1054.23      1032.313297  -2.078930         Buy         Buy      No\n",
      "27         1039.97       966.099983  -7.103091         Buy         Buy      No\n",
      "28         1176.90      1218.197366   3.508995        Hold        Hold      No\n",
      "29         1182.94      1171.722174  -0.948301         Buy        Hold     Yes\n",
      "30         1265.49      1269.179283   0.291530        Hold        Hold      No\n",
      "31         1537.67      1525.215253  -0.809975        Hold        Hold      No\n",
      "32         1804.91      1743.922099  -3.379000        Hold        Hold      No\n",
      "33         2173.40      2036.705982  -6.289409        Hold        Hold      No\n",
      "34         2286.41      2152.650662  -5.850190        Hold        Hold      No\n",
      "35         2823.81      2884.133121   2.136232        Hold        Hold      No\n",
      "36         2548.29      2581.874478   1.317922         Buy         Buy      No\n",
      "37         2552.45      2462.391160  -3.528329         Buy        Hold     Yes\n",
      "38         2608.56      2555.728849  -2.025299        Hold        Hold      No\n",
      "39         1998.86      2206.578731  10.391860         Buy         Buy      No\n",
      "40         2754.86      2812.181472   2.080740        Hold        Hold      No\n",
      "41         2710.67      2754.631501   1.621795         Buy         Buy      No\n",
      "42         3650.62      3495.341621  -4.253480        Hold        Hold      No\n",
      "43         4087.66      4255.088215   4.095943        Hold        Hold      No\n",
      "44         4579.02      4472.074801  -2.335548        Hold        Hold      No\n",
      "45         4599.88      4550.122470  -1.081714        Hold        Hold      No\n",
      "46         3625.04      3721.404024   2.658289         Buy         Buy      No\n",
      "47         3926.07      3830.868059  -2.424866        Hold        Hold      No\n",
      "48         4229.36      4434.175170   4.842699        Hold        Hold      No\n",
      "49         5647.21      5599.362662  -0.847274        Hold        Hold      No\n",
      "50         6008.42      5899.525526  -1.812365        Hold        Hold      No\n",
      "51         6468.40      5983.313576  -7.499326        Hold        Hold      No\n",
      "52         7143.58      7547.141867   5.649294        Hold        Hold      No\n",
      "53         7790.15      7794.520121   0.056098        Hold        Hold      No\n",
      "54         9818.35      9464.337745  -3.605619        Hold        Hold      No\n",
      "\n",
      "This is a combined df of Ethereum with Ridge Regression:\n",
      "\n",
      "     Original_Value  Predicted_Value    % Error Action_Pred Action_Orig Mislead\n",
      "0            50.70        51.509305   1.596263        Hold        Hold      No\n",
      "1            43.44        43.690345   0.576301         Buy         Buy      No\n",
      "2            48.31        49.537657   2.541207        Hold        Hold      No\n",
      "3            70.16        58.311112 -16.888381        Hold        Hold      No\n",
      "4            94.01        95.396176   1.474498        Hold        Hold      No\n",
      "5            89.44        91.759273   2.593105         Buy         Buy      No\n",
      "6           174.45       177.543515   1.773296        Hold        Hold      No\n",
      "7           224.38       210.426512  -6.218686        Hold        Hold      No\n",
      "8           401.49       337.414148 -15.959514        Hold        Hold      No\n",
      "9           336.87       359.491406   6.715174        Hold         Buy     Yes\n",
      "10          294.92       321.182888   8.905089         Buy         Buy      No\n",
      "11          242.14       251.096166   3.698755         Buy         Buy      No\n",
      "12          234.39       180.086271 -23.168108         Buy         Buy      No\n",
      "13          204.32       202.342296  -0.967944        Hold         Buy     Yes\n",
      "14          256.51       219.392153 -14.470331        Hold        Hold      No\n",
      "15          300.10       299.055553  -0.348033        Hold        Hold      No\n",
      "16          317.52       316.590256  -0.292814        Hold        Hold      No\n",
      "17          387.74       377.648378  -2.602678        Hold        Hold      No\n",
      "18          288.75       292.649654   1.350530         Buy         Buy      No\n",
      "19          282.80       284.703741   0.673176         Buy         Buy      No\n",
      "20          299.15       294.567532  -1.531830        Hold        Hold      No\n",
      "21          311.12       304.280547  -2.198333        Hold        Hold      No\n",
      "22          333.38       334.586298   0.361839        Hold        Hold      No\n",
      "23          297.93       294.834689  -1.038939         Buy         Buy      No\n",
      "24          305.71       287.090732  -6.090500         Buy        Hold     Yes\n",
      "25          307.91       305.992594  -0.622716        Hold        Hold      No\n",
      "26          360.40       362.197778   0.498829        Hold        Hold      No\n",
      "\n",
      "This is a combined df of Litecoin with Ridge Regression:\n",
      "\n",
      "     Original_Value  Predicted_Value    % Error Action_Pred Action_Orig Mislead\n",
      "0             4.08         4.005591  -1.823743        Hold        Hold      No\n",
      "1             3.78         3.635101  -3.833308         Buy         Buy      No\n",
      "2             3.64         3.604418  -0.977522         Buy         Buy      No\n",
      "3             3.80         4.000283   5.270594        Hold        Hold      No\n",
      "4             3.89         3.859542  -0.782985         Buy        Hold     Yes\n",
      "5             3.82         3.897683   2.033592        Hold         Buy     Yes\n",
      "6             3.84         3.855874   0.413388         Buy        Hold     Yes\n",
      "7             3.84         3.931780   2.390117        Hold        Hold      No\n",
      "8             3.82         3.893622   1.927274         Buy         Buy      No\n",
      "9             3.84         4.006125   4.326171        Hold        Hold      No\n",
      "10            4.02         4.065773   1.138637        Hold        Hold      No\n",
      "11            3.87         3.890680   0.534367         Buy         Buy      No\n",
      "12            3.88         3.907057   0.697346        Hold        Hold      No\n",
      "13            3.93         4.028007   2.493829        Hold        Hold      No\n",
      "14            3.95         3.959451   0.239278         Buy        Hold     Yes\n",
      "15            3.64         3.541850  -2.696429         Buy         Buy      No\n",
      "16            3.66         3.701873   1.144062        Hold        Hold      No\n",
      "17            4.56         5.153131  13.007268        Hold        Hold      No\n",
      "18            3.96         3.955180  -0.121706         Buy         Buy      No\n",
      "19            3.90         3.997644   2.503688        Hold         Buy     Yes\n",
      "20            3.71         3.829899   3.231766         Buy         Buy      No\n",
      "21            4.08         4.154546   1.827097        Hold        Hold      No\n",
      "22            3.76         3.828231   1.814648         Buy         Buy      No\n",
      "23            3.78         3.862735   2.188761        Hold        Hold      No\n",
      "24            3.92         3.860516  -1.517461         Buy        Hold     Yes\n",
      "25            3.80         3.827280   0.717886         Buy         Buy      No\n",
      "26            4.03         4.100176   1.741329        Hold        Hold      No\n",
      "27            4.19         4.251795   1.474809        Hold        Hold      No\n",
      "28            9.37        11.052088  17.951846        Hold        Hold      No\n",
      "29           10.71        10.384534  -3.038902         Buy        Hold     Yes\n",
      "30           15.21        15.046621  -1.074156        Hold        Hold      No\n",
      "31           23.39        20.999423 -10.220508        Hold        Hold      No\n",
      "32           28.91        28.292697  -2.135259        Hold        Hold      No\n",
      "33           25.38        24.306598  -4.229324         Buy         Buy      No\n",
      "34           25.30        19.772669 -21.847159         Buy         Buy      No\n",
      "35           29.68        28.578592  -3.710945        Hold        Hold      No\n",
      "36           46.04        47.436914   3.034131        Hold        Hold      No\n",
      "37           40.54        39.137385  -3.459829         Buy         Buy      No\n",
      "38           51.13        53.288334   4.221268        Hold        Hold      No\n",
      "39           38.92        42.016812   7.956865         Buy         Buy      No\n",
      "40           44.41        44.175033  -0.529085        Hold        Hold      No\n",
      "41           42.13        42.674909   1.293398         Buy         Buy      No\n",
      "42           47.10        47.446798   0.736300        Hold        Hold      No\n",
      "43           46.23        44.677296  -3.358650         Buy         Buy      No\n",
      "44           63.17        65.740252   4.068786        Hold        Hold      No\n",
      "45           78.48        88.016762  12.151837        Hold        Hold      No\n",
      "46           48.26        41.657394 -13.681322         Buy         Buy      No\n",
      "47           51.58        48.225748  -6.503009        Hold        Hold      No\n",
      "48           51.40        51.675363   0.535726        Hold         Buy     Yes\n",
      "49           59.43        59.664854   0.395178        Hold        Hold      No\n",
      "50           56.81        55.531309  -2.250820         Buy         Buy      No\n",
      "51           55.75        56.835495   1.947076        Hold         Buy     Yes\n",
      "52           64.27        64.445191   0.272586        Hold        Hold      No\n",
      "53           69.64        69.374076  -0.381855        Hold        Hold      No\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "54           91.60        87.412520  -4.571485        Hold        Hold      No\n",
      "\n",
      "This is a combined df of Zcash with Ridge Regression:\n",
      "\n",
      "     Original_Value  Predicted_Value    % Error Action_Pred Action_Orig Mislead\n",
      "0           214.31       239.668065  11.832422        Hold        Hold      No\n",
      "1           227.71       238.703803   4.827984         Buy        Hold     Yes\n",
      "2           283.29       288.803273   1.946159        Hold        Hold      No\n",
      "3           213.79       210.085449  -1.732799         Buy         Buy      No\n",
      "4           193.16       169.866398 -12.059227         Buy         Buy      No\n",
      "5           285.36       237.937025 -16.618648        Hold        Hold      No\n",
      "6           257.61       250.150356  -2.895712        Hold         Buy     Yes\n",
      "7           232.63       242.757413   4.353442         Buy         Buy      No\n",
      "8           216.04       210.213985  -2.696730         Buy         Buy      No\n",
      "9           218.16       226.516187   3.830302        Hold        Hold      No\n",
      "10          253.60       247.362243  -2.459683        Hold        Hold      No\n",
      "11          302.17       308.175339   1.987404        Hold        Hold      No\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.1103306171755349,\n",
       " 1.1912183993022312,\n",
       " -1.1062509448585558,\n",
       " 1.1055453718351231)"
      ]
     },
     "execution_count": 293,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea367e0d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HUB27pPnkbQ4qm9IsQmWup33a4yuZ8HGSDXsK75/VC4CpC1KcOaGRxqShogxu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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea35607240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OjJ8pK9wd1FqL+1BgCHASMF1Elvo/y0RkafbjhZK9aUOgmrKu46uvGfqD9pjZ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\n6ke4KgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea3710d6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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up+bauItUtWdw6ZV26amqvbIVMs/YCY1C5Jyqy3dSpdx3jjyylLJy+8beTi09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\nMla4jTEmZKxwG2NMyFjhNsaYkPk/eYFUd1Ran24AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea350c8f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Twt0JHfVxVxljasOfldN+ao0xKxcrZMS97DqA6pSjPT/YNsv0k4GlxQ5TQfSb\naSfouIiFpy3uaGneUZl5be54agpwmZNE5e8b4qmvXYeIEi3chfcx9iQPFR0jgN9mmX4B9rwGlV8t\nB7ZQHdDCXWDJRMxgR1hR0XKB5werZ0yJpxYCp7uJU9bech0garRwF4f2c0dPHXBJq6nx1H+w16ZX\n+aOFu5O0cBeHnmUaTUd4frBDlun/BzQUO0wZ08LdSVq4i+N1YJbrEKpLrvb8IPOaPvHUp2Rrjauu\n+JZ4Kuk6RNRo4S6CZCLWBDzoOofqkk2xLeyW/gJML3KWcvSM6wBRpIW7eP7rOoDqsj97fjA4Y0o8\ntQg4zU2csqInNnWBFu7ieRod+T2qaoFLW02Npx4AHi3ECo99cBGDLpnPJtcsyJg+4fUGhl21gI2v\nWcBZTy5u8/GNTYbNr1vAz++oXz7tsPvr+ck/FnD20ysed8HzS3hwitPzip5yufKo0sJdJMlEbCkQ\nuM6huuwQzw92yTL9/4C2K2gXHT2ihscO75sx7dlpy3jw46W8e8JKfPDbfvxu255tPv7vrzew0YAV\n/97vzrKXun73xH68+EUjqcWGmfObmPh1I/tuWJPv+Lmaqv3bXaOFu7i0uyTarvL8ILPKxVNTyXZ9\nk27a8Uc9WLVP5rgl/3ijAX/7XvTqYacPWin7v++X85oIPl3Gr0auKOw1VbBoKTQZQ0OjoboKznt2\nCefv3Cvf0TtDu0m6SAt3cf2PArTOVNEMJ3u/doIiXJb0kzlNvDh9GVvdsICdbl7IpK+yDxhz2mOL\nuXj33lSl1f2NBlazdl0VI69byMHDa/js+yYMsPng6qzLKJInXK48yrRwF1EyEVsIPOA6h+qW8zw/\nWDNjSjy1GDil0Cte1gQ/LIbXjluJS/bozcH31dNyzNhHPlnKoJWEUUNaF+Qr9urN5BP6cea2vTj3\n2SWcv0sv/vLCEg6+t57r3yz6Yen1FGj/QCXQwl1817oOoLqlH3B5q6nxVAC0O7h2d621snDARj0Q\nEbZcs5oqgdn1mYX75S8aeejjZXhXzOeX9y3imWnLOPz+RRnzPDhlKVsMrmZhg+H97xq556C+3Pbu\nUuqXFnXMj4B4qr7j2VQ2WriLLJmIPY8dGUdF10GeH+yRZfqpwKIs0/Nivw1reGaaHQLzkzmNNDTC\ngL6Z/eAX7d6bL8+oJXlaLXcd2Idd1+nB7Qf0WX7/0kbD319vYNx2PalfumL07yYDDcUdqvfeoq6t\nzGjhdkNb3dE3wfODzMM67BESF+Vj4Yf8p55tblzIx3OaWOuy+dz4VgPHbl7D1B8Mm1yzgF/et4hb\n9uuDiPD1/Cb2/ndujderJzUCXIwoAAAK10lEQVRw1GY19K0RfrJ6FQbY9B8L2G5oNf17S4ePz5N6\n9AirbpGWfWSq8Dw/qMOOY7iS6yyqW85OJmKZhTpe1wt4H1jfSaJouI946iDXIaJMW9wOJBOxFHCn\n6xyq287x/GDtjCnx1BLsaDmqbbrtd5MWbnf+4TqA6ra+wBWtpsZTjwP3Fz1NNMykwDtxK4EWbkeS\nidhb6AAL5WB/zw/2yjL9NGxfrsp0E/HUMtchok4Lt1sXug6g8mKC5weZpyDGUzOA8W7ilKwm4J+u\nQ5QDLdwOJROxR9CLyJeD9YGzsky/FB29PN3/iKe+cB2iHGjhdu981wFUXvzB8wMvY0o81YDuqEyn\nh8HmiRZu9x4C3nQdQnVbH+DKVlPjqafQk00APkNPcc8bLdyOhaPA/9F1DpUXYzw/+HmW6acDC7JM\nryQJ4qkm1yHKhRbuEpBMxB5HBxQuF3/3/KB3xpR46isqu0tsBnCr6xDlRAt36fiD6wAqL9Yl+3t5\nBZV7jZqLiaecDrNTbrRwl4hkIvYqcJvrHCovzvL8YL2MKbZwneQmjlOzgBtchyg3WrhLy5nAD65D\nqG7rTfYdlc9Read7Xxper1zlkRbuEpJMxL4Dfu86h8qLvT0/2C/L9DOBecUO48jXwNWuQ5QjLdyl\n5wbgFdchVF5c4flBn4wp8dRMIO4kTfGdp4MlFIYW7hITHh54AqDXc4i+H5H9UM8JwHtFzlJs7wM3\nuw5RrrRwl6BkIvYe2a46p6JonOcHP86YYi+yVO47Kk8jnupwTB0RKenj20VkZxHZ1nWOlrRwl644\nkHScQXVfT+CqVlPjqRcp36OIHiSeetp1CBHp0eJ2V4a03xnQwq1yE44IfwjaZVIO9vT84MAs08cB\nqWKHKbBFwBmdfVDYsn1ORO4TkSki8m8RkfC+0SLyioi8IyITRaRWRHqLyL9E5D0ReVtEdgnnPVpE\n7hWRh4EnwuU+KyJ3EHZPicjh4XImi8h1zQVdRPYSkbfC9TwtIh622/L0cN4d8vIK5YEW7hKWTMRe\nQ0+HLxeXeX6QOVRdPDULONdNnII5l3hqahcfuzn2OubDsScybSciPYG7gVONMZsBu2M/HE4CMMZs\nim3g3CIizWesbgMcZYzZNby9JfBHY8xwEdkIGAtsZ4wZATQCh4nIQOB64Bfheg4yxiSxF8a63Bgz\nwhjzYhefV95p4S59lwCPuQ6hum0o2Yv0NcDkImcplNfp3r6ZicaYL40xTdjXxAOGATONMZMAjDHz\njDHLgO0Ju5qMMVOA6cAG4XKeNMZ832K508K/dwNGAZNEZHJ4e11ga+CF5vlaPL7kaOEuceFRJkdi\nh3xS0XaG5wcbZkyxO/B+C0R91O4G4Nhcdki2Y0na341AD0DI/tq0NyT9wnZuC3BL2IIeYYwZZoyJ\nt7OekqSFOwLCE3MOx44goqKrhuw7Kl8l+ofOjSeeKsS1WKYAQ0RkNEDYv90DeAE4LJy2AbA2uQ1a\n8TRwoIgMCh+7qoj8CDuM4E4isk7z9HD++UBtHp9PXmjhjohkIvYM8BfXOVS37eb5wdgs039PdC93\n8A6QKMSCjTEN2D7pCSLyDvAk9pIC1wDVIvIetg/8aGPMkraXtHx5HwLnYHdcvhsub7Ax5jvg18D9\n4XruDh/yMLB/qe2cFGMi8+2g4nl+UA08AGS75rOKjq+BYclELPMY5njdidiCFCULgS2Ip6a4DlJJ\ntMUdIclErBH4JTpiTtQNIftp79cRvff2RC3axact7gjy/GAN4DXsKdUqmpYBI5KJ2AcZU+N1W2L7\nW6PQqLqJeOo41yEqURQ2DtVCMhH7BtgbmOs6i+qyHmS7cl48NRG4sehpOu99dCBkZ7RwR1QyEfsQ\n2B97GJaKpp08Pzgsy/Q/AHOKHaYTFgAHEU8tch2kUmnhjrBkIvYcoF9Vo+1vnh+snDElnppD6Q5l\n1wQcqv3abmnhjrhkInY7Xbg2hCoZa5B9IOEbsGcilpoziacedh2i0unOyTLh+cHpwGWuc6guaQRG\nJhOxdzOmxutGARMpnQbWNcRT5X452kgolQ1CdVMyEbscbXlHVTVwtecHmadxx1NvYg8RLAX/A05x\nHUJZWrjLSFi8TyJC11xQy22PvSZNS38EvitylpYmA2O7eR0SlUfaVVKGPD84ErgJ25JT0fEt9ozK\nzMM843XHYN9PFz4Adiaemu1o/SoLbXGXoWQiditwMJlXW1OlbxAwPsv0m3EzgPQnwO5atEuPtrjL\nmOcH2wD3Y49cUNHQCIxOJmJvZ0yN140A3qB436I+B3YinvqqSOtTnaAt7jKWTMReBUYDb7nOonJW\nDVyTZUflZIp3AaovgN20aJcuLdxlLpmIfQnsANzjOovK2dbAsVmmnwvMKvC6P8G2tKcXeD2qG7Sr\npIJ4fnAO9mSP9kYPUaVhNnZHZeYQWvG6I4BbC7TOScDe2qdd+rTFXUGSidh44ADstSZUaRsAXNhq\najx1G1CIQWsfB3bRoh0NWrgrTDIRewAYSWmeTq0yHe/5wRZZpp+EvSxsvtwOjCGeajlWoypRWrgr\nUDIR+xTYDjiP/BYAlV9V2B2Vmf+n8dR7wIQ8reNC4EjiqaV5Wp4qAu3jrnBhi+42YMOO5lXOnJBM\nxDJPfY/X1WIHxx3cxWUuAI4inrq/m9mUA1q4FZ4f9AH+ir0wvu64LD3fAxskE7HMa3TH6w4F/t2F\n5X0C7Ec89VEesikHtKtEkUzEFiUTsVOAn2JPvFClZVWyjaIeT90BPNvJZT0EjNaiHW1auNVyyUTs\nSWBj7EX89ciT0nKM5wdeluknA7n0TzcAPralPS+fwVTxaVeJysrzg8HARdgr1mn3iVuvAackE7FJ\nWe+N110MjGvn8e8DhxNPvVOAbMoBLdyqXZ4fbAlcCWzlOksF+go4G7gtmYi1/Y8ar+sHfASs1eIe\nA1wOnE08pRccKyNauFWHwutmHA78GVjHcZxK8CX2286NyUQst4IbrzsYuDttyhfA0cRTne0DVxGg\nhVvlzPODHsAR2Fbg+o7jlKMvsAX7pmQi1tDpR8frngB2wX5D+hPxlO6nKFNauFWneX5QDYwFzgI2\ncxynHEzHnghzc5cKdrN43frAStqXXf60cKtu8fxgD+yOsT1cZ4mg14BrgTuSiZieuahypoVb5YXn\nBxsBR2O7Urp6Nl8lmIs9U/X6ZCL2nuswKpq0cKu8CrtR9sIW8X2Ank4DlY6XgX8C9yYTsUWuw6ho\n08KtCsbzg1WBQ7FFfJTbNE5Mxp6peHcyEfvQdRhVPrRwq6Lw/GAtbEv8Z8DuwMpuExVEA/Actlg/\nlEzEZriNo8qVFm5VdJ4f1ADbAntjC/mmbhN1yxfA88AjwGPJRExPJ1cFp4VbOef5wRrYQY1Hpf2U\n4g7Oxdjuj0nAK8BL4ZieShWVFm5VksJrpTQX8c2AdbFnbRaji2U2MDXt5zPgLeCDZCKmA08o57Rw\nq0gJd3h6wJC0n0FAX6AP0DvLT09gITA//FmQ9vd8IIU9CWYqMDWZiM0v2hNSqgu0cCulVMTo9biV\nUipitHArpVTEaOFWSqmI0cKtlFIRo4VbKaUiRgu3UkpFjBZupZSKGC3cSikVMVq4lVIqYrRwK6VU\nxGjhVkqpiNHCrZRSEaOFWymlIkYLt1JKRYwWbqWUihgt3EopFTFauJVSKmK0cCulVMRo4VZKqYjR\nwq2UUhHz/1I36qOHE5XKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea375c0358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VzFbY2+R3bZkST30H7AfcnG0hlbePXAcQJTnbcYtIDxE5DLgbOBV7YebBYgdW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\nD3yehTuIwUjKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea375f2c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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67tHYIcq2AC42xowwxlxqjNEDuQjpVGIWtp1bRcNlnh8MyClJZuYCZ7sJp0vR\nGnc7tFXjPhLYADgdGCsis8O/OSKit6cWR8fmjI6VgD8vV5rM3If2Wldumrjboa027m7GmH7h3wpZ\nf/2MMStUKsiIe9V1AKpdjvH8YLsC5acCiysdTBeiv0zbQcdFLD+tcUdL84nK3L65k5kpwNVOIoq/\nb0hmvnIdRJRo4i6/D7A3eajoGAacXKD8Uux9Daq08ge2UG3QxF1m6VTCYEdYUdFyqecHq+aUJDPz\ngDPdhBNrE1wHEDWauCtD27mjpx64crnSZObf2L7pVelo4m4nTdyVoXeZRtORnh/sWKD8/4CGSgcT\nY5q420kTd2W8AUx3HYTqkOs9P8jt0yeZ+YhCtXHVEd+SzKRdBxE1mrgrIJ1KNAGPuI5Ddcim2Bp2\nvj8C0yocSxw97zqAKNLEXTn/cR2A6rCLPT8YlFOSzCwAznATTqzojU0doIm7cp5DR36Pqn7AVcuV\nJjMPA/8txwqPe2QBA6+cwyY3zM0pH/VGA0P+NpeNb5jLuc8sbHH+xibD5jfO5Wd3z19advhD8/nx\n3+dy3nPL5rv0xUU8MsXpfUXPulx5VGnirpB0KrEYCFzHoTrsUM8PdilQ/n9Ayxm0g44ZVseTR/TO\nKXth6hIe+WAxk37Th3dP7stvt+ve4vzXvtHARv2XfbwnTbddXU86qS8vf9ZIZqHh6zlNjPuqkV9s\nWFfq8Iv1qbZvd4wm7srS5pJo+5vnB7lZLpn5lEL9m3TSTmvXsnKv3HFL/v5mA/4OPehRa8sH9in8\n8f1idhPBR0s4YYtlib2uGyxYDE3G0NBoqOkGF72wiEtG9ih16O2hzSQdpIm7sp6gDLUzVTFDKdyu\nnaIC3ZJ+OLOJl6ctYet/zWXn2+Yx/svCA8ac8eRCrti9J92y8v5GA2pYq74bW9w4j4OG1vHx900Y\nYPNBNQWXUSFPu1x5lGnirqB0KjEPeNh1HKpTLvL8YPWckmRmIXBauVe8pAl+WAivH9+HK/foyUEP\nzid/zNjHP1zMwD7C8MHLJ+Rr9urJxN/05eztenDhC4u4ZJce/PGlRRz0wHxueqvil6XPp0znB7oC\nTdyV9w/XAahO6Qv8dbnSZCYAWh1cu7PWWEHYf6NaRIStVq+hm8CM+bmJ+9XPGnn0gyV418zhkAcX\n8PzUJRzx0IKcaR6ZspgtB9Uwr8HwzneN3H9gb+6YtJj5iys65kdAMjO/7clUIZq4KyydSryIHRlH\nRdeBnh/sUaD8dGBBgfKS2HfDOp6faofA/HBmIw2N0L93bjv4n3bvyRdn9SN9Rj/uPaAXu65Ty537\n91r6+uJGw7VvNHDO9t2Zv3jU+Y4rAAALLElEQVTZ6N9NBhoqO1TvAxVdW8xo4nZDa93RN8rzg9zL\nOuwVEn8qxcIP/fd8tr15Hh/MbGKNq+dw84QGjtu8jk9/MGxyw1wOeXABo/fthYjw1Zwm9r6ruMrr\n9eMbOHqzOnrXCT9etRsG2PTvc9l+zRpW7Cltzl8i89ErrDpF8tvIVPl5flCPHcewj+tYVKecl04l\nchN1sr4H8A6wvpOIouFBkpkDXQcRZVrjdiCdSmSAe1zHoTrtAs8P1sopSWYWYUfLUS3TY7+TNHG7\n83fXAahO6w1cs1xpMvMU8FDFo4mGrynzSdyuQBO3I+lUYgI6wEIc7Of5wV4Fys/AtuWqXLeQzCxx\nHUTUaeJ263LXAaiSGOX5Qe4tiMnM58BlbsKpWk3AP10HEQeauB1KpxKPo53Ix8H6wLkFyq9CRy/P\n9gTJzGeug4gDTdzuXeI6AFUSv/f8wMspSWYa0BOV2fQy2BLRxO3eo8BbroNQndYLuG650mTmWfRm\nE4CP0VvcS0YTt2PhKPDnu45DlcQ+nh/8rED5mcDcAuVdSYpkpsl1EHGhibsKpFOJp9ABhePiWs8P\neuaUJDNf0rWbxD4HbncdRJxo4q4ev3cdgCqJdSn8Xl5D1+2j5gqSGafD7MSNJu4qkU4lXgPucB2H\nKolzPT9YL6fEJq5T3ITj1HTgX66DiBtN3NXlbOAH10GoTutJ4ROVY+h6t3tfFfZXrkpIE3cVSacS\n3wG/cx2HKom9PT/Yt0D52cDsSgfjyFfA9a6DiCNN3NXnX8BY10GokrjG84NeOSXJzNdA0kk0lXeR\nDpZQHpq4q0x4eeBvAO3PIfrWpvClnqOAyRWOpdLeAW5zHURcaeKuQulUYjKFep1TUXSO5wc/yimx\nnSzF/UTlGSQzbY6pIyJVfX27iIwUke1cx5FPE3f1SgJpxzGozusO/G250mTmZeJ7FdEjJDPPuQ5C\nRGrznndkSPuRgCZuVZxwRPhD0SaTONjT84MDCpSfA2QqHUyZLQDOau9MYc12jIg8KCJTROQuEZHw\ntREiMlZE3haRcSLST0R6isitIjJZRP4nIruE0x4jIg+IyGPA0+FyXxCRuwmbp0TkiHA5E0XkxuaE\nLiJ7iciEcD3PiYiHbbY8M5x2x5LsoRLQxF3F0qnE6+jt8HFxtecHuUPVJTPTgQvdhFM2F5LMfNrB\neTfH9mM+FHsj0/Yi0h24DzjdGLMZsDv2y+EUAGPMptgKzmgRab5jdVvgaGPMruHzrYDzjTFDRWQj\n4GBge2PMMKAROFxEBgA3Ab8M13OgMSaN7Rjrr8aYYcaYlzu4XSWnibv6XQk86ToI1WlrUjhJ3wBM\nrHAs5fIGnTs3M84Y84Uxpgm7TzxgCPC1MWY8gDFmtjFmCbADYVOTMWYKMA3YIFzOM8aY7/OWOzV8\nvBswHBgvIhPD5+sC2wAvNU+XN3/V0cRd5cKrTI7CDvmkou0szw82zCmxJ/BOBqI+ancDcFwxJyRb\nsSjrcSNQCwiF901rQ9LPa+W5AKPDGvQwY8wQY0yylfVUJU3cERDemHMEdgQRFV11FD5R+RrRv3Tu\nMpKZcvTFMgUYLCIjAML27VrgJeDwsGwDYC2KG7TiOeAAERkYzruyiKyNHUZwZxFZp7k8nH4O0K+E\n21MSmrgjIp1KPA/80XUcqtN28/zg4ALlvyO63R28DaTKsWBjTAO2TXqUiLwNPIPtUuAGoEZEJmPb\nwI8xxixqeUlLl/cecAH2xOWkcHmDjDHfAb8CHgrXc184y2PAftV2clKMicyvgy7P84Ma4GGgUJ/P\nKjq+AoakU4nca5iT9SdhE1KUzAO2JJmZ4jqQrkRr3BGSTiUagUPQEXOibjCFb3u/kei9tydp0q48\nrXFHkOcHqwGvY2+pVtG0BBiWTiXezSlN1m+FbW+NQqXqFpKZ410H0RVF4eBQedKpxDfA3sAs17Go\nDqulUM95ycw44OaKR9N+76ADITujiTui0qnEe8B+2MuwVDTt7PnB4QXKfw/MrHQw7TAXOJBkZoHr\nQLoqTdwRlk4lxgD6UzXa/uL5wQo5JcnMTKp3KLsm4DBt13ZLE3fEpVOJO+lA3xCqaqxG4YGE/4W9\nE7HanE0y85jrILo6PTkZE54fnAlc7ToO1SGNwBbpVGJSTmmyfjgwjuqpYN1AMhP37mgjoVoOCNVJ\n6VTir2jNO6pqgOs9P8i9jTuZeQt7iWA1eAI4zXUQytLEHSNh8j6FCPW5oJbaAdsnTb7zge8qHEu+\nicDBneyHRJWQNpXEkOcHRwG3YGtyKjq+xd5RmXuZZ7L+WOz76cK7wEiSmRmO1q8K0Bp3DKVTiduB\ng8jtbU1Vv4HAZQXKb8PNANIfArtr0q4+WuOOMc8PtgUewl65oKKhERiRTiX+l1OarB8GvEnlfkV9\nAuxMMvNlhdan2kFr3DGWTiVeA0YAE1zHoopWA9xQ4ETlRCrXAdVnwG6atKuXJu6YS6cSXwA7Ave7\njkUVbRvguALlFwLTy7zuD7E17WllXo/qBG0q6UI8P7gAe7NHa6OHqOowA3uiMncIrWT9kcDtZVrn\neGBvbdOuflrj7kLSqcRlwP7YviZUdesPXL5caTJzB1COQWufAnbRpB0Nmri7mHQq8TCwBdV5O7XK\ndaLnB1sWKD8F2y1sqdwJ7EMykz9Wo6pSmri7oHQq8RGwPXARpU0AqrS6YU9U5n5Ok5nJwKgSreNy\n4CiSmcUlWp6qAG3j7uLCGt0dwIZtTauc+U06lci99T1Z3w87OO6gDi5zLnA0ycxDnYxNOaCJW+H5\nQS/gz9iO8fXEZfX5HtggnUrk9tGdrD8MuKsDy/sQ2Jdk5v0SxKYc0KYSRTqVWJBOJU4DfoK98UJV\nl5UpNIp6MnM38EI7l/UoMEKTdrRp4lZLpVOJZ4CNsZ3465Un1eVYzw+8AuWnAsW0TzcAPramPbuU\nganK06YSVZDnB4OAP2F7rNPmE7deB05LpxLjC76arL8COKeV+d8BjiCZebsMsSkHNHGrVnl+sBVw\nHbC161i6oC+B84A70qlEyx/UZH1f4H1gjbxXDPBX4DySGe1wLEY0cas2hf1mHAFcDKzjOJyu4Avs\nr52b06lEcQk3WX8QcF9WyWfAMSQz7W0DVxGgiVsVzfODWuBIbC1wfcfhxNFn2IR9SzqVaGj33Mn6\np4FdsL+Q/kAyo+cpYkoTt2o3zw9qgIOBc4HNHIcTB9OwN8Lc1qGE3SxZvz7QR9uy408Tt+oUzw/2\nwJ4Y28N1LBH0OvAP4O50KqF3LqqiaeJWJeH5wUbAMdimlI7ezdcVzMLeqXpTOpWY7DoYFU2auFVJ\nhc0oe2GT+M+B7k4Dqh6vAv8EHkinEgtcB6OiTRO3KhvPD1YGDsMm8eFuo3FiIvZOxfvSqcR7roNR\n8aGJW1WE5wdrYGviPwV2B1ZwG1FZNABjsMn60XQq8bnbcFRcaeJWFef5QR2wHbA3NpFv6jaiTvkM\neBF4HHgynUro7eSq7DRxK+c8P1gNO6jx8Ky/ajzBuRDb/DEeGAu8Eo7pqVRFaeJWVSnsK6U5iW8G\nrIu9a7MSTSwzgE+z/j4GJgDvplMJHXhCOaeJW0VKeMLTAwZn/Q0EegO9gJ4F/roD84A54d/crMdz\ngAz2JphPgU/TqcScim2QUh2giVsppSJG++NWSqmI0cStlFIRo4lbKaUiRhO3UkpFjCZupZSKGE3c\nSikVMZq4lVIqYjRxK6VUxGjiVkqpiNHErZRSEaOJWymlIkYTt1JKRYwmbqWUihhN3EopFTGauJVS\nKmI0cSulVMRo4lZKqYjRxK2UUhGjiVsppSJGE7dSSkXM/wP5KCDs95CEfQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea35298f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ToRBVDFq4VeQ8P+iKXZl5KLA3sJnbRB0yDXgRe0zrkelUQk9SoYpO\nC7dyzvODPsBOTS6rOw2VWz3wMfAu8E54+UR71SpqWrhVyQk3M9wMW8AHh9c3AzYFukUQYTEwGfgW\nu8neOGA88HE6lVgcwfyVapUWbhUbYUFfC7uXYMOlD9ALeyTD7L8N1w12E7zF4aXp9emsLNKTgW/T\nqcTMyF6UUqtAC7dSSsVMpW2epZRSsaeFWymlYkYLt1JKxYwWbqWUihkt3EopFTNauJVSKma0cCul\nVMxo4VZKqZjRwq2UUjGjhVsppWJGC7dSSsWMFm6llIoZLdxKKRUzWriVUipmtHArpVTMaOFWSqmY\n0cKtlFIxo4VbKaViRgu3UkrFjBZupZSKmf8H2ihNjvTtOvkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ea3527cf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#16) Creating dataframes from each cryptocurrency of original and predicted values\n",
    "    #using pred_compare_df()\n",
    "\n",
    "#a) Bitcoin dataframe to compare original and predicted values\n",
    "combined_df_bc = pred_compare_df(Ytest_bc,pred_bitcoin_lreg)\n",
    "print(\"\\nThis is a combined df of Bitcoin:\\n\\n\", combined_df_bc)\n",
    "\n",
    "#a-1) plotting number of times mislead \n",
    "plt.figure()\n",
    "combined_df_bc[\"Mislead\"].value_counts().plot(kind=\"pie\", autopct='%1.1f%%', labels = [\"Correct\", \"Incorrect\"] )\n",
    "plt.title(\"Bitcoin Prediction Outcome with Linear Regression\")\n",
    "\n",
    "plt.axis('equal') #puts chart in 2d\n",
    "\n",
    "\n",
    "#b) Ethereum dataframe to compare original and predicted values\n",
    "combined_df_et = pred_compare_df(Ytest_et,pred_ethereum_lreg)\n",
    "print(\"\\nThis is a combined df of Ethereum:\\n\\n\", combined_df_et)\n",
    "\n",
    "#b-1) Pie chart \n",
    "plt.figure()\n",
    "combined_df_et[\"Mislead\"].value_counts().plot(kind=\"pie\", autopct='%1.1f%%', labels = [\"Correct\", \"Incorrect\"] )\n",
    "plt.title(\"Ethereum Prediction Outcome with Linear Regression\")\n",
    "\n",
    "plt.axis('equal') #puts chart in 2d\n",
    "\n",
    "\n",
    "#c) Litecoin dataframe to compare original and predicted values\n",
    "combined_df_lc = pred_compare_df(Ytest_lc,pred_litecoin_lreg)\n",
    "print(\"\\nThis is a combined df of Litecoin:\\n\\n\", combined_df_lc)\n",
    "\n",
    "#c-1) \n",
    "plt.figure()\n",
    "combined_df_lc[\"Mislead\"].value_counts().plot(kind=\"pie\", autopct='%1.1f%%', labels = [\"Correct\", \"Incorrect\"] )\n",
    "plt.title(\"Litecoin Prediction Outcome with Linear Regression\")\n",
    "\n",
    "plt.axis('equal') #puts chart in 2d\n",
    "\n",
    "#d) Zcash dataframe to compare original and predicted values\n",
    "combined_df_zc = pred_compare_df(Ytest_zc,pred_zcash_lreg)\n",
    "print(\"\\nThis is a combined df of Zcash:\\n\\n\", combined_df_zc)\n",
    "\n",
    "#d-1)\n",
    "plt.figure()\n",
    "combined_df_zc[\"Mislead\"].value_counts().plot(kind=\"pie\", autopct='%1.1f%%', labels = [\"Correct\", \"Incorrect\"] )\n",
    "plt.title(\"Zcash Prediction Outcome with Linear Regression\")\n",
    "\n",
    "plt.axis('equal') #puts chart in 2d\n",
    "\n",
    "##______________________________________________\n",
    "## Ridge Regression\n",
    "##parameter 'explode=(0,.1)' can be passed to df.plot.pie to seperate a pie sector\n",
    "\n",
    "#a) Bitcoin\n",
    "combined_df_bc_ridge = pred_compare_df(Ytest_bc,pred_bitcoin_ridge)\n",
    "print(\"\\nThis is a combined df of Bitcoin with Ridge Regression:\\n\\n\", combined_df_bc_ridge)\n",
    "\n",
    "#a-1) plotting number of times mislead \n",
    "plt.figure()\n",
    "combined_df_bc_ridge[\"Mislead\"].value_counts().plot(kind=\"pie\", autopct='%1.1f%%', labels = [\"Correct\", \"Incorrect\"])\n",
    "plt.title(\"Bitcoin Prediction Outcome with Ridge Regression\")\n",
    "plt.axis('equal') #puts chart in 2d\n",
    "\n",
    "#b) Ethereum\n",
    "combined_df_et_ridge = pred_compare_df(Ytest_et,pred_ethereum_ridge)\n",
    "print(\"\\nThis is a combined df of Ethereum with Ridge Regression:\\n\\n\", combined_df_et_ridge)\n",
    "\n",
    "#b-1) plotting number of times mislead \n",
    "plt.figure()\n",
    "combined_df_et_ridge[\"Mislead\"].value_counts().plot(kind=\"pie\", autopct='%1.1f%%', labels = [\"Correct\", \"Incorrect\"])\n",
    "plt.title(\"Ethereum Prediction Outcome with Ridge Regression\")\n",
    "plt.axis('equal') #puts chart in 2d\n",
    "\n",
    "#C) Litecoin\n",
    "combined_df_lc_ridge = pred_compare_df(Ytest_lc,pred_litecoin_ridge)\n",
    "print(\"\\nThis is a combined df of Litecoin with Ridge Regression:\\n\\n\", combined_df_lc_ridge)\n",
    "\n",
    "#C-1) plotting number of times mislead \n",
    "plt.figure()\n",
    "combined_df_lc_ridge[\"Mislead\"].value_counts().plot(kind=\"pie\", autopct='%1.1f%%', labels = [\"Correct\", \"Incorrect\"])\n",
    "plt.title(\"Litecoin Prediction Outcome with Ridge Regression\")\n",
    "plt.axis('equal') #puts chart in 2d\n",
    "\n",
    "#D) Zcash\n",
    "combined_df_zc_ridge = pred_compare_df(Ytest_zc,pred_zcash_ridge)\n",
    "print(\"\\nThis is a combined df of Zcash with Ridge Regression:\\n\\n\", combined_df_zc_ridge)\n",
    "\n",
    "#D-1) plotting number of times mislead \n",
    "plt.figure()\n",
    "combined_df_zc_ridge[\"Mislead\"].value_counts().plot(kind=\"pie\", autopct='%1.1f%%', labels = [\"Correct\", \"Incorrect\"])\n",
    "plt.title(\"Zcash Prediction Outcome with Ridge Regression\")\n",
    "plt.axis('equal') #puts chart in 2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating Function to Calculate Root Mean Squared Error (RMSE) for Each Model\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#18) Writing a function to calcuate the Root Mean Squared Error (RMSE)\n",
    "\n",
    "def rmse_df(df, crypto_name, model_type):\n",
    "    \n",
    "    #a) calculating MSE using sklearn\n",
    "    mse = mean_squared_error(df[\"Original_Value\"], df[\"Predicted_Value\"])\n",
    "\n",
    "    #b) taking square root to obtain RMSE\n",
    "    rmse = math.sqrt(mse)\n",
    "    \n",
    "    #c) rounding rmse to 2 decimals\n",
    "    rmse_round = round(rmse, 2)\n",
    "    \n",
    "    #d) generating print statement to return\n",
    "    p = \"The RMSE for {} using {} is: ${}.\\n\".format(crypto_name, model_type, rmse_round) \n",
    "\n",
    "    #e) returning print statement\n",
    "    return p, rmse_round"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calling Function to Calculate RMSE's\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The RMSE for Bitcoin using Linear Regression is: $121.22.\n",
      "\n",
      "The RMSE for Ethereum using Linear Regression is: $26.94.\n",
      "\n",
      "The RMSE for Litecoin using Linear Regression is: $2.97.\n",
      "\n",
      "The RMSE for Zcash using Linear Regression is: $19.09.\n",
      "\n",
      "The the sum of RMSE using Linear Regression is: 170.22 \n",
      "\n",
      "\n",
      "The RMSE for Bitcoin using Ridge Regression is: $120.29.\n",
      "\n",
      "The RMSE for Ethereum using Ridge Regression is: $19.84.\n",
      "\n",
      "The RMSE for Litecoin using Ridge Regression is: $2.07.\n",
      "\n",
      "The RMSE for Zcash using Ridge Regression is: $18.11.\n",
      "\n",
      "The the sum of RMSE using Ridge Regression is: 160.31\n"
     ]
    }
   ],
   "source": [
    "#19) Calling rmse_df to calculate root mean squared error\n",
    "    \n",
    "#a) Bitcoin RMSE\n",
    "rmse_bc = rmse_df(combined_df_bc, \"Bitcoin\", \"Linear Regression\")\n",
    "print(rmse_bc[0])\n",
    "\n",
    "#b) Ethereum\n",
    "rmse_et = rmse_df(combined_df_et, \"Ethereum\", \"Linear Regression\")\n",
    "print(rmse_et[0])\n",
    "\n",
    "#c) Litecoin\n",
    "rmse_lt = rmse_df(combined_df_lc, \"Litecoin\", \"Linear Regression\")\n",
    "print(rmse_lt[0])\n",
    "\n",
    "#d) Zcash\n",
    "rmse_zc = rmse_df(combined_df_zc, \"Zcash\", \"Linear Regression\")\n",
    "print(rmse_zc[0])\n",
    "\n",
    "#e) Summing RMSE's for comparison of optimal number features and model comparisons\n",
    "sum_rmse = rmse_bc[1] + rmse_et[1] + rmse_lt[1] + rmse_zc[1]\n",
    "print(\"The the sum of RMSE using Linear Regression is:\", sum_rmse,\"\\n\\n\")\n",
    "\n",
    "##_______________________________\n",
    "## Ridge Regression\n",
    "\n",
    "#a) Bitcoin RMSE\n",
    "rmse_bc_ridge = rmse_df(combined_df_bc_ridge, \"Bitcoin\", \"Ridge Regression\")\n",
    "print(rmse_bc_ridge[0])\n",
    "    \n",
    "#b) Ethereum\n",
    "rmse_et_ridge = rmse_df(combined_df_et_ridge, \"Ethereum\", \"Ridge Regression\")\n",
    "print(rmse_et_ridge[0])\n",
    "\n",
    "#c) Litecoin\n",
    "rmse_lt_ridge = rmse_df(combined_df_lc_ridge, \"Litecoin\", \"Ridge Regression\")\n",
    "print(rmse_lt_ridge[0])\n",
    "\n",
    "#d) Zcash\n",
    "rmse_zc_ridge = rmse_df(combined_df_zc_ridge, \"Zcash\", \"Ridge Regression\")\n",
    "print(rmse_zc_ridge[0])\n",
    "\n",
    "#e) Summing RMSE's for comparison of optimal number features and model comparisons\n",
    "sum_rmse_ridge = rmse_bc_ridge[1] + rmse_et_ridge[1] + rmse_lt_ridge[1] + rmse_zc_ridge[1]\n",
    "print(\"The the sum of RMSE using Ridge Regression is:\", sum_rmse_ridge)"
   ]
  }
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