SLR

SLRProject.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "% matplotlib inline\n",
    "\n",
    "# The above command sets the backend of matplotlib to the 'inline' backend. \n",
    "# It means the output of plotting commands is displayed inline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import necessary libraries\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the data\n",
    "\n",
    "url = \"C:/project_datasets/SALES.txt\"\n",
    "df = pd.read_csv(url, sep='\\t', header=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(36, 2)\n"
     ]
    }
   ],
   "source": [
    "# Exploratory data analysis\n",
    "\n",
    "# View the dimensions of df\n",
    "\n",
    "print(df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      0     1\n",
      "0  12.0  15.0\n",
      "1  20.5  16.0\n",
      "2  21.0  18.0\n",
      "3  15.5  27.0\n",
      "4  15.3  21.0\n"
     ]
    }
   ],
   "source": [
    "# View the top 5 rows of df\n",
    "\n",
    "print(df.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rename columns of df dataframe\n",
    "\n",
    "df.columns = ['Sales', 'Advertising']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Sales  Advertising\n",
      "0   12.0         15.0\n",
      "1   20.5         16.0\n",
      "2   21.0         18.0\n",
      "3   15.5         27.0\n",
      "4   15.3         21.0\n"
     ]
    }
   ],
   "source": [
    "# View the top 5 rows of df with column names renamed\n",
    "\n",
    "print(df.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 36 entries, 0 to 35\n",
      "Data columns (total 2 columns):\n",
      "Sales          36 non-null float64\n",
      "Advertising    36 non-null float64\n",
      "dtypes: float64(2)\n",
      "memory usage: 656.0 bytes\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "# View dataframe summary\n",
    "\n",
    "print(df.info())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Sales  Advertising\n",
      "count  36.000000    36.000000\n",
      "mean   24.255556    28.527778\n",
      "std     6.185118    18.777625\n",
      "min    12.000000     1.000000\n",
      "25%    20.300000    15.750000\n",
      "50%    24.250000    23.000000\n",
      "75%    28.600000    41.000000\n",
      "max    36.500000    65.000000\n"
     ]
    }
   ],
   "source": [
    "# View descriptive statistics\n",
    "\n",
    "print(df.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Declare feature variable and target array\n",
    "\n",
    "X = df['Sales'].values\n",
    "y = df['Advertising'].values\n",
    "\n",
    "# Sales and Advertising data values are given by X and y respectively.\n",
    "\n",
    "# Values attribute of pandas dataframe returns the numpy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(36,)\n",
      "(36,)\n"
     ]
    }
   ],
   "source": [
    "# Print the dimensions of X and y\n",
    "\n",
    "print(X.shape)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reshape X and y\n",
    "\n",
    "X = X.reshape(-1,1)\n",
    "y = y.reshape(-1,1)\n",
    "\n",
    "# Since we are working with only one feature variable, so we need to do reshaping using NumPy's reshape() method. \n",
    "# It specifies first dimension to be -1, which means \"unspecified\". \n",
    "# Its value is inferred from the length of the array and the remaining dimensions. \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(36, 1)\n",
      "(36, 1)\n"
     ]
    }
   ],
   "source": [
    "# Print the dimensions of X and y after reshaping\n",
    "\n",
    "print(X.shape)\n",
    "print(y.shape)\n",
    "\n",
    "# We can see the difference in dimensions of X and y before and after reshaping.\n",
    "# It is essential in this case because getting the feature and target variable arrays into the right format for scikit-learn \n",
    "# is an important precursor to model building."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizing the relationship between X and y by scatterplot\n",
    "\n",
    "# Plot scatter plot between X and y\n",
    "\n",
    "plt.scatter(X, y, color = 'blue', label='Scatter Plot')\n",
    "plt.title('Relationship between Sales and Advertising')\n",
    "plt.xlabel('Sales')\n",
    "plt.ylabel('Advertising')\n",
    "plt.legend(loc=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split X and y into training and test data sets\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train,X_test,y_train,y_test = train_test_split(X, y, test_size=0.33, random_state=42)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(24, 1)\n",
      "(24, 1)\n",
      "(12, 1)\n",
      "(12, 1)\n"
     ]
    }
   ],
   "source": [
    "# Print the dimensions of X_train,X_test,y_train,y_test\n",
    "\n",
    "print(X_train.shape)\n",
    "print(y_train.shape)\n",
    "print(X_test.shape)\n",
    "print(y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fit the linear model\n",
    "\n",
    "# Instantiate the linear regression object lm\n",
    "from sklearn.linear_model import LinearRegression\n",
    "lm = LinearRegression()\n",
    "\n",
    "\n",
    "# Train the model using training data sets\n",
    "lm.fit(X_train,y_train)\n",
    "\n",
    "\n",
    "# Predict on the test data\n",
    "y_pred=lm.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE value: 11.2273\n"
     ]
    }
   ],
   "source": [
    "# Calculate and print Root Mean Square Error(RMSE)\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "mse = mean_squared_error(y_test, y_pred)\n",
    "rmse = np.sqrt(mse)\n",
    "print(\"RMSE value: {:.4f}\".format(rmse))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 Score value: 0.5789\n"
     ]
    }
   ],
   "source": [
    "# Calculate and print r2_score\n",
    "\n",
    "from sklearn.metrics import r2_score\n",
    "print (\"R2 Score value: {:.4f}\".format(r2_score(y_test, y_pred)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated model slope, a: [[1.60509347]]\n",
      "Estimated model intercept, b: (array([-11.16003616]),)\n"
     ]
    }
   ],
   "source": [
    "# Compute model slope and intercept\n",
    "\n",
    "a = lm.coef_\n",
    "b = lm.intercept_,\n",
    "print(\"Estimated model slope, a:\" , a)\n",
    "print(\"Estimated model intercept, b:\" , b) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# So, our fitted regression line is \n",
    "\n",
    "# y = 1.60509347 * x - 11.16003616 \n",
    "\n",
    "# That is our linear model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.10108551],\n",
       "       [21.74438002],\n",
       "       [22.54692675],\n",
       "       [13.71891266],\n",
       "       [13.39789396]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predicting Advertising values\n",
    "\n",
    "lm.predict(X)[0:5]\n",
    "\n",
    "# Predicting Advertising values on first five Sales values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[27.36220717]]\n"
     ]
    }
   ],
   "source": [
    "# To make an individual prediction using the linear regression model.\n",
    "\n",
    "print(str(lm.predict(24)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the Regression Line\n",
    "\n",
    "\n",
    "plt.scatter(X, y, color = 'blue', label='Scatter Plot')\n",
    "plt.plot(X_test, y_pred, color = 'black', linewidth=3, label = 'Regression Line')\n",
    "plt.title('Relationship between Sales and Advertising')\n",
    "plt.xlabel('Sales')\n",
    "plt.ylabel('Advertising')\n",
    "plt.legend(loc=4)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting residual errors\n",
    "\n",
    "plt.scatter(lm.predict(X_train), lm.predict(X_train) - y_train, color = 'red', label = 'Train data')\n",
    "plt.scatter(lm.predict(X_test), lm.predict(X_test) - y_test, color = 'blue', label = 'Test data')\n",
    "plt.hlines(xmin = 0, xmax = 50, y = 0, linewidth = 3)\n",
    "plt.title('Residual errors')\n",
    "plt.legend(loc = 4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set score: 0.2861\n",
      "Test set score: 0.5789\n"
     ]
    }
   ],
   "source": [
    "# Checking for Overfitting or Underfitting the data\n",
    "\n",
    "print(\"Training set score: {:.4f}\".format(lm.score(X_train,y_train)))\n",
    "\n",
    "print(\"Test set score: {:.4f}\".format(lm.score(X_test,y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['lm_regressor.pkl']"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Save model for future use\n",
    "\n",
    "from sklearn.externals import joblib\n",
    "joblib.dump(lm, 'lm_regressor.pkl')\n",
    "\n",
    "# To load the model\n",
    "\n",
    "# lm2=joblib.load('lm_regressor.pkl')"
   ]
  }
 ],
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