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Univariate Linear Regression.ipynb
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{ | |
"nbformat": 4, | |
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"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
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"file_extension": ".py", | |
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"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.6.8" | |
}, | |
"colab": { | |
"name": "Univariate Linear Regression.ipynb", | |
"provenance": [], | |
"collapsed_sections": [], | |
"include_colab_link": true | |
} | |
}, | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "view-in-github", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"<a href=\"https://colab.research.google.com/gist/Sanket758/d122a83ce5b6be6825879c757b64737d/univariate-linear-regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "8kEPw4kM2caj", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"<h2 align=\"center\"> Univariate Linear Regression </h2>" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "FBIDo13l2cau", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"### Task 2: Load the Data and Libraries\n", | |
"---" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "D0RepdgM2caz", | |
"colab_type": "code", | |
"colab": {} | |
}, | |
"source": [ | |
"import matplotlib.pyplot as plt \n", | |
"plt.style.use('ggplot')\n", | |
"%matplotlib inline" | |
], | |
"execution_count": 0, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "R2KvfVUK2cbN", | |
"colab_type": "code", | |
"colab": {} | |
}, | |
"source": [ | |
"import numpy as np\n", | |
"import pandas as pd \n", | |
"import seaborn as sns \n", | |
"plt.rcParams['figure.figsize'] = (12, 8)" | |
], | |
"execution_count": 0, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "W0LYZO6p2cbl", | |
"colab_type": "code", | |
"colab": {} | |
}, | |
"source": [ | |
"data = pd.read_csv('bike_sharing_data.txt')" | |
], | |
"execution_count": 0, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "a43nYPlq2cb-", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 204 | |
}, | |
"outputId": "8b4f6d4c-991c-4bc4-8a59-dd157c8ad5ba" | |
}, | |
"source": [ | |
"data.head()" | |
], | |
"execution_count": 77, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/html": [ | |
"<div>\n", | |
"<style scoped>\n", | |
" .dataframe tbody tr th:only-of-type {\n", | |
" vertical-align: middle;\n", | |
" }\n", | |
"\n", | |
" .dataframe tbody tr th {\n", | |
" vertical-align: top;\n", | |
" }\n", | |
"\n", | |
" .dataframe thead th {\n", | |
" text-align: right;\n", | |
" }\n", | |
"</style>\n", | |
"<table border=\"1\" class=\"dataframe\">\n", | |
" <thead>\n", | |
" <tr style=\"text-align: right;\">\n", | |
" <th></th>\n", | |
" <th>Population</th>\n", | |
" <th>Profit</th>\n", | |
" </tr>\n", | |
" </thead>\n", | |
" <tbody>\n", | |
" <tr>\n", | |
" <th>0</th>\n", | |
" <td>6.1101</td>\n", | |
" <td>17.5920</td>\n", | |
" </tr>\n", | |
" <tr>\n", | |
" <th>1</th>\n", | |
" <td>5.5277</td>\n", | |
" <td>9.1302</td>\n", | |
" </tr>\n", | |
" <tr>\n", | |
" <th>2</th>\n", | |
" <td>8.5186</td>\n", | |
" <td>13.6620</td>\n", | |
" </tr>\n", | |
" <tr>\n", | |
" <th>3</th>\n", | |
" <td>7.0032</td>\n", | |
" <td>11.8540</td>\n", | |
" </tr>\n", | |
" <tr>\n", | |
" <th>4</th>\n", | |
" <td>5.8598</td>\n", | |
" <td>6.8233</td>\n", | |
" </tr>\n", | |
" </tbody>\n", | |
"</table>\n", | |
"</div>" | |
], | |
"text/plain": [ | |
" Population Profit\n", | |
"0 6.1101 17.5920\n", | |
"1 5.5277 9.1302\n", | |
"2 8.5186 13.6620\n", | |
"3 7.0032 11.8540\n", | |
"4 5.8598 6.8233" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 77 | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "YF5XcdAz2ccY", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"### Task 3: Visualize the Data\n", | |
"---" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "FXXiI_jT2cce", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 534 | |
}, | |
"outputId": "f304597a-cb81-48c2-d0a4-7a0eb78cd994" | |
}, | |
"source": [ | |
"ax = sns.scatterplot(x='Population', y='Profit', data=data)\n", | |
"ax.set_title('Population vs Profit')" | |
], | |
"execution_count": 78, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 1.0, 'Population vs Profit')" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 78 | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 864x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [], | |
"needs_background": "light" | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "35m7MoOR2cc7", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"### Task 4: Compute the Cost $J(\\theta)$\n", | |
"---" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "0njQULsq2cc_", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"The objective of linear regression is to minimize the cost function\n", | |
"\n", | |
"$$J(\\theta) = \\frac{1}{2m} \\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)} )^2$$\n", | |
"\n", | |
"where $h_{\\theta}(x)$ is the hypothesis and given by the linear model\n", | |
"\n", | |
"$$h_{\\theta}(x) = \\theta^Tx = \\theta_0 + \\theta_1x_1$$" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "7j86GmPK2cdC", | |
"colab_type": "code", | |
"colab": {} | |
}, | |
"source": [ | |
"def compute_cost(X,y, theta):\n", | |
" m = len(y)\n", | |
" y_hat = X.dot(theta)\n", | |
" error = (y_hat - y) ** 2\n", | |
" return (1 / (2*m)) * np.sum(error)" | |
], | |
"execution_count": 0, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "KgDmtqP42cdN", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 34 | |
}, | |
"outputId": "cdadc10e-718d-436d-d6c5-136c1cb330fa" | |
}, | |
"source": [ | |
"m = data.Profit.values.size\n", | |
"X = np.append(np.ones((m,1)), data.Population.values.reshape(m,1), axis=1)\n", | |
"y = data.Profit.values.reshape(m,1)\n", | |
"theta = np.zeros((2,1))\n", | |
"compute_cost(X,y, theta)" | |
], | |
"execution_count": 80, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"32.072733877455676" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 80 | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "1G9TFPoI2cdX", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"### Task 5: Gradient Descent\n", | |
"---" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "GfNfcbbr2cdb", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"Minimize the cost function $J(\\theta)$ by updating the below equation and repeat unitil convergence\n", | |
" \n", | |
"$\\theta_j := \\theta_j - \\alpha \\frac{1}{m} \\sum_{i=1}^m (h_{\\theta}(x^{(i)}) - y^{(i)})x_j^{(i)}$ (simultaneously update $\\theta_j$ for all $j$)." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "grkOq-wd2cdd", | |
"colab_type": "code", | |
"colab": {} | |
}, | |
"source": [ | |
"def gradient_descent(X,y, theta, alpha, n_iter):\n", | |
" m = len(y)\n", | |
" costs = []\n", | |
" for i in range(n_iter):\n", | |
" y_hat = X.dot(theta)\n", | |
" error = np.dot(X.T, (y_hat-y))\n", | |
" theta -= alpha * (1/m) * error\n", | |
" costs.append(compute_cost(X,y,theta))\n", | |
" return theta, costs" | |
], | |
"execution_count": 0, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "Me2fovhQ2cdr", | |
"colab_type": "code", | |
"colab": {} | |
}, | |
"source": [ | |
"theta, costs = gradient_descent(X,y, theta, alpha=0.01, n_iter=2000)" | |
], | |
"execution_count": 0, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "yHG70Jen2cd0", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 34 | |
}, | |
"outputId": "b4a4d1cc-81c7-4669-bb30-0dc7f2d6128b" | |
}, | |
"source": [ | |
"print('h(x)= {} + {}x1'.format(str(round(theta[0,0],2)),\n", | |
" str(round(theta[1,0],2))))" | |
], | |
"execution_count": 83, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"text": [ | |
"h(x)= -3.79 + 1.18x1\n" | |
], | |
"name": "stdout" | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "TDGbWpOL2cd6", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"### Task 6: Visualising the Cost Function $J(\\theta)$\n", | |
"---" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "2aA8rn2g2cd7", | |
"colab_type": "code", | |
"colab": {} | |
}, | |
"source": [ | |
"from mpl_toolkits.mplot3d import Axes3D" | |
], | |
"execution_count": 0, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "WAdO_Vj22ceC", | |
"colab_type": "code", | |
"colab": {} | |
}, | |
"source": [ | |
"theta_0 = np.linspace(-10,10,100)\n", | |
"theta_1 = np.linspace(-1,4,100)\n", | |
"\n", | |
"cost_values = np.zeros((len(theta_0), len(theta_1)))\n", | |
"\n", | |
"for i in range(len(theta_0)):\n", | |
" for j in range(len(theta_1)):\n", | |
" t = np.array(theta_0[i], theta_1[j])\n", | |
" cost_values[i,j] = compute_cost(X,y,t)" | |
], | |
"execution_count": 0, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "HZZ-8DeQ2ceI", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 466 | |
}, | |
"outputId": "37b4862a-1ea7-4e5b-fd4d-aada01311e7a" | |
}, | |
"source": [ | |
"fig = plt.figure(figsize=(15,8))\n", | |
"ax = fig.gca(projection='3d')\n", | |
"\n", | |
"surf = ax.plot_surface(theta_0, theta_1, cost_values, cmap='viridis')\n", | |
"fig.colorbar(surf, shrink=0.5, aspect=5)\n", | |
"\n", | |
"plt.xlabel('$\\Theta_0$')\n", | |
"plt.ylabel('$\\Theta_1$')\n", | |
"ax.set_zlabel('$J(\\Theta)$)')\n", | |
"ax.view_init(30,330)\n", | |
"plt.show()" | |
], | |
"execution_count": 88, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 1080x576 with 2 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [], | |
"needs_background": "light" | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "Wu_dhYG12ceP", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"### Task 7: Plotting the Convergence\n", | |
"---" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "mKrmGaHw2ceQ", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"Plot $J(\\theta)$ against the number of iterations of gradient descent:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "w-mNVyLo2ceS", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 534 | |
}, | |
"outputId": "54c430ac-ac13-4f2d-e482-bd194d66f9fe" | |
}, | |
"source": [ | |
"plt.plot(costs)\n", | |
"plt.xlabel('Number of iterations')\n", | |
"plt.ylabel('$J(\\Theta)$')\n", | |
"plt.title('Values of cost function over iterations of gradient descent')" | |
], | |
"execution_count": 89, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 1.0, 'Values of cost function over iterations of gradient descent')" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 89 | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 864x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [], | |
"needs_background": "light" | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "Nh4mS_QL2ceY", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"### Task 8: Training Data with Linear Regression Fit\n", | |
"---" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "UFolJlT12ceZ", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 51 | |
}, | |
"outputId": "a9da4b01-ffcd-42d1-e35f-c0e42a8ecc41" | |
}, | |
"source": [ | |
"theta" | |
], | |
"execution_count": 91, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"array([[-3.78806857],\n", | |
" [ 1.18221277]])" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 91 | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "j9x8SFSv2ceg", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 34 | |
}, | |
"outputId": "0fa4ec27-1c02-4e55-fdbb-2fd40a443600" | |
}, | |
"source": [ | |
"theta = np.squeeze(theta)\n", | |
"theta" | |
], | |
"execution_count": 93, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"array([-3.78806857, 1.18221277])" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 93 | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab_type": "code", | |
"outputId": "1d030989-41f2-407f-b9e5-9648178bc8fe", | |
"id": "j1rpBDfCEY2Y", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 622 | |
} | |
}, | |
"source": [ | |
"ax = sns.scatterplot(x='Population', y='Profit', data=data)\n", | |
"\n", | |
"x_value = [x for x in range(5,25)]\n", | |
"y_value = [(x * theta[1] + theta[0]) for x in x_value]\n", | |
"sns.lineplot(x_value, y_value, c='g')\n", | |
"plt.xlabel('Population')\n", | |
"plt.ylabel('Profit')\n", | |
"plt.title('Linear Regression')" | |
], | |
"execution_count": 95, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"text": [ | |
"/usr/local/lib/python3.6/dist-packages/seaborn/relational.py:823: MatplotlibDeprecationWarning: Saw kwargs ['c', 'color'] which are all aliases for 'color'. Kept value from 'color'. Passing multiple aliases for the same property will raise a TypeError in 3.3.\n", | |
" line, = ax.plot([], [], **kws)\n", | |
"/usr/local/lib/python3.6/dist-packages/seaborn/relational.py:834: MatplotlibDeprecationWarning: Saw kwargs ['c', 'color'] which are all aliases for 'color'. Kept value from 'color'. Passing multiple aliases for the same property will raise a TypeError in 3.3.\n", | |
" line, = ax.plot(x, y, **kws)\n" | |
], | |
"name": "stderr" | |
}, | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 1.0, 'Linear Regression')" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 95 | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 864x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [], | |
"needs_background": "light" | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "gaNA4pE42ceu", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"### Task 9: Inference using the optimized $\\theta$ values\n", | |
"---" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "KHiABSYn2cev", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"$h_\\theta(x) = \\theta^Tx$" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "N7ZLGkKg2cew", | |
"colab_type": "code", | |
"colab": {} | |
}, | |
"source": [ | |
"def predict(x, theta):\n", | |
" y_hat = np.dot(theta.T, x)\n", | |
" return y_hat" | |
], | |
"execution_count": 0, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "2DA_-9jM2ce2", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 34 | |
}, | |
"outputId": "bcac9a05-5b2c-478b-ace1-437c5573ca92" | |
}, | |
"source": [ | |
"y_pred_1 = predict(np.array([1,4]), theta) * 10000\n", | |
"print('For population of 40000 people, model predicts profit of $',str(round(y_pred_1))) " | |
], | |
"execution_count": 100, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"text": [ | |
"For population of 40000 people, model predicts profit of $ 9408.0\n" | |
], | |
"name": "stdout" | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "CgXNwuJ22ce8", | |
"colab_type": "code", | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 34 | |
}, | |
"outputId": "58b9da70-ce97-4a2d-cb62-e572d93f9c18" | |
}, | |
"source": [ | |
"y_pred_2 = predict(np.array([1,8.5]), theta) * 10000\n", | |
"print('For population of 85000 people, model predicts profit of $',str(round(y_pred_2))) " | |
], | |
"execution_count": 101, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"text": [ | |
"For population of 85000 people, model predicts profit of $ 62607.0\n" | |
], | |
"name": "stdout" | |
} | |
] | |
} | |
] | |
} |
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