{ "cells": [ { "cell_type": "markdown", "id": "15c4831f-b5a6-4465-83c4-584f3197cba3", "metadata": {}, "source": [ "## Multiple Linear Regression" ] }, { "cell_type": "code", "execution_count": 1, "id": "437a6b6d-10b2-4d53-845d-c135966b3ed1", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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OrderPIDMS SubClassMS ZoningLot FrontageLot AreaStreetAlleyLot ShapeLand Contour...Pool AreaPool QCFenceMisc FeatureMisc ValMo SoldYr SoldSale TypeSale ConditionSalePrice
0152630110020RL141.031770PaveNaNIR1Lvl...0NaNNaNNaN052010WDNormal215000
1252635004020RH80.011622PaveNaNRegLvl...0NaNMnPrvNaN062010WDNormal105000
2352635101020RL81.014267PaveNaNIR1Lvl...0NaNNaNGar21250062010WDNormal172000
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3 rows × 82 columns

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" ], "text/plain": [ " Order PID MS SubClass MS Zoning Lot Frontage Lot Area Street \\\n", "0 1 526301100 20 RL 141.0 31770 Pave \n", "1 2 526350040 20 RH 80.0 11622 Pave \n", "2 3 526351010 20 RL 81.0 14267 Pave \n", "\n", " Alley Lot Shape Land Contour ... Pool Area Pool QC Fence Misc Feature \\\n", "0 NaN IR1 Lvl ... 0 NaN NaN NaN \n", "1 NaN Reg Lvl ... 0 NaN MnPrv NaN \n", "2 NaN IR1 Lvl ... 0 NaN NaN Gar2 \n", "\n", " Misc Val Mo Sold Yr Sold Sale Type Sale Condition SalePrice \n", "0 0 5 2010 WD Normal 215000 \n", "1 0 6 2010 WD Normal 105000 \n", "2 12500 6 2010 WD Normal 172000 \n", "\n", "[3 rows x 82 columns]" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "from matplotlib.pyplot import subplots\n", "\n", "house = pd.read_csv('house.csv')\n", "house.head(3)" ] }, { "cell_type": "code", "execution_count": 2, "id": "a884a475-15de-4395-9cce-feb389e0f2cd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SalePrice1st Flr SF2nd Flr SFTotal Bsmt SFGarage AreaWood Deck SFOpen Porch SFLot AreaYear BuiltYr Sold
0215000165601080.0528.0210623177019602010
11050008960882.0730.014001162219612010
2172000132901329.0312.0393361426719582010
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" ], "text/plain": [ " SalePrice 1st Flr SF 2nd Flr SF Total Bsmt SF Garage Area \\\n", "0 215000 1656 0 1080.0 528.0 \n", "1 105000 896 0 882.0 730.0 \n", "2 172000 1329 0 1329.0 312.0 \n", "\n", " Wood Deck SF Open Porch SF Lot Area Year Built Yr Sold \n", "0 210 62 31770 1960 2010 \n", "1 140 0 11622 1961 2010 \n", "2 393 36 14267 1958 2010 " ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "house = house[house['Bldg Type'] == '1Fam']\n", "house = house[house['Sale Condition'] == 'Normal']\n", "sales = house[['SalePrice', '1st Flr SF', '2nd Flr SF', 'Total Bsmt SF', \n", " 'Garage Area', 'Wood Deck SF', 'Open Porch SF', 'Lot Area', \n", " 'Year Built', 'Yr Sold']]\n", "sales.head(3)" ] }, { "cell_type": "code", "execution_count": 3, "id": "c6586bfa-881f-4bb4-8830-a93e68f97122", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.6424662541030226)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sales['SalePrice'].corr(sales['1st Flr SF'])" ] }, { "cell_type": "code", "execution_count": 4, "id": "36bfa44d-8d4e-43b1-9ffb-ec913f27263e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.3575218942800825)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sales['SalePrice'].corr(sales['2nd Flr SF'])" ] }, { "cell_type": "code", "execution_count": 5, "id": "8899c0f5-8735-4baa-83f8-b3109d4165bf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.7821920556134877)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sales['SalePrice'].corr((sales['2nd Flr SF'] + sales['1st Flr SF']))" ] }, { "cell_type": "code", "execution_count": 7, "id": "1ed4e83d-4004-4956-8329-8526784311da", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2002, 3)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = sales.shape[0] # Number of observations\n", "X = np.ones((n, 1))\n", "X = np.insert(X, 1, sales['1st Flr SF'], axis=1)\n", "X = np.insert(X, 2, sales['2nd Flr SF'], axis=1)\n", "y = sales['SalePrice'].reset_index(drop=True)\n", "X.shape" ] }, { "cell_type": "code", "execution_count": 9, "id": "5991a480-6e65-46cf-9419-e3797ceeb473", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE = 1705349005.3197255\n", "Theta = [-29985.3612312 155.19406373 91.35680257]\n" ] } ], "source": [ "Z = np.matmul(X.T, X)\n", "t = np.linalg.inv(Z)@X.T@y\n", "MSE = (1/n) * np.linalg.norm(y - X@t)**2\n", "print('MSE = ', MSE)\n", "print('Theta = ', t)" ] }, { "cell_type": "code", "execution_count": 17, "id": "b63dcceb-40f5-469a-b136-1e8089d818ab", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE, Theta: 37483374720.76574 [0. 0. 0.]\n", "MSE, Theta: 35329134615.48689 [3.58369254e-03 4.44420993e+00 1.45915604e+00]\n", "MSE, Theta: 33305851706.1281 [7.05555785e-03 8.74978866e+00 2.87760804e+00]\n", "MSE, Theta: 31405556990.79167 [1.04190511e-02 1.29210261e+01 4.25659660e+00]\n", "MSE, Theta: 29620766460.99461 [1.36775206e-02 1.69620795e+01 5.59732406e+00]\n", "MSE, Theta: 27944451584.46335 [1.68342113e-02 2.08769776e+01 6.90095566e+00]\n", "MSE, Theta: 26370011584.380478 [1.98922677e-02 2.46696247e+01 8.16862069e+00]\n", "MSE, Theta: 24891247405.749187 [2.28547373e-02 2.83438043e+01 9.40141360e+00]\n", "MSE, Theta: 23502337266.195404 [2.57245732e-02 3.19031829e+01 1.06003951e+01]\n", "MSE, Theta: 22197813694.776936 [2.85046374e-02 3.53513139e+01 1.17665931e+01]\n", "MSE, Theta: 20972541968.237617 [3.11977034e-02 3.86916405e+01 1.29010040e+01]\n", "MSE, Theta: 19821699859.656364 [3.38064589e-02 4.19274997e+01 1.40045933e+01]\n", "MSE, Theta: 19821699859.656364 [3.38064589e-02 4.19274997e+01 1.40045933e+01]\n" ] } ], "source": [ "#Using Gradient Descent\n", "learning_rate = 0.00000001\n", "t = np.zeros(3).T\n", "MSE = (1/n) * np.linalg.norm(y - X@t)**2\n", "print('MSE, Theta:', MSE, t)\n", "for i in range(11):\n", " t = t + (2*learning_rate/n) * (X.T @ (y - X@t))\n", " MSE = (1/n) * np.linalg.norm(y - X@t)**2\n", " print('MSE, Theta:', MSE, t)\n", "\n", "MSE = (1/n) * np.linalg.norm(y - X@t)**2\n", "print('MSE, Theta:', MSE, t)" ] }, { "cell_type": "code", "execution_count": null, "id": "3c521454-43b7-427b-bee5-6e61879f313c", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 5 }