{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "af3aad53-34f4-44ff-95aa-173ec916783b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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
\n", "

3 rows × 82 columns

\n", "
" ], "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": "5a57462e-a2d4-46c6-a624-0bcea044517b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SalePrice1st Flr SF2nd Flr SFTotal Bsmt SFGarage AreaWood Deck SFOpen Porch SFLot AreaYear BuiltYr Sold
0215000165601080.0528.0210623177019602010
11050008960882.0730.014001162219612010
2172000132901329.0312.0393361426719582010
\n", "
" ], "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": "dc99c17d-d999-4bbb-af21-5ac1f91ea888", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1.000e+00, 1.656e+03, 0.000e+00],\n", " [1.000e+00, 8.960e+02, 0.000e+00],\n", " [1.000e+00, 1.329e+03, 0.000e+00],\n", " ...,\n", " [1.000e+00, 9.700e+02, 0.000e+00],\n", " [1.000e+00, 1.389e+03, 0.000e+00],\n", " [1.000e+00, 9.960e+02, 1.004e+03]])" ] }, "execution_count": 3, "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" ] }, { "cell_type": "code", "execution_count": 4, "id": "e3e94320-676a-49aa-aaa1-c635fb82ef7e", "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": 7, "id": "9a3d9c66-62ba-45d9-b880-1cab30593a19", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE, Theta: 37417784909.067505 [1.07477231e-04 1.33284713e-01 4.37624711e-02]\n" ] }, { "data": { "text/plain": [ "array([[1.000e+00, 1.656e+03, 0.000e+00],\n", " [1.000e+00, 8.960e+02, 0.000e+00],\n", " [1.000e+00, 1.329e+03, 0.000e+00],\n", " ...,\n", " [1.000e+00, 9.700e+02, 0.000e+00],\n", " [1.000e+00, 1.389e+03, 0.000e+00],\n", " [1.000e+00, 9.960e+02, 1.004e+03]])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "learning_rate = 0.0000000001\n", "t = np.zeros(3).T\n", "for i in range(3):\n", " t = t + (2*learning_rate/n) * (X.T @ (y - X@t))\n", " loss = (1/n) * np.linalg.norm(y - X@t)**2\n", "\n", "MSE = (1/n) * np.linalg.norm(y - X@t)**2\n", "print('MSE, Theta:', MSE, t)\n", "\n", "X" ] }, { "cell_type": "code", "execution_count": 8, "id": "278ae7ed-ad33-4497-b7cb-e722260e5241", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE = 1705349005.3197255\n", "Theta = [179184.62687313 56135.61010536 39157.22624338]\n" ] } ], "source": [ "from sklearn.preprocessing import StandardScaler\n", "\n", "# Scale the features\n", "scaler = StandardScaler()\n", "X_scaled = scaler.fit_transform(X)\n", "X_scaled[:, 0] = np.ones(sales.shape[0])\n", "\n", "Z = np.matmul(X_scaled.T, X_scaled)\n", "t = np.linalg.inv(Z)@X_scaled.T@y\n", "MSE = (1/n) * np.linalg.norm(y - X_scaled@t)**2\n", "print('MSE = ', MSE)\n", "print('Theta = ', t)" ] }, { "cell_type": "code", "execution_count": 11, "id": "8626e088-be46-4f84-b869-0faade136a01", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMSE, Theta: 1705349005.3197255 [179184.62687313 56135.61010536 39157.22624338]\n" ] } ], "source": [ "learning_rate = 0.01\n", "t = np.zeros(3).T\n", "for i in range(2000):\n", " t = t + (2*learning_rate/n) * (X_scaled.T @ (y - X_scaled@t))\n", " #MSE = (1/n) * np.linalg.norm(y - X_scaled@t)**2\n", " #print('RMSE, Theta:', MSE, t)\n", "\n", "MSE = (1/n) * np.linalg.norm(y - X_scaled@t)**2\n", "print('RMSE, Theta:', MSE, t)" ] }, { "cell_type": "code", "execution_count": 17, "id": "a94812fa-0837-4cd1-a571-cdbfe8764724", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMSE, Theta: 1766798902.7592735 [174477.21671957 49694.33814832 37747.92307174]\n" ] } ], "source": [ "# This is stochastic gradient descent\n", "learning_rate = 0.01\n", "t = np.zeros(3)\n", "n = sales.shape[0]\n", "for i in range(1200):\n", " for j in range(n):\n", " t = t + (2*learning_rate) * (y[j] - X_scaled[j, :]@t) * X_scaled[j, :]\n", " \n", "MSE = (1/n) * np.linalg.norm(y - X_scaled@t)**2\n", "print('RMSE, Theta:', MSE, t)" ] }, { "cell_type": "code", "execution_count": 30, "id": "b3610460-6519-4075-bf65-0e325bc80f32", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMSE, Theta: 1705564912.1929908 [178949.12523594 55787.08837227 39290.02664459]\n" ] } ], "source": [ "# This is batch gradient descent\n", "learning_rate = 0.01\n", "t = np.zeros(3)\n", "n = sales.shape[0]\n", "m=100\n", "for i in range(100):\n", " for j in range(n//m):\n", " t = t + (2*learning_rate/m) * X_scaled[j*m:(j+1)*m, :].T @ (y[j*m:(j+1)*m] - X_scaled[j*m:(j+1)*m, :]@t)\n", " \n", "MSE = (1/n) * np.linalg.norm(y - X_scaled@t)**2\n", "print('RMSE, Theta:', MSE, t)" ] }, { "cell_type": "code", "execution_count": 21, "id": "9ac7b373-7e89-4d38-9b9f-3b84b77af34f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SalePrice1st Flr SF2nd Flr SFTotal Bsmt SFGarage AreaWood Deck SFOpen Porch SFLot AreaYear BuiltYr Sold
SalePrice1.0000000.6424660.3575220.6529790.6385940.3526990.3369090.2908230.5651650.025949
1st Flr SF0.6424661.000000-0.2305610.7650520.4645660.2476850.2208880.3038340.3163390.026647
2nd Flr SF0.357522-0.2305611.000000-0.1822130.1728520.0979260.2276840.0259480.079553-0.020525
Total Bsmt SF0.6529790.765052-0.1822131.0000000.4565920.2375350.2041100.2089330.4256170.047675
Garage Area0.6385940.4645660.1728520.4565921.0000000.2379450.2409430.1837170.4871350.029293
Wood Deck SF0.3526990.2476850.0979260.2375350.2379451.0000000.0552360.1278370.2549860.019196
Open Porch SF0.3369090.2208880.2276840.2041100.2409430.0552361.0000000.0951890.190891-0.031687
Lot Area0.2908230.3038340.0259480.2089330.1837170.1278370.0951891.0000000.083281-0.008188
Year Built0.5651650.3163390.0795530.4256170.4871350.2549860.1908910.0832811.0000000.046000
Yr Sold0.0259490.026647-0.0205250.0476750.0292930.019196-0.031687-0.0081880.0460001.000000
\n", "
" ], "text/plain": [ " SalePrice 1st Flr SF 2nd Flr SF Total Bsmt SF Garage Area \\\n", "SalePrice 1.000000 0.642466 0.357522 0.652979 0.638594 \n", "1st Flr SF 0.642466 1.000000 -0.230561 0.765052 0.464566 \n", "2nd Flr SF 0.357522 -0.230561 1.000000 -0.182213 0.172852 \n", "Total Bsmt SF 0.652979 0.765052 -0.182213 1.000000 0.456592 \n", "Garage Area 0.638594 0.464566 0.172852 0.456592 1.000000 \n", "Wood Deck SF 0.352699 0.247685 0.097926 0.237535 0.237945 \n", "Open Porch SF 0.336909 0.220888 0.227684 0.204110 0.240943 \n", "Lot Area 0.290823 0.303834 0.025948 0.208933 0.183717 \n", "Year Built 0.565165 0.316339 0.079553 0.425617 0.487135 \n", "Yr Sold 0.025949 0.026647 -0.020525 0.047675 0.029293 \n", "\n", " Wood Deck SF Open Porch SF Lot Area Year Built Yr Sold \n", "SalePrice 0.352699 0.336909 0.290823 0.565165 0.025949 \n", "1st Flr SF 0.247685 0.220888 0.303834 0.316339 0.026647 \n", "2nd Flr SF 0.097926 0.227684 0.025948 0.079553 -0.020525 \n", "Total Bsmt SF 0.237535 0.204110 0.208933 0.425617 0.047675 \n", "Garage Area 0.237945 0.240943 0.183717 0.487135 0.029293 \n", "Wood Deck SF 1.000000 0.055236 0.127837 0.254986 0.019196 \n", "Open Porch SF 0.055236 1.000000 0.095189 0.190891 -0.031687 \n", "Lot Area 0.127837 0.095189 1.000000 0.083281 -0.008188 \n", "Year Built 0.254986 0.190891 0.083281 1.000000 0.046000 \n", "Yr Sold 0.019196 -0.031687 -0.008188 0.046000 1.000000 " ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sales.corr()" ] }, { "cell_type": "code", "execution_count": 29, "id": "79f238b7-34e2-4fb1-888e-cdedc3aeeda8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "One feature: 0.41276288766116953\n", "Two features: 0.6827991925732996\n", "Three features: 0.7726766859516288\n", "Four features: 0.7880072396536026\n" ] } ], "source": [ "from sklearn.linear_model import LinearRegression\n", "\n", "model = LinearRegression()\n", "model.fit(sales[['1st Flr SF']], sales['SalePrice'])\n", "r_sq = model.score(sales[['1st Flr SF']], sales['SalePrice'])\n", "print('One feature:', r_sq)\n", "\n", "model = LinearRegression()\n", "model.fit(sales[['1st Flr SF', '2nd Flr SF']], sales['SalePrice'])\n", "r_sq = model.score(sales[['1st Flr SF', '2nd Flr SF']], sales['SalePrice'])\n", "print('Two features:', r_sq)\n", "\n", "model = LinearRegression()\n", "model.fit(sales[['1st Flr SF', '2nd Flr SF', 'Year Built']], sales['SalePrice'])\n", "r_sq = model.score(sales[['1st Flr SF', '2nd Flr SF', 'Year Built']], sales['SalePrice'])\n", "print('Three features:', r_sq)\n", "\n", "model = LinearRegression()\n", "model.fit(sales[['1st Flr SF', '2nd Flr SF', 'Year Built', 'Garage Area']], sales['SalePrice'])\n", "r_sq = model.score(sales[['1st Flr SF', '2nd Flr SF', 'Year Built', 'Garage Area']], sales['SalePrice'])\n", "print('Four features:', r_sq)" ] }, { "cell_type": "code", "execution_count": null, "id": "c833bbda-470e-43aa-9511-71c180ff5208", "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 }