| # Install on Terminal of MacOS # 1. pandas #pip3 install -U pandas # 2. matplotlib #pip3 install -U matplotlib # 3. scikit-learn (sklearn) #pip3 install -U scikit-learn # 4. statsmodels #pip3 install -U statsmodels # 5. NumPy #pip3 install -U numpy |
1_MacOS_Terminal.txt
| ########## Run Terminal on MacOS and execute ### TO UPDATE cd "YOUR_WORKING_DIRECTORY" #Raw Data X vs Raw Data Y #python3 mlrrwstnmslr.py df.csv Y RM r #Standardized Data X vs Raw Data Y python3 mlrrwstnmslr.py df.csv Y RM s #Normalized Data X vs Raw Data Y #python3 mlrrwstnmslr.py df.csv Y RM n |
Input Data files
df.csv
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491,0.10574,0.0,27.74,0.0,0.609,5.983,98.8,1.8681,4.0,711.0,20.1,390.11,18.07,13.6 492,0.11132,0.0,27.74,0.0,0.609,5.983,83.5,2.1099,4.0,711.0,20.1,396.9,13.35,20.1 493,0.17331,0.0,9.69,0.0,0.585,5.707,54.0,2.3817,6.0,391.0,19.2,396.9,12.01,21.8 494,0.27957,0.0,9.69,0.0,0.585,5.926,42.6,2.3817,6.0,391.0,19.2,396.9,13.59,24.5 495,0.17899,0.0,9.69,0.0,0.585,5.67,28.8,2.7986,6.0,391.0,19.2,393.29,17.6,23.1 496,0.2896,0.0,9.69,0.0,0.585,5.39,72.9,2.7986,6.0,391.0,19.2,396.9,21.14,19.7 497,0.26838,0.0,9.69,0.0,0.585,5.794,70.6,2.8927,6.0,391.0,19.2,396.9,14.1,18.3 498,0.23912,0.0,9.69,0.0,0.585,6.019,65.3,2.4091,6.0,391.0,19.2,396.9,12.92,21.2 499,0.17783,0.0,9.69,0.0,0.585,5.569,73.5,2.3999,6.0,391.0,19.2,395.77,15.1,17.5 500,0.22438,0.0,9.69,0.0,0.585,6.027,79.7,2.4982,6.0,391.0,19.2,396.9,14.33,16.8 501,0.06263,0.0,11.93,0.0,0.573,6.593,69.1,2.4786,1.0,273.0,21.0,391.99,9.67,22.4 502,0.04527,0.0,11.93,0.0,0.573,6.12,76.7,2.2875,1.0,273.0,21.0,396.9,9.08,20.6 503,0.06076,0.0,11.93,0.0,0.573,6.976,91.0,2.1675,1.0,273.0,21.0,396.9,5.64,23.9 504,0.10959,0.0,11.93,0.0,0.573,6.794,89.3,2.3889,1.0,273.0,21.0,393.45,6.48,22.0 505,0.04741,0.0,11.93,0.0,0.573,6.03,80.8,2.505,1.0,273.0,21.0,396.9,7.88,11.9 |
Python files
mlrrwstnmslr.py
| ############### Multiple Linear Regression of Raw Data, Standardized Data, and Normalized Data (plus Single Linear Regression) ############### ########## Run this script on Terminal of MacOS as follows: # #python3 mlrrwstnm.py (csv data file) (dependent variable Y) (specified single independent variable x) (x conversion) # #For instance, #python3 mlrrwstnm.py df.csv Y RM s ########## import import sys import pandas as pd import numpy as np import matplotlib.pyplot as plt from sklearn import datasets from sklearn import linear_model from sklearn.preprocessing import StandardScaler from sklearn.preprocessing import MinMaxScaler import statsmodels.api as sm ########## arguments dfname = str(sys.argv[1]) # e.g., df.csv yname = str(sys.argv[2]) # e.g., Y (dependent vairible) xname = str(sys.argv[3]) # e.g., RM (one of multiple indepdent variables to show) xconv = str(sys.argv[4]) # e.g., r (raw X data), s (standardized X data), or n (normalized X data) ########### load csv dataset ##dt = datasets.load_boston() ## ## Boston house price dataset dict-keys ## ##print(type(dt)) ##<class 'sklearn.utils.Bunch'> ## ##print(dt.keys()) ##dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename']) ## ##print(pd.DataFrame(dt.data, columns=boston.feature_names)) ''' CRIM ZN INDUS CHAS NOX ... RAD TAX PTRATIO B LSTAT 0 0.00632 18.0 2.31 0.0 0.538 ... 1.0 296.0 15.3 396.90 4.98 1 0.02731 0.0 7.07 0.0 0.469 ... 2.0 242.0 17.8 396.90 9.14 2 0.02729 0.0 7.07 0.0 0.469 ... 2.0 242.0 17.8 392.83 4.03 3 0.03237 0.0 2.18 0.0 0.458 ... 3.0 222.0 18.7 394.63 2.94 4 0.06905 0.0 2.18 0.0 0.458 ... 3.0 222.0 18.7 396.90 5.33 .. ... ... ... ... ... ... ... ... ... ... ... 501 0.06263 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 391.99 9.67 502 0.04527 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 396.90 9.08 503 0.06076 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 396.90 5.64 504 0.10959 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 393.45 6.48 505 0.04741 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 396.90 7.88 [506 rows x 13 columns] ''' ## ''' CRIM crime rate ZN density of residential area INDUS rate of industrial area (non-retail) CHAS Charles River (1: around the river, 0: others) NOX NOx concentration RM average number of rooms par house AGE rate of houses built before 1940 DIS weighted distance from five employers in Boston RAD accessibility to major roads TAX income tax (rates) par $10,000 PTRATIO number of students par teacher B rate of African Americans 1000(Bk – 0.63)^2 LSTAT rate of low income earners ''' ## ##df = pd.DataFrame(dt.data, columns=dt.feature_names) #data: independent variables ##df['Y'] = dt.target # Y: target/dependent variable is added ###df.to_csv('df.csv', header=True, index=True) df = pd.read_csv(dfname, index_col=0) # #print(df) #[506 rows x 14 columns] # #print(df.columns) ''' Index(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'Y'], dtype='object') ''' ########### set Y (dependent variable) Y = df.eval(yname) # #print(Y) ''' 0 24.0 1 21.6 2 34.7 3 33.4 4 36.2 ... 501 22.4 502 20.6 503 23.9 504 22.0 505 11.9 Name: Y, Length: 506, dtype: float64 ''' ########### set X (independent variables) if xconv == 'r': #r: raw X data print('r: raw X data') # ##### Raw data X # #print("########## Raw Data X ##########") X = df.drop(yname, axis=1) Xconv = X # no conversion, but to have the same variable, call X as Xconv # #print(Xconv.columns) ''' Index(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='object') ''' # #print(Xconv.describe()) ''' CRIM ZN INDUS CHAS ... TAX PTRATIO B LSTAT count 506.000000 506.000000 506.000000 506.000000 ... 506.000000 506.000000 506.000000 506.000000 mean 3.613524 11.363636 11.136779 0.069170 ... 408.237154 18.455534 356.674032 12.653063 std 8.601545 23.322453 6.860353 0.253994 ... 168.537116 2.164946 91.294864 7.141062 min 0.006320 0.000000 0.460000 0.000000 ... 187.000000 12.600000 0.320000 1.730000 25% 0.082045 0.000000 5.190000 0.000000 ... 279.000000 17.400000 375.377500 6.950000 50% 0.256510 0.000000 9.690000 0.000000 ... 330.000000 19.050000 391.440000 11.360000 75% 3.677082 12.500000 18.100000 0.000000 ... 666.000000 20.200000 396.225000 16.955000 max 88.976200 100.000000 27.740000 1.000000 ... 711.000000 22.000000 396.900000 37.970000 [8 rows x 13 columns] ''' elif xconv == 's': X = df.drop(yname, axis=1) # #s: standardized X data print('s: standardized X data') # # Standardized data X (average == 0, standard deviation == 1 for all x) # scaler = StandardScaler() scaler.fit(X) # #print("########## Standardized Data X ##########") #print("scaler.fit(X) ->" + str(scaler.fit(X))) #print("scaler.mean_ ->" + str(scaler.mean_)) #print("scaler.transform ->" + str(scaler.transform(X))) # Xconv = scaler.transform(X) Xconv = pd.DataFrame(Xconv) #Xconv.columns = boston.feature_names Xconv.columns = X.columns # #print(Xconv.describe()) elif xconv == 'n': X = df.drop(yname, axis=1) # #n: normalized X data print('n: normalized X data') # # Normalized data X (all x are normalized to take values from 0 to 1) mscaler = MinMaxScaler() mscaler.fit(X) # #print("########## Normalized Data X ##########") #print("mscaler.fit(X) ->" + str(mscaler.fit(X))) #print("mscaler.data_max_ ->" + str(mscaler.data_max_)) #print("mscaler.data_range_ ->" + str(mscaler.data_range_)) #print("mscaler.transform ->" + str(mscaler.transform(X))) # Xconv = mscaler.transform(X) Xconv = pd.DataFrame(Xconv) #Xconv.columns = boston.feature_names Xconv.columns = X.columns # #print(Xconv.describe()) ''' CRIM ZN INDUS CHAS ... TAX PTRATIO B LSTAT count 506.000000 506.000000 506.000000 506.000000 ... 506.000000 506.000000 506.000000 506.000000 mean 0.040544 0.113636 0.391378 0.069170 ... 0.422208 0.622929 0.898568 0.301409 std 0.096679 0.233225 0.251479 0.253994 ... 0.321636 0.230313 0.230205 0.197049 min 0.000000 0.000000 0.000000 0.000000 ... 0.000000 0.000000 0.000000 0.000000 25% 0.000851 0.000000 0.173387 0.000000 ... 0.175573 0.510638 0.945730 0.144040 50% 0.002812 0.000000 0.338343 0.000000 ... 0.272901 0.686170 0.986232 0.265728 75% 0.041258 0.125000 0.646628 0.000000 ... 0.914122 0.808511 0.998298 0.420116 max 1.000000 1.000000 1.000000 1.000000 ... 1.000000 1.000000 1.000000 1.000000 [8 rows x 13 columns] ''' else: print('Speficy X data conversion: r (raw X data), s (standardized X data), or n (normalized X data)') sys.exit(1) #error status = 1 ########## Multiple Linear Regression clf = linear_model.LinearRegression(fit_intercept=True, normalize=False, copy_X=True, n_jobs=1) clf.fit(Xconv, Y) #SGDRegressor #clf_SGD = linear_model.SGDRegressor(max_iter=500) #clf_SGD.fit(Xconv, Y) # # smX = sm.add_constant(Xconv) estX = sm.OLS(Y, smX) estXfit = estX.fit() # #print(estXfit.summary()) #print(type(estXfit.summary())) #<class 'statsmodels.iolib.summary.Summary'> with open('estXfit.summary.txt', 'w') as f: print(estXfit.summary(), file=f) Yprednp = clf.predict(Xconv) # predicted Y by using all Xs #print(type(Yprednp)) #<class 'numpy.ndarray'> Ypred = pd.DataFrame(Yprednp) Ypred = Ypred.rename(columns={0: 'Ypred'}) #print(type(Ypred)) #<class 'pandas.core.frame.DataFrame'> ########## print out #print(pd.DataFrame({"Name":Xconv.columns, # "Coefficients":clf.coef_}).sort_values(by='Coefficients') ) # sorting by coefficients #print('intercept = ' + str(clf.intercept_)) # intercept #print('R^2 = ' + str(clf.score(Xconv,Y))) # R^2 with open('clifCoefficients.txt', 'w') as f: print(pd.DataFrame({"Name":Xconv.columns, "Coefficients":clf.coef_}).sort_values(by='Coefficients') , file=f) with open('clifIntercept.txt', 'w') as f: print(str(clf.intercept_), file=f) with open('clifR2.txt', 'w') as f: print(str(clf.score(Xconv,Y)), file=f) ########## plot plt.figure(1) plt.title('Multiple Linear Regression') plt.xlabel(xname, fontsize=14) plt.ylabel(yname, fontsize=14) if xconv == 'r': plt.scatter(Xconv[xname], Y, c='blue', label='Y & Raw Data X') elif xconv == 's': plt.scatter(Xconv[xname], Y, c='blue', label='Y & Standardized Data X') elif xconv == 'n': plt.scatter(Xconv[xname], Y, c='blue', label='Y & Normalized Data X') else: #This section is not executed since exit is done in the previous section. print('Speficy X data conversion: r (raw X data), s (standardized X data), or n (normalized X data)') sys.exit(1) #error status = 1 #plt.scatter(Xconv.eval(xname), clf.predict(Xconv), c='red', label='Multiple Regression Analysis') plt.scatter(Xconv[xname], Ypred, c='red', label='Ypred(Predicted Y) & X') plt.xlim(min(Xconv[xname]), max(Xconv[xname])) plt.ylim( min(min(Y), min(Ypred['Ypred'])), max(max(Y), max(Ypred['Ypred'])) ) plt.legend(loc='lower right', fontsize=12) # #print(max(Y)) #print(max(Ypred['Ypred'])) # plt.text(min(Xconv[xname]), max(max(Y), max(Ypred['Ypred']))*0.90, 'R^2 = ' + str(round(clf.score(Xconv,Y), 4)), fontsize=10) plt.savefig("Figure_Multiple_Linear_Regression_" + xconv + ".png") plt.show() ########## output data files #print(X) # #print(type(X)) #<class 'pandas.core.frame.DataFrame'> #print(Xconv) # #print(type(Xconv)) #<class 'pandas.core.frame.DataFrame'> #print(Y) #print(type(Y)) #<class 'pandas.core.series.Series'> X_Y = pd.concat([X, Y], axis=1) Xconv_Y = pd.concat([Xconv, Y], axis=1) Xconv_Y_Ypred = pd.concat([Xconv_Y, Ypred], axis=1) X_Y.to_csv('X_Y.csv', header=True, index=True) Xconv_Y.to_csv('Xconv_Y.csv', header=True, index=True) Xconv_Y_Ypred.to_csv('Xconv_Y_Ypred.csv', header=True, index=True) ########## Single Linear Regeression by using xname: data generation dfcoef = pd.DataFrame({"Name":Xconv.columns, "Coefficients":clf.coef_}).sort_values(by='Coefficients') # #print(dfcoef) ''' Name Coefficients 12 LSTAT -3.743627 7 DIS -3.104044 9 TAX -2.076782 10 PTRATIO -2.060607 4 NOX -2.056718 0 CRIM -0.928146 6 AGE 0.019466 2 INDUS 0.140900 3 CHAS 0.681740 11 B 0.849268 1 ZN 1.081569 8 RAD 2.662218 5 RM 2.674230 ''' # #print(dfcoef[dfcoef.Name == xname]['Coefficients']) # Name Coefficients #5 RM 2.67423 # #print(dfcoef[dfcoef.Name == xname]['Coefficients']) #5 2.67423 #Name: Coefficients, dtype: float64 # #print(type(dfcoef[dfcoef.Name == xname]['Coefficients'])) #<class 'pandas.core.series.Series'> # #print(float(dfcoef[dfcoef.Name == xname]['Coefficients'])) #2.6742301652393117 # #print('intercept = ' + str(clf.intercept_)) #intercept = 22.532806324110673 # #print('R^2 = ' + str(clf.score(Xconv,Y))) #R^2 = 0.7406426641094094 #print(Xconv_Y_Ypred[xname]) ''' 0 0.413672 1 0.194274 2 1.282714 3 1.016303 4 1.228577 ... 501 0.439316 502 -0.234548 503 0.984960 504 0.725672 505 -0.362767 ''' YpredSingle = clf.intercept_ + float(dfcoef[dfcoef.Name == xname]['Coefficients']) * Xconv_Y_Ypred[xname] #print(YpredSingle) #print(type(YpredSingle)) #<class 'pandas.core.series.Series'> # # YpredSingle = pd.DataFrame(YpredSingle) #print(type(YpredSingle)) #<class 'pandas.core.frame.DataFrame'> # #print(YpredSingle.columns) #Index(['RM'], dtype='object') # #YpredSingle = YpredSingle.rename(columns={xname: 'YpredSingle_' + str(xname)}) YpredSingle = YpredSingle.rename(columns={xname: 'YpredSingle'}) #print(YpredSingle.columns) #Index(['YpredSingle'], dtype='object') Xconv_Y_Ypred_YpredSingle = pd.concat([Xconv_Y_Ypred, YpredSingle], axis=1) Xconv_Y_Ypred_YpredSingle.to_csv('Xconv_Y_Ypred_YpredSingle.csv', header=True, index=True) ########## Single Linear Regeression by using xname: plot plt.figure(2) plt.title('Single Linear Regression') plt.xlabel(xname, fontsize=14) plt.ylabel(yname, fontsize=14) if xconv == 'r': plt.scatter(Xconv[xname], Y, c='blue', label='Y & Raw Data X') elif xconv == 's': plt.scatter(Xconv[xname], Y, c='blue', label='Y & Standardized Data X') elif xconv == 'n': plt.scatter(Xconv[xname], Y, c='blue', label='Y & Normalized Data X') else: #This section is not executed since exit is done in the previous section. print('Speficy X data conversion: r (raw X data), s (standardized X data), or n (normalized X data)') sys.exit(1) #error status = 1 #plt.scatter(Xconv.eval(xname), clf.predict(Xconv), c='red', label='Multiple Regression Analysis') plt.scatter(Xconv_Y_Ypred_YpredSingle.eval(xname), Xconv_Y_Ypred_YpredSingle.YpredSingle, c='red', label='YpredSingle (Predicted Y) & X') plt.xlim(min(Xconv_Y_Ypred_YpredSingle.eval(xname)), max(Xconv_Y_Ypred_YpredSingle.eval(xname))) plt.ylim( min(min(Y), min(Ypred['Ypred']), min(YpredSingle['YpredSingle'])), max(max(Y), max(Ypred['Ypred']), max(YpredSingle['YpredSingle'])) ) plt.legend(loc='lower right', fontsize=12) # #print(max(Y)) #print(max(Ypred['Ypred'])) # #plt.text(min(Xconv[xname]), max(max(Y), max(Ypred['Ypred'])), 'R^2 = ' + str(round(clf.score(Xconv,Y), 4)), fontsize=10) plt.savefig("Figure_Single_Linear_Regression_" + xconv + ".png") plt.show() |
Output Files
| OLS Regression Results ============================================================================== Dep. Variable: Y R-squared: 0.741 Model: OLS Adj. R-squared: 0.734 Method: Least Squares F-statistic: 108.1 Date: Sun, 07 Jun 2020 Prob (F-statistic): 6.72e-135 Time: 07:56:06 Log-Likelihood: -1498.8 No. Observations: 506 AIC: 3026. Df Residuals: 492 BIC: 3085. Df Model: 13 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 22.5328 0.211 106.814 0.000 22.118 22.947 CRIM -0.9281 0.282 -3.287 0.001 -1.483 -0.373 ZN 1.0816 0.320 3.382 0.001 0.453 1.710 INDUS 0.1409 0.421 0.334 0.738 -0.687 0.969 CHAS 0.6817 0.219 3.118 0.002 0.252 1.111 NOX -2.0567 0.442 -4.651 0.000 -2.926 -1.188 RM 2.6742 0.293 9.116 0.000 2.098 3.251 AGE 0.0195 0.371 0.052 0.958 -0.710 0.749 DIS -3.1040 0.420 -7.398 0.000 -3.928 -2.280 RAD 2.6622 0.577 4.613 0.000 1.528 3.796 TAX -2.0768 0.633 -3.280 0.001 -3.321 -0.833 PTRATIO -2.0606 0.283 -7.283 0.000 -2.617 -1.505 B 0.8493 0.245 3.467 0.001 0.368 1.331 LSTAT -3.7436 0.362 -10.347 0.000 -4.454 -3.033 ============================================================================== Omnibus: 178.041 Durbin-Watson: 1.078 Prob(Omnibus): 0.000 Jarque-Bera (JB): 783.126 Skew: 1.521 Prob(JB): 8.84e-171 Kurtosis: 8.281 Cond. No. 9.82 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. |
| Name Coefficients 12 LSTAT -3.743627 7 DIS -3.104044 9 TAX -2.076782 10 PTRATIO -2.060607 4 NOX -2.056718 0 CRIM -0.928146 6 AGE 0.019466 2 INDUS 0.140900 3 CHAS 0.681740 11 B 0.849268 1 ZN 1.081569 8 RAD 2.662218 5 RM 2.674230 |
| 22.532806324110673 |
| 0.7406426641094094 |
| ,CRIM,ZN,INDUS,CHAS,NOX,RM,AGE,DIS,RAD,TAX,PTRATIO,B,LSTAT,Y 0,0.00632,18.0,2.31,0.0,0.5379999999999999,6.575,65.2,4.09,1.0,296.0,15.3,396.9,4.98,24.0 1,0.02731,0.0,7.07,0.0,0.469,6.421,78.9,4.9671,2.0,242.0,17.8,396.9,9.14,21.6 2,0.02729,0.0,7.07,0.0,0.469,7.185,61.1,4.9671,2.0,242.0,17.8,392.83,4.03,34.7 3,0.032369999999999996,0.0,2.18,0.0,0.45799999999999996,6.997999999999999,45.8,6.0622,3.0,222.0,18.7,394.63,2.94,33.4 4,0.06905,0.0,2.18,0.0,0.45799999999999996,7.147,54.2,6.0622,3.0,222.0,18.7,396.9,5.33,36.2 5,0.02985,0.0,2.18,0.0,0.45799999999999996,6.43,58.7,6.0622,3.0,222.0,18.7,394.12,5.21,28.7 6,0.08829,12.5,7.87,0.0,0.524,6.0120000000000005,66.6,5.5605,5.0,311.0,15.2,395.6,12.43,22.9 7,0.14455,12.5,7.87,0.0,0.524,6.172000000000001,96.1,5.9505,5.0,311.0,15.2,396.9,19.15,27.1 8,0.21124,12.5,7.87,0.0,0.524,5.631,100.0,6.0821,5.0,311.0,15.2,386.63,29.93,16.5 9,0.17004,12.5,7.87,0.0,0.524,6.004,85.9,6.5921,5.0,311.0,15.2,386.71,17.1,18.9 10,0.22489,12.5,7.87,0.0,0.524,6.377000000000001,94.3,6.3467,5.0,311.0,15.2,392.52,20.45,15.0 11,0.11747,12.5,7.87,0.0,0.524,6.0089999999999995,82.9,6.2267,5.0,311.0,15.2,396.9,13.27,18.9 12,0.09378,12.5,7.87,0.0,0.524,5.888999999999999,39.0,5.4509,5.0,311.0,15.2,390.5,15.71,21.7 13,0.62976,0.0,8.14,0.0,0.5379999999999999,5.949,61.8,4.7075,4.0,307.0,21.0,396.9,8.26,20.4 14,0.6379600000000001,0.0,8.14,0.0,0.5379999999999999,6.096,84.5,4.4619,4.0,307.0,21.0,380.02,10.26,18.2 15,0.62739,0.0,8.14,0.0,0.5379999999999999,5.834,56.5,4.4986,4.0,307.0,21.0,395.62,8.47,19.9 16,1.05393,0.0,8.14,0.0,0.5379999999999999,5.935,29.3,4.4986,4.0,307.0,21.0,386.85,6.58,23.1 17,0.7842,0.0,8.14,0.0,0.5379999999999999,5.99,81.7,4.2579,4.0,307.0,21.0,386.75,14.67,17.5 18,0.80271,0.0,8.14,0.0,0.5379999999999999,5.456,36.6,3.7965,4.0,307.0,21.0,288.99,11.69,20.2 19,0.7258,0.0,8.14,0.0,0.5379999999999999,5.727,69.5,3.7965,4.0,307.0,21.0,390.95,11.28,18.2 20,1.25179,0.0,8.14,0.0,0.5379999999999999,5.57,98.1,3.7979,4.0,307.0,21.0,376.57,21.02,13.6 21,0.8520399999999999,0.0,8.14,0.0,0.5379999999999999,5.965,89.2,4.0123,4.0,307.0,21.0,392.53,13.83,19.6 22,1.2324700000000002,0.0,8.14,0.0,0.5379999999999999,6.142,91.7,3.9769,4.0,307.0,21.0,396.9,18.72,15.2 23,0.9884299999999999,0.0,8.14,0.0,0.5379999999999999,5.813,100.0,4.0952,4.0,307.0,21.0,394.54,19.88,14.5 24,0.75026,0.0,8.14,0.0,0.5379999999999999,5.9239999999999995,94.1,4.3996,4.0,307.0,21.0,394.33,16.3,15.6 25,0.84054,0.0,8.14,0.0,0.5379999999999999,5.599,85.7,4.4546,4.0,307.0,21.0,303.42,16.51,13.9 26,0.67191,0.0,8.14,0.0,0.5379999999999999,5.813,90.3,4.6819999999999995,4.0,307.0,21.0,376.88,14.81,16.6 27,0.9557700000000001,0.0,8.14,0.0,0.5379999999999999,6.047000000000001,88.8,4.4534,4.0,307.0,21.0,306.38,17.28,14.8 28,0.77299,0.0,8.14,0.0,0.5379999999999999,6.495,94.4,4.4547,4.0,307.0,21.0,387.94,12.8,18.4 29,1.00245,0.0,8.14,0.0,0.5379999999999999,6.6739999999999995,87.3,4.239,4.0,307.0,21.0,380.23,11.98,21.0 30,1.13081,0.0,8.14,0.0,0.5379999999999999,5.712999999999999,94.1,4.2330000000000005,4.0,307.0,21.0,360.17,22.6,12.7 31,1.3547200000000001,0.0,8.14,0.0,0.5379999999999999,6.072,100.0,4.175,4.0,307.0,21.0,376.73,13.04,14.5 32,1.38799,0.0,8.14,0.0,0.5379999999999999,5.95,82.0,3.99,4.0,307.0,21.0,232.6,27.71,13.2 33,1.15172,0.0,8.14,0.0,0.5379999999999999,5.7010000000000005,95.0,3.7872,4.0,307.0,21.0,358.77,18.35,13.1 34,1.6128200000000001,0.0,8.14,0.0,0.5379999999999999,6.096,96.9,3.7598,4.0,307.0,21.0,248.31,20.34,13.5 35,0.06417,0.0,5.96,0.0,0.499,5.933,68.2,3.3603,5.0,279.0,19.2,396.9,9.68,18.9 36,0.09744,0.0,5.96,0.0,0.499,5.841,61.4,3.3779,5.0,279.0,19.2,377.56,11.41,20.0 37,0.08014,0.0,5.96,0.0,0.499,5.85,41.5,3.9342,5.0,279.0,19.2,396.9,8.77,21.0 38,0.17505,0.0,5.96,0.0,0.499,5.966,30.2,3.8473,5.0,279.0,19.2,393.43,10.13,24.7 39,0.027630000000000002,75.0,2.95,0.0,0.428,6.595,21.8,5.4011,3.0,252.0,18.3,395.63,4.32,30.8 40,0.033589999999999995,75.0,2.95,0.0,0.428,7.024,15.8,5.4011,3.0,252.0,18.3,395.62,1.98,34.9 41,0.12744,0.0,6.91,0.0,0.44799999999999995,6.77,2.9,5.7209,3.0,233.0,17.9,385.41,4.84,26.6 42,0.1415,0.0,6.91,0.0,0.44799999999999995,6.169,6.6,5.7209,3.0,233.0,17.9,383.37,5.81,25.3 43,0.15936,0.0,6.91,0.0,0.44799999999999995,6.211,6.5,5.7209,3.0,233.0,17.9,394.46,7.44,24.7 44,0.12269000000000001,0.0,6.91,0.0,0.44799999999999995,6.069,40.0,5.7209,3.0,233.0,17.9,389.39,9.55,21.2 45,0.17142000000000002,0.0,6.91,0.0,0.44799999999999995,5.682,33.8,5.1004,3.0,233.0,17.9,396.9,10.21,19.3 46,0.18836,0.0,6.91,0.0,0.44799999999999995,5.7860000000000005,33.3,5.1004,3.0,233.0,17.9,396.9,14.15,20.0 47,0.22926999999999997,0.0,6.91,0.0,0.44799999999999995,6.03,85.5,5.6894,3.0,233.0,17.9,392.74,18.8,16.6 48,0.25387,0.0,6.91,0.0,0.44799999999999995,5.399,95.3,5.87,3.0,233.0,17.9,396.9,30.81,14.4 49,0.21977,0.0,6.91,0.0,0.44799999999999995,5.602,62.0,6.0877,3.0,233.0,17.9,396.9,16.2,19.4 50,0.08872999999999999,21.0,5.64,0.0,0.439,5.962999999999999,45.7,6.8147,4.0,243.0,16.8,395.56,13.45,19.7 51,0.04337,21.0,5.64,0.0,0.439,6.115,63.0,6.8147,4.0,243.0,16.8,393.97,9.43,20.5 52,0.0536,21.0,5.64,0.0,0.439,6.511,21.1,6.8147,4.0,243.0,16.8,396.9,5.28,25.0 53,0.04981,21.0,5.64,0.0,0.439,5.997999999999999,21.4,6.8147,4.0,243.0,16.8,396.9,8.43,23.4 54,0.0136,75.0,4.0,0.0,0.41,5.888,47.6,7.3197,3.0,469.0,21.1,396.9,14.8,18.9 55,0.01311,90.0,1.22,0.0,0.40299999999999997,7.249,21.9,8.6966,5.0,226.0,17.9,395.93,4.81,35.4 56,0.02055,85.0,0.74,0.0,0.41,6.382999999999999,35.7,9.1876,2.0,313.0,17.3,396.9,5.77,24.7 57,0.01432,100.0,1.32,0.0,0.41100000000000003,6.816,40.5,8.3248,5.0,256.0,15.1,392.9,3.95,31.6 58,0.15445,25.0,5.13,0.0,0.45299999999999996,6.145,29.2,7.8148,8.0,284.0,19.7,390.68,6.86,23.3 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Figures
Figure_Multiple_Linear_Regression_r.png
Figure_Multiple_Linear_Regression_s.png
Figure_Multiple_Linear_Regression_n.png
Figure_Single_Linear_Regression_s.png
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