The Financial Journal (Global): Multiple Linear Regression in Python (Training Data, Predictive Model Building by Training Data, Test Data, and Model Predictions for Test Data)

Multiple Linear Regression in Python (Training Data, Predictive Model Building by Training Data, Test Data, and Model Predictions for Test Data)

**0_MacOS_Python_setup.txt**
# Install on Terminal of MacOS # 1. pandas #pip3 install -U pandas # 2. matplotlib, from mpl_toolkits.mplot3d import Axes3D #pip3 install -U matplotlib # 3. scikit-learn (sklearn) #pip3 install -U scikit-learn # 4. statsmodels #pip3 install -U statsmodels # 5. tkinter #pip3 install -U tkinter # 6. NumPy #pip3 install -U numpy # 7. seaborn #pip3 install -U seaborn

1_MacOS_Terminal.txt

########## Run Terminal on MacOS and execute
### TO UPDATE
cd "YOUR_WORKING_DIRECTORY"

python3 lrm03.py training.csv test.csv

Data files

training.csv

Year,Month,x1,x2,y
2017,12,2.75,5.3,1464.00
2017,11,2.5,5.3,1394.00
2017,10,2.5,5.3,1357.00
2017,9,2.5,5.3,1293.00
2017,8,2.5,5.4,1256.00
2017,7,2.5,5.6,1254.00
2017,6,2.5,5.5,1234.00
2017,5,2.25,5.5,1195.00
2017,4,2.25,5.5,1159.00
2017,3,2.25,5.6,1167.00
2017,2,2,5.7,1130.00
2017,1,2,5.9,1075.00
2016,12,2,6,1047.00
2016,11,1.75,5.9,965.00
2016,10,1.75,5.8,943.00
2016,9,1.75,6.1,958.00
2016,8,1.75,6.2,971.00
2016,7,1.75,6.1,949.00
2016,6,1.75,6.1,884.00
2016,5,1.75,6.1,866.00
2016,4,1.75,5.9,876.00
2016,3,1.75,6.2,822.00
2016,2,1.75,6.2,704.00
2016,1,1.75,6.1,719.00

test.csv

Year,Month,x1,x2,y
2019,12,3.75,4.5,1831.75
2019,11,3.5,4.5,1744.17
2019,10,3.5,4.7,1697.88
2019,9,3.5,4.7,1786.3
2019,8,3.25,4.8,1735.18
2019,7,3.25,4.8,1732.42
2019,6,3.25,4.7,1704.79
2019,5,3.25,4.7,1650.91
2019,4,3.25,4.7,1601.18
2019,3,3.25,4.8,1612.23
2019,2,3,4.9,1561.11
2019,1,3,4.9,1485.13
2018,12,3,5,1446.45
2018,11,3,4.9,1580.77
2018,10,3,4.8,1544.73
2018,9,3,5.1,1569.3
2018,8,3,5.2,1590.6
2018,7,3,5.1,1554.56
2018,6,3,5.3,1586.29
2018,5,3,5.3,1553.99
2018,4,2.75,5.1,1571.93
2018,3,2.75,5.4,1475.03
2018,2,2.75,5.4,1404.79
2018,1,2.75,5.3,1434.72

Python files

**lrm03.py**
########## Multiple Linear Regression in Python (Training Data, Predictive Model Building by Training Data, Test Data, and Model Predictions for Test Data) ########## # # Run this script on Terminal of MacOS as follows: # python3 lrm01.py training.csv test.csv # # Reference: # Example of Multiple Linear Regression in Python # https://datatofish.com/multiple-linear-regression-python/ ##### Checking for Linearity import pandas as pd import matplotlib.pyplot as plt import sys import numpy as np import seaborn as sns from mpl_toolkits.mplot3d import Axes3D ###training.csv trainingcsv = sys.argv[1] # the first argument after lrm01.py # # 'y' (dependent variable) : e.g., Stock_Index_Price # 'x1' (independent variable 1) : e.g., Interest_Rate # 'x2' (independent variable 2) : e.g., Unemployment_Rate # # #trainingcsv = {'Year': [2017,2017,2017,2017,2017,2017,2017,2017,2017,2017,2017,2017,2016,2016,2016,2016,2016,2016,2016,2016,2016,2016,2016,2016], # 'Month': [12, 11,10,9,8,7,6,5,4,3,2,1,12,11,10,9,8,7,6,5,4,3,2,1], # 'x1': [2.75,2.5,2.5,2.5,2.5,2.5,2.5,2.25,2.25,2.25,2,2,2,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75], # 'x2': [5.3,5.3,5.3,5.3,5.4,5.6,5.5,5.5,5.5,5.6,5.7,5.9,6,5.9,5.8,6.1,6.2,6.1,6.1,6.1,5.9,6.2,6.2,6.1], # 'y': [1464,1394,1357,1293,1256,1254,1234,1195,1159,1167,1130,1075,1047,965,943,958,971,949,884,866,876,822,704,719] # } # #df = pd.DataFrame(trainingcsv,columns=['Year','Month','x1','x2','y']) ###test.csv testcsv = sys.argv[2] # the second argument after lrm01.py ### Read csv files # #training data dftmp = pd.read_csv(trainingcsv, index_col=0) #dfnp = dftmp.values #covert pandas to numpy.ndarray df = dftmp # # #test data dftesttmp = pd.read_csv(testcsv, index_col=0) #dftestnp = dftesttmp.values #covert pandas to numpy.ndarray dftest = dftesttmp ### plot 1: Training Data y and x1 # # 'y' (dependent variable) : e.g., Stock_Index_Price # 'x1' (independent variable 1) : e.g., Interest_Rate # plt.scatter(df['x1'], df['y'], color='red', label="Training Data y and x1") plt.legend() plt.title('y vs x1', fontsize=14) plt.xlabel('x1', fontsize=14) plt.ylabel('y', fontsize=14) plt.grid(True) plt.savefig("Figure_1_y_x1_training.png") # added to save a figure plt.show() ### plot 2: Training Data y and x2 # # 'y' (dependent variable) : e.g., Stock_Index_Price # 'x2' (independent variable 2) : e.g., Unemployment_Rate # plt.scatter(df['x2'], df['y'], color='green', label="Training Data y and x2") plt.legend() plt.title('y vs x2', fontsize=14) plt.xlabel('x2', fontsize=14) plt.ylabel('y', fontsize=14) plt.grid(True) plt.savefig("Figure_2_y_x2_training.png") # added to save a figure plt.show() ### plot 3: Test Data y and x1 # # 'y' (dependent variable) : e.g., Stock_Index_Price # 'x1' (independent variable 1) : e.g., Interest_Rate # plt.scatter(dftest['x1'], dftest['y'], color='red', label="Test Data y and x1") plt.legend() plt.title('y vs x1', fontsize=14) plt.xlabel('x1', fontsize=14) plt.ylabel('y', fontsize=14) plt.grid(True) plt.savefig("Figure_3_y_x1_test.png") # added to save a figure plt.show() ### plot 4: Test Data y and x2 # # 'y' (dependent variable) : e.g., Stock_Index_Price # 'x2' (independent variable 2) : e.g., Unemployment_Rate # plt.scatter(dftest['x2'], dftest['y'], color='green', label="Test Data y and x2") plt.legend() plt.title('y vs x2', fontsize=14) plt.xlabel('x2', fontsize=14) plt.ylabel('y', fontsize=14) plt.grid(True) plt.savefig("Figure_4_y_x2_test.png") # added to save a figure plt.show() ##### Performing the Multiple Linear Regression (for Training Data) from sklearn import linear_model import statsmodels.api as sm X = df[['x1','x2']] Y = df['y'] ### with sklearn regr = linear_model.LinearRegression() regr.fit(X, Y) print('\n') print('==============================') print('Prediction model (for Training Data): \n') print('Intercept: \n', regr.intercept_) print('Coefficients: \n', regr.coef_) with open('coef.txt', 'w') as f: print('Intercept: ' + str(regr.intercept_), file=f) print('Coefficients:' + str(regr.coef_), file=f) ### with statsmodels X = sm.add_constant(X) # adding a constant # # X: raw training data that has const=1, x1, and x2. pd.DataFrame(data=X).to_csv("X.csv", header=True, index=False) model = sm.OLS(Y, X).fit() predictions = model.predict(X) # # YPRED # y : raw data Y # y_pred : predicted data by using raw training data x1 and x2 plus intercentpt. YYPRED = pd.concat([Y, predictions], axis=1).rename(columns={0: 'y_pred'}) pd.DataFrame(data=YYPRED).to_csv("YYPRED.csv", header=True, index=False) # #resultstmp have: y, y_pred, const, x1, and x2; all data except for y_pred & const=1 are raw training data resultstmp = pd.concat([YYPRED, X], axis=1) #print(resultstmp) resultstmp.to_csv("resultstmp.csv", header=True, index=False) # resultsint = pd.Series(regr.intercept_, index=resultstmp.index, name='coef_const') resultscoef1 = pd.Series(regr.coef_[0], index=resultstmp.index, name='coef_x1') resultscoef2 = pd.Series(regr.coef_[1], index=resultstmp.index, name='coef_x2') # pd.DataFrame(data=resultsint).to_csv("resultsint.csv", header=True, index=False) pd.DataFrame(data=resultscoef1).to_csv("resultscoef1.csv", header=True, index=False) pd.DataFrame(data=resultscoef2).to_csv("resultscoef2.csv", header=True, index=False) # RESULTS = pd.concat([resultstmp, resultsint, resultscoef1, resultscoef2], axis=1) RESULTS.to_csv("RESULTS.csv", header=True, index=False) # See "RESULTS.csv" # y, y_pred, const, x1, x2, coef_const, coef_x1, and coef_x2; the last three were coefficients for intercept, x1, and x2, respectively. # # For instance, # y_pred (B2) = F2C2 + G2D2 + H2E2 # y_pred (B2) = coef_const(F2)const(C2) + coef_1(G2)x1(D2) + coef_1(H2)x2(E2) # 1422.862389 = 1798.4039781 + 345.5400872.75 + (-250.1465714)5.3 print_model = model.summary() print(print_model) ''' Intercept: 1798.4039776258546 Coefficients: [ 345.54008701 -250.14657137] Predicted y: [1422.86238865] OLS Regression Results ============================================================================== Dep. Variable: Stock_Index_Price R-squared: 0.898 Model: OLS Adj. R-squared: 0.888 Method: Least Squares F-statistic: 92.07 Date: Fri, 29 May 2020 Prob (F-statistic): 4.04e-11 Time: 08:43:16 Log-Likelihood: -134.61 No. Observations: 24 AIC: 275.2 Df Residuals: 21 BIC: 278.8 Df Model: 2 Covariance Type: nonrobust ============================================================================== coef std err t P>\|t\| [0.025 0.975] ------------------------------------------------------------------------------ const 1798.4040 899.248 2.000 0.059 -71.685 3668.493 x1 345.5401 111.367 3.103 0.005 113.940 577.140 x2 -250.1466 117.950 -2.121 0.046 -495.437 -4.856 ============================================================================== Omnibus: 2.691 Durbin-Watson: 0.530 Prob(Omnibus): 0.260 Jarque-Bera (JB): 1.551 Skew: -0.612 Prob(JB): 0.461 Kurtosis: 3.226 Cond. No. 394. ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. ''' ##### Applying the Multiple Linear Regression (to Test Data) #from sklearn import linear_model #import statsmodels.api as sm XTEST = dftest[['x1','x2']] YTEST = dftest['y'] ### with statsmodels XTEST = sm.add_constant(XTEST) # adding a constant # # XTEST: raw test data that has const=1, x1, and x2. pd.DataFrame(data=XTEST).to_csv("XTEST.csv", header=True, index=False) #modeltest = sm.OLS(YTEST, XTEST).fit() # Test Data is not used to build a model. #predictionstest = modeltest.predict(XTEST) # Test Data is not used to build a model. predictionstest = model.predict(XTEST) # # YTESTPRED # y : raw data YTEST # y_pred : predicted data by using raw training data x1 and x2 plus intercept. YYPREDTEST = pd.concat([YTEST, predictionstest], axis=1).rename(columns={0: 'y_pred'}) pd.DataFrame(data=YYPREDTEST).to_csv("YYPREDTEST.csv", header=True, index=False) # resultstmptest = pd.concat([YYPREDTEST, XTEST], axis=1) # resultstmptest.to_csv("resultstmptest.csv", header=True, index=False) # resultsinttest = pd.Series(regr.intercept_, index=resultstmptest.index, name='coef_const') pd.DataFrame(data=resultsinttest).to_csv("resultsinttest.csv", header=True, index=False) # resultscoef1test = pd.Series(regr.coef_[0], index=resultstmptest.index, name='coef_x1') pd.DataFrame(data=resultscoef1test).to_csv("resultscoef1test.csv", header=True, index=False) # resultscoef2test = pd.Series(regr.coef_[1], index=resultstmptest.index, name='coef_x2') pd.DataFrame(data=resultscoef2test).to_csv("resultscoef2test.csv", header=True, index=False) # pd.concat([resultstmptest, resultsinttest, resultscoef1test, resultscoef2test], axis=1) RESULTSTEST = pd.concat([resultstmptest, resultsinttest, resultscoef1test, resultscoef2test], axis=1) RESULTSTEST.to_csv("RESULTSTEST.csv", header=True, index=False) ##### 3D plot ###Training Data: df (y, x1, x2) XXX = df[['x1']] YYY = df[['x2']] ZZZ = df['y'] ### Predictions (y_pred) and Training Data (y, x1, x2) ZZZPRED = YYPRED['y_pred'] ### Test Data: dftest (y, x1, x2) XXXTEST = dftest[['x1']] YYYTEST = dftest[['x2']] ZZZTEST = dftest['y'] ### Predictions (y_pred) and Test Data (y, x1, x2); Test Data is not used to build a predictive model ZZZPREDTEST = YYPREDTEST['y_pred'] ###graph sns.set_style("darkgrid") # #frames of a graph fig = plt.figure() ax = Axes3D(fig) # #axis labels ax.set_xlabel("X1") ax.set_ylabel("X2") ax.set_zlabel("Y") ###plot ##linestyle='None' means no line # # Training Data (y, x1, x2) ax.plot(XXX,YYY,ZZZ, marker="o",linestyle='None', label='Training Data (y, x1, x2)') # # Predictions (y_pred) and Training Data (x1, x2) ax.plot(XXX,YYY,ZZZPRED, marker="", linestyle='None', label='Predictions (y_pred) and Training Data (x1, x2)') # # Test Data (y, x1, x2) ax.plot(XXXTEST,YYYTEST,ZZZTEST, marker="+", linestyle='None', label='Test Data (y, x1, x2)') # # Predictions (y_pred) and Test Data (x1, x2) ax.plot(XXXTEST,YYYTEST,ZZZPREDTEST, marker="x", linestyle='None', label='Predictions (y_pred) and Test Data (x1, x2); Test Data is not used to build a predictive model') ax.legend() ###show a prediction equation on the plot # minx = min(XXX.min()[0],XXXTEST.min()[0]) miny = min(YYY.min()[0], YYYTEST.min()[0]) minz = min(ZZZ.min(), ZZZPRED.min(), ZZZTEST.min(), ZZZPREDTEST.min()) # ax.text(minx + (abs(minx) * 0.05), miny + (abs(miny) * 0.05), minz + (abs(minz) * 0.05), 'y_pred (Training Data) = ' + str(np.round(regr.intercept_, decimals=2)) + ' + (' + str(np.round(regr.coef_[0], decimals=2)) + '* x1) + (' + str(np.round(regr.coef_[1], decimals=2)) + '* x2)', color='black') ax.text(minx, miny, minz, 'y_pred (Test Data) = ' + str(np.round(regr.intercept_, decimals=2)) + ' + (' + str(np.round(regr.coef_[0], decimals=2)) + '* x1) + (' + str(np.round(regr.coef_[1], decimals=2)) + '* x2)', color='black') plt.savefig("Figure_5_y_x1_x2_y_pred_training_data_n_predictive_model_results_and_test_data_n_model_predications.png") # added to save a figure plt.show()