The Financial Journal (Global): Multiple Linear Regression

Showing posts with label Multiple Linear Regression. Show all posts

Tuesday, July 14, 2020

Package: Data Generation, Data Loading and Standardization, Initial Data Analysis, Multiple Linear Regression, Polynominal Liner Regression in Python

Package: Data Generation, Data Loading and Standardization, Initial Data Analysis, Multiple Linear Regression, Polynominal Liner Regression in Python

**0_MacOS_Python_setup.txt**
# Install on Terminal of MacOS # 1. pandas #pip3 install -U pandas # 2. NumPy #pip3 install -U numpy # 3. matplotlib #pip3 install -U matplotlib # 4. scikit-learn (sklearn) #pip3 install -U scikit-learn # 5. statsmodels #pip3 install -U statsmodels

1_MacOS_Terminal.txt

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

python3 stpkg00.py

#python3 stpkg01.py
python3 stpkg01.py yX.csv y

python3 stpkg02.py yXSTD.csv

#Multiple Linear Regression
python3 stpkg03.py yXSTD.csv y x1 x2 x3

#Polynomial SINGLE Linear Regression
python3 stpkg04.py yXSTD.csv y x1 3

Input data files

N/A

NaN

Python files

stpkg00.py

#################### Data Generation ####################

'''

x1raw = σ(1,1)
x2raw = σ(2,2)
x3raw = x1 + σ(2,2)

x1 = σ(0,1)
x2 = σ(0,1)
x3 = σ(0,1)

y = 1.0 + (2.0 * x1) + (0.5 * x2) + (0.1 * x3) + (0.05 * x1 * x2) + (0.2 * (x1)^2) + (0.02 * (x1)^3) + σ(0,1)
'''

import scipy as sp
import pandas as pd
from sklearn.preprocessing import StandardScaler
#import math
import numpy as np

sp.random.seed(0)

#numbe of samples
n = 100

x1 = sp.random.normal(1,1,n)
x2 = sp.random.normal(2,2,n)
x3 = x1 + sp.random.normal(2,2,n)
#
#print(x1)
#[ 2.76405235 ...
#print(type(x1))
#<class 'numpy.ndarray'>
#
#print(x2)
#[ 5.76630139e+00 ...
#
#print(x3)
#[ 4.02568867 ...

x1 = pd.DataFrame(x1)
x1 = x1.rename(columns={0: 'x1'})
#print(x1)

x2 = pd.DataFrame(x2)
x2 = x2.rename(columns={0: 'x2'})
#print(x2)

x3 = pd.DataFrame(x3)
x3 = x3.rename(columns={0: 'x3'})
#print(x3)

X = pd.concat([x1, x2, x3], axis=1)
#print(X)
#print(X.describe()) #standard deviation (sample, NOT population)

X.to_csv('X.csv', header=True, index=False)

#scaler = StandardScaler()
scaler = StandardScaler()
scaler.fit(X)

#print(scaler.mean_) # mean
#[1.05980802 2.16402594 2.94134349]
#
#print(scaler.var_) # variance
#print(type(scaler.var_))
#<class 'numpy.ndarray'>
#print((scaler.var_) ** 0.5) # standard deviation　(population)
#[1.00788224 2.06933399 2.22108027]

XSTD = pd.DataFrame(scaler.transform(X))
XSTD = XSTD.rename(columns={0: 'x1', 1: 'x2', 2: 'x3'})
XSTD.to_csv('XSTD.csv', header=True, index=False)
#print(XSTD)
'''
x1 x2 x3
0 1.690916 1.740790 0.488206
1 0.337687 -1.381867 -0.008980
2 0.911743 -1.307182 1.457270
3 2.164028 0.857652 1.625370
4 1.793612 -1.213082 1.443657
.. ... ... ...
95 0.641707 -0.245064 1.368259
96 -0.048922 0.666666 0.119134
97 1.712564 0.716647 1.355392
98 0.066579 2.011491 -0.276140
99 0.339505 1.212482 0.540619

[100 rows x 3 columns]
#
print(XSTD.describe())
'''
'''
x1 x2 x3
count 1.000000e+02 1.000000e+02 1.000000e+02
mean -1.143530e-16 1.576517e-16 -5.440093e-17
std 1.005038e+00 1.005038e+00 1.005038e+00
min -2.592364e+00 -2.228172e+00 -2.412135e+00
25% -6.981616e-01 -7.997189e-01 -6.266296e-01
50% 3.401995e-02 -5.543630e-02 1.232380e-02
75% 6.719727e-01 7.398196e-01 6.364589e-01
max 2.192663e+00 2.224031e+00 2.300629e+00
'''

#print(XSTD['x1'])
#print(type(XSTD['x1']))
#<class 'pandas.core.series.Series'>
#
#print(np.array(XSTD['x1']))
#print(type(np.array(XSTD['x1'])))
#<class 'numpy.ndarray'>

tmpy = (2.0 * np.array(XSTD['x1']))
tmpy = tmpy + (0.5 * np.array(XSTD['x2']))
tmpy = tmpy + (0.1 * np.array(XSTD['x3']))
tmpy = tmpy + (0.05 * np.array(XSTD['x1']) * np.array(XSTD['x2']))
tmpy = tmpy + (0.2 * (np.array(XSTD['x1']) ** 2))
tmpy = tmpy + (0.02 * (np.array(XSTD['x1']) ** 3))
tmpy = tmpy + sp.random.normal(0,1,n)
tmpy = tmpy + 1.0
#print(tmpy)
#print(type(tmpy))
#<class 'numpy.ndarray'>
y = pd.DataFrame(tmpy)
y = y.rename(columns={0: 'y'})
y.to_csv('y.csv', header=True, index=False)

#print(y)
#print(type(y))
#<class 'pandas.core.frame.DataFrame'>

#y = 1.0 + (2.0 * x1) + (0.5 * x2) + (0.1 * x3) + (0.05 * x1 * x2) + (0.2 * (x1)^2) + (0.02 * (x1)^3) + σ(0,1)
#y = 1.0 + (2.0 * x1) + (0.5 * x2) + (0.1 * x3) + (0.05 * x1 * x2) + (0.2 * (x1**2)) + (0.02 * (x1**3)) + sp.random.normal(0,1,n)
#y = 1.0 + (2.0 * 1.690916) + (0.5 * 1.740790) + (0.1 * 0.488206) + (0.05 * 1.690916 * 1.740790) + (0.2 * (1.690916**2)) + (0.02 * (1.690916**3)) + 0
#print(1.0 + (2.0 * 1.690916) + (0.5 * 1.740790) + (0.1 * 0.488206) + (0.05 * 1.690916 * 1.740790) + (0.2 * (1.690916**2)) + (0.02 * (1.690916**3)) + 0)
#6.11675670334485

yX = pd.concat([y, x1, x2, x3], axis=1)
yX.to_csv('yX.csv', header=True, index=False)

stpkg01.py

#################### Data Loading and Standardization

########## data file(s) to load
# yX.csv (which includes dependent variable y and indepdent variables X: x1, x2, ...)
##########

########## Run this code as follows
#python3 stpkg01.py yX.csv y
#python3 stpkg01.py (data file to load) (dependent variable/target in yX.csv)

########## import
import sys
import pandas as pd
from sklearn.preprocessing import StandardScaler

#print(sys.argv[0])
#stpkg01.py
#
dfname = sys.argv[1]
yname = sys.argv[2]
##########

########## loading data
#yX = pd.read_csv('yX.csv', header = 0)
yX = pd.read_csv(dfname, header = 0)
#
print(yX)
#print(yX.describe())

#X = yX.drop(['y'], axis=1)
X = yX.drop([yname], axis=1)
#print(X)
X.to_csv('X.csv', header=True, index=False)

#y = yX['y']
y = yX[yname]
y.to_csv('y.csv', header=True, index=False)

scaler = StandardScaler()
scaler.fit(X)

#print(scaler.mean_) # mean
#[1.05980802 2.16402594 2.94134349]
#
#print((scaler.var_) ** 0.5) # standard deviation　(population)
#[1.00788224 2.06933399 2.22108027]

XSTD = pd.DataFrame(scaler.transform(X), columns = X.columns)
print(XSTD.describe())
'''
x1 x2 x3
count 1.000000e+02 1.000000e+02 1.000000e+02
mean -1.187939e-16 1.620926e-16 -2.320366e-16
std 1.005038e+00 1.005038e+00 1.005038e+00
min -2.592364e+00 -2.228172e+00 -2.412135e+00
25% -6.981616e-01 -7.997189e-01 -6.266296e-01
50% 3.401995e-02 -5.543630e-02 1.232380e-02
75% 6.719727e-01 7.398196e-01 6.364589e-01
max 2.192663e+00 2.224031e+00 2.300629e+00
'''
XSTD.to_csv('XSTD.csv', header=True, index=False)

yXSTD = pd.concat([y, XSTD], axis=1)
yXSTD.to_csv('yXSTD.csv', header=True, index=False)

stpkg02.py

#################### Initial Data Analysis

########## Run this code as follows
#python3 stpkg02.py yXSTD.csv
#python3 stpkg02.py (data file to load)

########## import
import sys
import pandas as pd
from pandas.plotting import scatter_matrix
import matplotlib.pyplot as plt
import seaborn as sns

#print(sys.argv[0])
#stpkg02.py
#
dfname = sys.argv[1]
##########

########## loading data
#yXSTD = pd.read_csv('yXSTD.csv', header = 0)
yXSTD = pd.read_csv(dfname, header = 0)

#print(yXSTD.describe())
'''
y x1 x2 x3
count 100.000000 1.000000e+02 1.000000e+02 1.000000e+02
mean 1.008893 -1.232348e-16 1.576517e-16 -2.364775e-16
std 2.384226 1.005038e+00 1.005038e+00 1.005038e+00
min -4.001685 -2.592364e+00 -2.228172e+00 -2.412135e+00
25% -0.432215 -6.981616e-01 -7.997189e-01 -6.266296e-01
50% 0.755357 3.401995e-02 -5.543630e-02 1.232380e-02
75% 2.321260 6.719727e-01 7.398196e-01 6.364589e-01
max 6.808487 2.192663e+00 2.224031e+00 2.300629e+00
'''

########## scatter matrix

#scatter_matrix(yXSTD, figsize=(6.4, 4.8)) #640 x 480
scatter_matrix(yXSTD, figsize=(800/100, 600/100))
plt.suptitle('Scatter Matrix')
plt.savefig("Fig_02_1.png")
plt.show()
plt.close()

########## correlation

cor = yXSTD.corr()

#print(cor)

ax = sns.heatmap(
cor,
annot=True,
fmt='.4f', #f for fixed number of decimal places (4 in this case); g is for variable numbers
vmin=-1, vmax=1, center=0,
#cmap='Blues',
cmap=sns.diverging_palette(20, 220, n=200),
square=True
)
ax.set_xticklabels(
ax.get_xticklabels(),
#rotation=45,
horizontalalignment='right'
);

plt.suptitle('Correlation Heatmap')
plt.savefig("Fig_02_2.png")
plt.show()
plt.close()

stpkg03.py

#################### Multiple Linear Regression

########## Run this code as follows
#python3 stpkg03.py yXSTD.csv y x1 x2 x3
#python3 stpkg03.py (data file to load) (dependent variable/target in yXSTD.csv) (3 specified independent variables in yXSTD.csv for multiple linear regression)

########## import
import sys
import pandas as pd
from sklearn.model_selection import train_test_split
#from sklearn.linear_model import LinearRegression
from sklearn import linear_model
import statsmodels.api as sm
import matplotlib.pyplot as plt
#from pandas.plotting import scatter_matrix
#import seaborn as sns

#print(sys.argv[0])
#stpkg03.py
#
dfname = sys.argv[1]
yname = sys.argv[2]
x1name = sys.argv[3]
x2name = sys.argv[4]
x3name = sys.argv[5]
##########

########## loading data
#yXSTD = pd.read_csv('yXSTD.csv', header = 0)
yXSTD = pd.read_csv(dfname, header = 0)

#print(yXSTD.describe())
'''
y x1 x2 x3
count 100.000000 1.000000e+02 1.000000e+02 1.000000e+02
mean 1.008893 -1.232348e-16 1.576517e-16 -2.364775e-16
std 2.384226 1.005038e+00 1.005038e+00 1.005038e+00
min -4.001685 -2.592364e+00 -2.228172e+00 -2.412135e+00
25% -0.432215 -6.981616e-01 -7.997189e-01 -6.266296e-01
50% 0.755357 3.401995e-02 -5.543630e-02 1.232380e-02
75% 2.321260 6.719727e-01 7.398196e-01 6.364589e-01
max 6.808487 2.192663e+00 2.224031e+00 2.300629e+00
'''

XSTD = yXSTD.drop([yname], axis=1)
#print(XSTD)
#print(type(XSTD))
#X.to_csv('XSTD.csv', header=True, index=False)

y = yXSTD[yname]
y = pd.DataFrame(y)
#print(y)
#print(type(y))
#y.to_csv('y.csv', header=True, index=False)
##########

########## creating training and test data

XSTD_train, XSTD_test, y_train, y_test = train_test_split(XSTD, y, test_size=0.2, random_state = 0)

#print(XSTD_train.shape)
#print(XSTD_test.shape)
#print(y_train.shape)
#print(y_test.shape)
'''
(80, 3)
(20, 3)
(80, 1)
(20, 1)
'''
lr = linear_model.LinearRegression().fit(XSTD_train, y_train)
print(f"R2 of Training Data: {lr.score(XSTD_train, y_train):.4}")
print(f"R2 of Test Data (based on a model by Training Data): {lr.score(XSTD_test, y_test):.4}")

########## Multiple Linear Regression (with Training Data)

smXSTD_train = sm.add_constant(XSTD_train)

model = sm.OLS(y_train, smXSTD_train)

results = model.fit()

print(results.summary())
'''
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.839
Model: OLS Adj. R-squared: 0.832
Method: Least Squares F-statistic: 131.5
Date: Sun, 12 Jul 2020 Prob (F-statistic): 5.23e-30
Time: 18:49:50 Log-Likelihood: -111.79
No. Observations: 80 AIC: 231.6
Df Residuals: 76 BIC: 241.1
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 1.0679 0.113 9.487 0.000 0.844 1.292
x1 1.8865 0.137 13.767 0.000 1.614 2.159
x2 0.5003 0.111 4.490 0.000 0.278 0.722
x3 0.3011 0.135 2.230 0.029 0.032 0.570
==============================================================================
Omnibus: 0.606 Durbin-Watson: 2.329
Prob(Omnibus): 0.739 Jarque-Bera (JB): 0.733
Skew: -0.178 Prob(JB): 0.693
Kurtosis: 2.694 Cond. No. 1.96
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
'''
with open('results.summary.txt', 'w') as f:
print(results.summary(), file=f)

#print(results.params)
#print(type(results.params))
#<class 'pandas.core.series.Series'>
#
#print(results.params.shape)
#(4,)
#
#print(len(results.params))
#4

b0 = results.params['const']
b1 = results.params[x1name]
b2 = results.params[x2name]
b3 = results.params[x3name]

#print(b0) #1.0679105398301059
#print(b1) #1.8865026849796247
#print(b2) #0.5003158682861151
#print(b3) #0.3010874982341183

#print('R2: ', results.rsquared)
#R2: 0.8385140722177117

#################### traing data integration

#print(pd.concat([y_train, XSTD_train], axis=1))
yXypred_train = pd.concat([y_train, XSTD_train, b0 + (b1 * XSTD_train[x1name]) + (b2 * XSTD_train[x2name]) + (b3 * XSTD_train[x3name])], axis=1)
yXypred_train = yXypred_train.rename(columns={0: 'ypred'})

yXypred_train = pd.concat([yXypred_train, yXypred_train[yname] - yXypred_train['ypred']], axis=1)
yXypred_train = yXypred_train.rename(columns={0: 'residual'})

yXypred_train.to_csv('yXypred_train.csv', header=True, index=False)

#print(yXypred_train.columns)
#Index(['y', 'x1', 'x2', 'x3', 'ypred'], dtype='object')

########## plot: training data (x1, y) and predicted data (x1, ypred)

#print(max(yXypred_train[x1name]))
#2.164027787075764
#
#print(min(yXypred_train[x1name]))
#-4.001684888412238
#
#print(max(yXypred_train[yname]))
#6.808486625095364
#
#print(min(yXypred_train[yname]))
#-2.5923641824877004

plt.figure(figsize=(8, 8))
#
plt.scatter(yXypred_train[x1name], yXypred_train[yname], color = 'blue', label='Training Data')
#
plt.scatter(yXypred_train[x1name], yXypred_train['ypred'], color = 'red', label='Predicted Data')
#
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title(x1name + ": Training Data, " + yname + ": Training Data and Predicted Data")
plt.xlabel(x1name)
plt.ylabel(yname)
plt.grid(True)
#
plt.text(min(yXypred_train[x1name]), max(yXypred_train[yname]) * 1.00, "y = b0 + (b1 * x1) + (b2 * x2) + (b3 * x3)", size = 10, color = "black")
plt.text(min(yXypred_train[x1name]), max(yXypred_train[yname]) * 0.90, "b0 = " + str(b0), size = 10, color = "black")
plt.text(min(yXypred_train[x1name]), max(yXypred_train[yname]) * 0.80, "b1 = " + str(b1), size = 10, color = "black")
plt.text(min(yXypred_train[x1name]), max(yXypred_train[yname]) * 0.70, "b2 = " + str(b2), size = 10, color = "black")
plt.text(min(yXypred_train[x1name]), max(yXypred_train[yname]) * 0.60, "b3 = " + str(b3), size = 10, color = "black")
plt.text(min(yXypred_train[x1name]), max(yXypred_train[yname]) * 0.50, "R2 = " + str(results.rsquared), size = 10, color = "black")
#
plt.savefig('Fig_03_1a.png')
plt.show()

########## plot: training data (x1) and residual data (y - ypred)

plt.figure(figsize=(8, 8))
#
plt.scatter(yXypred_train[x1name], yXypred_train['residual'], color = 'green', label='Residual (actual - predicted)')
#
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title(x1name + ": Training Data, " + 'residual' + ": Residual (actual - predicted)")
plt.xlabel(x1name)
plt.ylabel('Residual')
plt.grid(True)
#
plt.savefig('Fig_03_1b.png')
plt.show()

#################### test data integration

yXypred_test = pd.concat([y_test, XSTD_test, b0 + (b1 * XSTD_test[x1name]) + (b2 * XSTD_test[x2name]) + (b3 * XSTD_test[x3name])], axis=1)
yXypred_test = yXypred_test.rename(columns={0: 'ypred'})

yXypred_test = pd.concat([yXypred_test, yXypred_test[yname] - yXypred_test['ypred']], axis=1)
yXypred_test = yXypred_test.rename(columns={0: 'residual'})

yXypred_test.to_csv('yXypred_test.csv', header=True, index=False)

#print(yXypred_test.columns)
#Index(['y', 'x1', 'x2', 'x3', 'ypred'], dtype='object')

########## plot: test data (x1, y) and predicted data (x1, ypred)

plt.figure(figsize=(8, 8))
#
plt.scatter(yXypred_test[x1name], yXypred_test[yname], color = 'blue', label='Test Data')
#
plt.scatter(yXypred_test[x1name], yXypred_test['ypred'], color = 'red', label='Predicted Data')
#
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title(x1name + ": Test Data, " + yname + ": Test Data and Predicted Data (based on Training Data)")
plt.xlabel(x1name)
plt.ylabel(yname)
plt.grid(True)
#
plt.text(min(yXypred_test[x1name]), max(yXypred_test[yname]) * 1.00, "y = b0 + (b1 * x1) + (b2 * x2) + (b3 * x3)", size = 10, color = "black")
plt.text(min(yXypred_test[x1name]), max(yXypred_test[yname]) * 0.90, "b0 = " + str(b0), size = 10, color = "black")
plt.text(min(yXypred_test[x1name]), max(yXypred_test[yname]) * 0.80, "b1 = " + str(b1), size = 10, color = "black")
plt.text(min(yXypred_test[x1name]), max(yXypred_test[yname]) * 0.70, "b2 = " + str(b2), size = 10, color = "black")
plt.text(min(yXypred_test[x1name]), max(yXypred_test[yname]) * 0.60, "b3 = " + str(b3), size = 10, color = "black")
#
plt.savefig('Fig_03_2a.png')
plt.show()

########## plot: test data (x1) and residual data (y - ypred)

plt.figure(figsize=(8, 8))
#
plt.scatter(yXypred_test[x1name], yXypred_test['residual'], color = 'green', label='Residual (actual - predicted)')
#
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title(x1name + ": Training Data, " + 'residual' + ": Residual (actual - predicted)")
plt.xlabel(x1name)
plt.ylabel('Residual')
plt.grid(True)
#
plt.savefig('Fig_03_2b.png')
plt.show()

stpkg04.py

#################### Multiple Linear Regression

########## Run this code as follows
#python3 stpkg04.py yXSTD.csv y x1 3
#python3 stpkg04.py (data file to load) (dependent variable/target in yXSTD.csv) (one specified independent variables in yXSTD.csv for polynominal linear regression)

########## import
import sys
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.metrics import r2_score
import matplotlib.pyplot as plt

#print(sys.argv[0])
#stpkg04.py
#
dfname = sys.argv[1]
yname = sys.argv[2]
x1name = sys.argv[3]
x1dim = int(sys.argv[4])
#x2name = sys.argv[4]
#x3name = sys.argv[5]
##########

########## loading data
#yXSTD = pd.read_csv('yXSTD.csv', header = 0)
yXSTD = pd.read_csv(dfname, header = 0)

#print(yXSTD.describe())
'''
y x1 x2 x3
count 100.000000 1.000000e+02 1.000000e+02 1.000000e+02
mean 1.008893 -1.232348e-16 1.576517e-16 -2.364775e-16
std 2.384226 1.005038e+00 1.005038e+00 1.005038e+00
min -4.001685 -2.592364e+00 -2.228172e+00 -2.412135e+00
25% -0.432215 -6.981616e-01 -7.997189e-01 -6.266296e-01
50% 0.755357 3.401995e-02 -5.543630e-02 1.232380e-02
75% 2.321260 6.719727e-01 7.398196e-01 6.364589e-01
max 6.808487 2.192663e+00 2.224031e+00 2.300629e+00
'''

XSTD = yXSTD.drop([yname], axis=1)
#print(XSTD)
#print(type(XSTD))
#X.to_csv('XSTD.csv', header=True, index=False)

x1 = XSTD[x1name]
x1 = pd.DataFrame(x1)
#print(x1)
#print(type(x1))
#<class 'pandas.core.frame.DataFrame'>

y = yXSTD[yname]
y = pd.DataFrame(y)
#print(y)
#print(type(y))
#y.to_csv('y.csv', header=True, index=False)
##########

########## creating training and test data

x1_train, x1_test, y_train, y_test = train_test_split(x1, y, test_size=0.2, random_state = 0)

#print(XSTD_train.shape)
#print(XSTD_test.shape)
#print(y_train.shape)
#print(y_test.shape)
'''
(80, 3)
(20, 3)
(80, 1)
(20, 1)
'''
#lr = linear_model.LinearRegression().fit(XSTD_train, y_train)
#print(f"R2 of Training Data: {lr.score(XSTD_train, y_train):.4}")
#print(f"R2 of Test Data (based on a model by Training Data): {lr.score(XSTD_test, y_test):.4}")

########## Polynominal Linear Regression (for Training Data)
clf = LinearRegression()

clf.fit(x1_train, y_train)

#dimension
#print(x1dim)

pf = PolynomialFeatures(degree = x1dim, include_bias = False)
x_poly = pf.fit_transform(x1_train)

poly_reg = LinearRegression()
poly_reg_fit = poly_reg.fit(x_poly, y_train)

#print(poly_reg_fit.coef_)
#[[2.05425368 0.11273714 0.03563863]]
#print(type(poly_reg_fit.coef_))
#<class 'numpy.ndarray'>
#print(poly_reg_fit.coef_[0][0])
#2.0542536782376684
#
#print(poly_reg_fit.intercept_)
#[0.99017672]

polypred = poly_reg.predict(x_poly)

#predicted y
#ypred = clf.predict(y_train)
#ypred = clf.predict(x1_train)
#print(ypred)
#print(type(ypred))
#<class 'numpy.ndarray'>

##### output data

ypred_train = poly_reg_fit.intercept_[0] + (poly_reg_fit.coef_[0][0] * x1_train) + (poly_reg_fit.coef_[0][1] * (x1_train ** 2)) + (poly_reg_fit.coef_[0][2] * (x1_train **3))
ypred_train = ypred_train.rename(columns={x1name: 'ypred'})
#print(ypred_test)

yx1ypred_train = pd.concat([y_train, x1_train, ypred_train], axis=1)
yx1ypred_train.to_csv('yx1ypred_train.csv', header=True, index=False)

yx1ypredres_train = pd.concat([yx1ypred_train, yx1ypred_train[yname] - yx1ypred_train['ypred']], axis=1)
yx1ypredres_train = yx1ypredres_train.rename(columns={0: 'residual'})
yx1ypredres_train.to_csv('yx1ypredres_train.csv', header=True, index=False)

##### plot

plt.scatter(yx1ypredres_train[x1name], yx1ypredres_train[yname], c = 'blue', label = 'Training Data')
plt.scatter(yx1ypredres_train[x1name], yx1ypredres_train['ypred'], c = 'red', label = 'Predicted Data')
#
plt.text(min(yx1ypredres_train[x1name]), max(yx1ypredres_train[yname]) * 1.00, "y = b0 + (b1 * x1) + (b2 * x1^2) + (b3 * x1^3)", size = 10, color = "black")
plt.text(min(yx1ypredres_train[x1name]), max(yx1ypredres_train[yname]) * 0.90, "b0 = " + str(poly_reg_fit.intercept_[0]), size = 10, color = "black")
plt.text(min(yx1ypredres_train[x1name]), max(yx1ypredres_train[yname]) * 0.80, "b1 = " + str(poly_reg_fit.coef_[0][0]), size = 10, color = "black")
plt.text(min(yx1ypredres_train[x1name]), max(yx1ypredres_train[yname]) * 0.70, "b2 = " + str(poly_reg_fit.coef_[0][1]), size = 10, color = "black")
plt.text(min(yx1ypredres_train[x1name]), max(yx1ypredres_train[yname]) * 0.60, "b3 = " + str(poly_reg_fit.coef_[0][2]), size = 10, color = "black")
plt.text(min(yx1ypredres_train[x1name]), max(yx1ypredres_train[yname]) * 0.50, "R^2={}".format(r2_score(y_train, polypred)), size = 10, color = "black")
#
plt.xlabel(x1name + ': Training Data')
plt.ylabel(yname)
plt.grid(True)
#
#plt.legend()
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title("Polynominal Regression: " + x1name)
plt.savefig('Fig_04_1a.png')
plt.show()

'''
#plt.scatter(x1_train, y_train, c = 'blue', label = "R^2={}".format(r2_score(y_train, polypred)))
plt.scatter(x1_train, y_train, c = 'blue', label = 'Training Data')
plt.scatter(x1_train, polypred, c = 'red', label = 'Predicted Data')
#plt.plot(x1_train, polypred, c = 'red')
#
plt.text(min(x1_train[x1name]), max(y_train[yname]) * 1.00, "y = b0 + (b1 * x1) + (b2 * x1^2) + (b3 * x1^3)", size = 10, color = "black")
plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.90, "b0 = " + str(poly_reg_fit.intercept_[0]), size = 10, color = "black")
plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.80, "b1 = " + str(poly_reg_fit.coef_[0][0]), size = 10, color = "black")
plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.70, "b2 = " + str(poly_reg_fit.coef_[0][1]), size = 10, color = "black")
plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.60, "b3 = " + str(poly_reg_fit.coef_[0][2]), size = 10, color = "black")
plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.50, "R^2={}".format(r2_score(y_train, polypred)), size = 10, color = "black")
#
plt.xlabel(x1name + ': Training Data')
plt.ylabel(yname)
plt.grid(True)
#
#plt.legend()
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title("Polynominal Regression: " + x1name)
plt.savefig('Fig_04_1a.png')
plt.show()
'''

##### residual plot

plt.scatter(yx1ypredres_train[x1name], yx1ypredres_train['residual'], c = 'green', label = 'Redisual: Training Data')
#
plt.xlabel(x1name + ': Training Data')
plt.ylabel(yname)
plt.grid(True)
#
#plt.legend()
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title("Polynominal Regression, Residual: " + x1name)
plt.savefig('Fig_04_1b.png')
plt.show()

'''
ypred = pd.DataFrame(ypred)
#print(ypred)
#print(type(ypred))
#<class 'pandas.core.frame.DataFrame'>
ypred = ypred.rename(columns={0: 'ypred'})
#
#print(ypred)
#
#print(y_train)
#print(type(y_train))
#
#print(x1_train)
#print(type(x1_train))

y_train.reset_index(drop=True, inplace=True)
y_train = y_train.rename(columns={0: 'y'})
#print(y_train)

x1_train.reset_index(drop=True, inplace=True)
x1_train = x1_train.rename(columns={0: 'x1'})
#print(x1_train)

#yx1ypred_train = pd.concat([y_train, x1_train, ypred], axis=1, ignore_index = True)
yx1ypred_train = pd.concat([y_train, x1_train, ypred], axis=1)
yx1ypred_train.to_csv('yx1ypred_train.csv', header=True, index=False)

yx1ypredres_train = pd.concat([yx1ypred_train, yx1ypred_train[yname] - yx1ypred_train['ypred']], axis=1)
yx1ypredres_train = yx1ypredres_train.rename(columns={0: 'residual'})
yx1ypredres_train.to_csv('yx1ypredres_train.csv', header=True, index=False)

plt.scatter(yx1ypredres_train[x1name], yx1ypredres_train['residual'], c = 'green', label = 'Redisual: Training Data')
#plt.scatter(x1_train, polypred, c = 'red', label = 'Predicted Data')
#plt.plot(x1_train, polypred, c = 'red')
#
#plt.text(min(x1_train[x1name]), max(y_train[yname]) * 1.00, "y = b0 + (b1 * x1) + (b2 * x1^2) + (b3 * x1^3)", size = 10, color = "black")
#plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.90, "b0 = " + str(poly_reg_fit.intercept_[0]), size = 10, color = "black")
#plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.80, "b1 = " + str(poly_reg_fit.coef_[0][0]), size = 10, color = "black")
#plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.70, "b2 = " + str(poly_reg_fit.coef_[0][1]), size = 10, color = "black")
#plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.60, "b3 = " + str(poly_reg_fit.coef_[0][2]), size = 10, color = "black")
#plt.text(min(x1_train[x1name]), max(y_train[yname]) * 0.50, "R^2={}".format(r2_score(y_train, polypred)), size = 10, color = "black")
#
plt.xlabel(x1name + ': Training Data')
plt.ylabel(yname)
plt.grid(True)
#
#plt.legend()
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title("Polynominal Regression, Residual: " + x1name)
plt.savefig('Fig_04_1b.png')
plt.show()
'''

########## Polynominal Linear Regression (for Test Data)

##### output data

#x1_test
#y_test

ypred_test = poly_reg_fit.intercept_[0] + (poly_reg_fit.coef_[0][0] * x1_test) + (poly_reg_fit.coef_[0][1] * (x1_test ** 2)) + (poly_reg_fit.coef_[0][2] * (x1_test **3))
ypred_test = ypred_test.rename(columns={x1name: 'ypred'})
#print(ypred_test)

yx1ypred_test = pd.concat([y_test, x1_test, ypred_test], axis=1)
yx1ypred_test.to_csv('yx1ypred_test.csv', header=True, index=False)

yx1ypredres_test = pd.concat([yx1ypred_test, yx1ypred_test[yname] - yx1ypred_test['ypred']], axis=1)
yx1ypredres_test = yx1ypredres_test.rename(columns={0: 'residual'})
yx1ypredres_test.to_csv('yx1ypredres_test.csv', header=True, index=False)

##### plot

plt.scatter(yx1ypredres_test[x1name], yx1ypredres_test[yname], c = 'blue', label = 'Test Data')
plt.scatter(yx1ypredres_test[x1name], yx1ypredres_test['ypred'], c = 'red', label = 'Predicted Data')
#
plt.text(min(yx1ypredres_test[x1name]), max(yx1ypredres_test[yname]) * 1.00, "y = b0 + (b1 * x1) + (b2 * x1^2) + (b3 * x1^3)", size = 10, color = "black")
plt.text(min(yx1ypredres_test[x1name]), max(yx1ypredres_test[yname]) * 0.90, "b0 = " + str(poly_reg_fit.intercept_[0]), size = 10, color = "black")
plt.text(min(yx1ypredres_test[x1name]), max(yx1ypredres_test[yname]) * 0.80, "b1 = " + str(poly_reg_fit.coef_[0][0]), size = 10, color = "black")
plt.text(min(yx1ypredres_test[x1name]), max(yx1ypredres_test[yname]) * 0.70, "b2 = " + str(poly_reg_fit.coef_[0][1]), size = 10, color = "black")
plt.text(min(yx1ypredres_test[x1name]), max(yx1ypredres_test[yname]) * 0.60, "b3 = " + str(poly_reg_fit.coef_[0][2]), size = 10, color = "black")
#plt.text(min(yx1ypredres_test[x1name]), max(yx1ypredres_test[yname]) * 0.50, "R^2={}".format(r2_score(y_train, polypred)), size = 10, color = "black")
#
plt.xlabel(x1name + ': Test Data')
plt.ylabel(yname)
plt.grid(True)
#
#plt.legend()
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title("Polynominal Regression: " + x1name)
plt.savefig('Fig_04_2a.png')
plt.show()

##### residual plot

plt.scatter(yx1ypredres_test[x1name], yx1ypredres_test['residual'], c = 'green', label = 'Redisual: Test Data')
#
plt.xlabel(x1name + ': Test Data')
plt.ylabel(yname)
plt.grid(True)
#
#plt.legend()
plt.legend(bbox_to_anchor=(1, 0), loc='lower right', borderaxespad=1, fontsize=10)
plt.title("Polynominal Regression, Residual: " + x1name)
plt.savefig('Fig_04_2b.png')
plt.show()

Figures

Fig_02_1.png

Fig_02_2.png

Fig_03_1a.png

Fig_03_1b.png

Fig_03_2a.png

Fig_03_2b.png

Fig_04_1a.png

Fig_04_1b.png

Fig_04_2a.png

Fig_04_2b.png

References

Tuesday, June 9, 2020

Multiple Linear Regression of Raw Data, Standardized Data, and Normalized Data, Single Linear Regression), plus Multiple Linear Regression by two selected independent variables x1 and x2

Multiple Linear Regression of Raw Data, Standardized Data, and Normalized Data, Single Linear Regression), plus Multiple Linear Regression by two selected independent variables x1 and x2

**0_MacOS_Python_setup.txt**
# 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"

####Multiple Linear Regression & Single Linear Regression

#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

####Multiple Linear Regression with specified Xs (e.g., RM, LSAT)

python3 othermlr.py Xconv_Y_Ypred_YpredSingle.csv clifIntercept.txt clifCoefficients.txt Y RM LSTAT

Input Data files

df.csv

,CRIM,ZN,INDUS,CHAS,NOX,RM,AGE,DIS,RAD,TAX,PTRATIO,B,LSTAT,Y
0,0.00632,18.0,2.31,0.0,0.538,6.575,65.2,4.09,1.0,296.0,15.3,396.9,4.98,24.0
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
3,0.03237,0.0,2.18,0.0,0.458,6.998,45.8,6.0622,3.0,222.0,18.7,394.63,2.94,33.4
4,0.06905,0.0,2.18,0.0,0.458,7.147,54.2,6.0622,3.0,222.0,18.7,396.9,5.33,36.2
5,0.02985,0.0,2.18,0.0,0.458,6.43,58.7,6.0622,3.0,222.0,18.7,394.12,5.21,28.7
6,0.08829,12.5,7.87,0.0,0.524,6.012,66.6,5.5605,5.0,311.0,15.2,395.6,12.43,22.9
7,0.14455,12.5,7.87,0.0,0.524,6.172,96.1,5.9505,5.0,311.0,15.2,396.9,19.15,27.1
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
10,0.22489,12.5,7.87,0.0,0.524,6.377,94.3,6.3467,5.0,311.0,15.2,392.52,20.45,15.0
11,0.11747,12.5,7.87,0.0,0.524,6.009,82.9,6.2267,5.0,311.0,15.2,396.9,13.27,18.9
12,0.09378,12.5,7.87,0.0,0.524,5.889,39.0,5.4509,5.0,311.0,15.2,390.5,15.71,21.7
13,0.62976,0.0,8.14,0.0,0.538,5.949,61.8,4.7075,4.0,307.0,21.0,396.9,8.26,20.4
14,0.63796,0.0,8.14,0.0,0.538,6.096,84.5,4.4619,4.0,307.0,21.0,380.02,10.26,18.2
15,0.62739,0.0,8.14,0.0,0.538,5.834,56.5,4.4986,4.0,307.0,21.0,395.62,8.47,19.9
16,1.05393,0.0,8.14,0.0,0.538,5.935,29.3,4.4986,4.0,307.0,21.0,386.85,6.58,23.1
17,0.7842,0.0,8.14,0.0,0.538,5.99,81.7,4.2579,4.0,307.0,21.0,386.75,14.67,17.5
18,0.80271,0.0,8.14,0.0,0.538,5.456,36.6,3.7965,4.0,307.0,21.0,288.99,11.69,20.2
19,0.7258,0.0,8.14,0.0,0.538,5.727,69.5,3.7965,4.0,307.0,21.0,390.95,11.28,18.2
20,1.25179,0.0,8.14,0.0,0.538,5.57,98.1,3.7979,4.0,307.0,21.0,376.57,21.02,13.6
21,0.85204,0.0,8.14,0.0,0.538,5.965,89.2,4.0123,4.0,307.0,21.0,392.53,13.83,19.6
22,1.23247,0.0,8.14,0.0,0.538,6.142,91.7,3.9769,4.0,307.0,21.0,396.9,18.72,15.2
23,0.98843,0.0,8.14,0.0,0.538,5.813,100.0,4.0952,4.0,307.0,21.0,394.54,19.88,14.5
24,0.75026,0.0,8.14,0.0,0.538,5.924,94.1,4.3996,4.0,307.0,21.0,394.33,16.3,15.6
25,0.84054,0.0,8.14,0.0,0.538,5.599,85.7,4.4546,4.0,307.0,21.0,303.42,16.51,13.9
26,0.67191,0.0,8.14,0.0,0.538,5.813,90.3,4.682,4.0,307.0,21.0,376.88,14.81,16.6
27,0.95577,0.0,8.14,0.0,0.538,6.047,88.8,4.4534,4.0,307.0,21.0,306.38,17.28,14.8
28,0.77299,0.0,8.14,0.0,0.538,6.495,94.4,4.4547,4.0,307.0,21.0,387.94,12.8,18.4
29,1.00245,0.0,8.14,0.0,0.538,6.674,87.3,4.239,4.0,307.0,21.0,380.23,11.98,21.0
30,1.13081,0.0,8.14,0.0,0.538,5.713,94.1,4.233,4.0,307.0,21.0,360.17,22.6,12.7
31,1.35472,0.0,8.14,0.0,0.538,6.072,100.0,4.175,4.0,307.0,21.0,376.73,13.04,14.5
32,1.38799,0.0,8.14,0.0,0.538,5.95,82.0,3.99,4.0,307.0,21.0,232.6,27.71,13.2
33,1.15172,0.0,8.14,0.0,0.538,5.701,95.0,3.7872,4.0,307.0,21.0,358.77,18.35,13.1
34,1.61282,0.0,8.14,0.0,0.538,6.096,96.9,3.7598,4.0,307.0,21.0,248.31,20.34,13.5
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
39,0.02763,75.0,2.95,0.0,0.428,6.595,21.8,5.4011,3.0,252.0,18.3,395.63,4.32,30.8
40,0.03359,75.0,2.95,0.0,0.428,7.024,15.8,5.4011,3.0,252.0,18.3,395.62,1.98,34.9
41,0.12744,0.0,6.91,0.0,0.448,6.77,2.9,5.7209,3.0,233.0,17.9,385.41,4.84,26.6
42,0.1415,0.0,6.91,0.0,0.448,6.169,6.6,5.7209,3.0,233.0,17.9,383.37,5.81,25.3
43,0.15936,0.0,6.91,0.0,0.448,6.211,6.5,5.7209,3.0,233.0,17.9,394.46,7.44,24.7
44,0.12269,0.0,6.91,0.0,0.448,6.069,40.0,5.7209,3.0,233.0,17.9,389.39,9.55,21.2
45,0.17142,0.0,6.91,0.0,0.448,5.682,33.8,5.1004,3.0,233.0,17.9,396.9,10.21,19.3
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310,2.63548,0.0,9.9,0.0,0.544,4.973,37.8,2.5194,4.0,304.0,18.4,350.45,12.64,16.1
311,0.79041,0.0,9.9,0.0,0.544,6.122,52.8,2.6403,4.0,304.0,18.4,396.9,5.98,22.1
312,0.26169,0.0,9.9,0.0,0.544,6.023,90.4,2.834,4.0,304.0,18.4,396.3,11.72,19.4
313,0.26938,0.0,9.9,0.0,0.544,6.266,82.8,3.2628,4.0,304.0,18.4,393.39,7.9,21.6
314,0.3692,0.0,9.9,0.0,0.544,6.567,87.3,3.6023,4.0,304.0,18.4,395.69,9.28,23.8
315,0.25356,0.0,9.9,0.0,0.544,5.705,77.7,3.945,4.0,304.0,18.4,396.42,11.5,16.2
316,0.31827,0.0,9.9,0.0,0.544,5.914,83.2,3.9986,4.0,304.0,18.4,390.7,18.33,17.8
317,0.24522,0.0,9.9,0.0,0.544,5.782,71.7,4.0317,4.0,304.0,18.4,396.9,15.94,19.8
318,0.40202,0.0,9.9,0.0,0.544,6.382,67.2,3.5325,4.0,304.0,18.4,395.21,10.36,23.1
319,0.47547,0.0,9.9,0.0,0.544,6.113,58.8,4.0019,4.0,304.0,18.4,396.23,12.73,21.0
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321,0.18159,0.0,7.38,0.0,0.493,6.376,54.3,4.5404,5.0,287.0,19.6,396.9,6.87,23.1
322,0.35114,0.0,7.38,0.0,0.493,6.041,49.9,4.7211,5.0,287.0,19.6,396.9,7.7,20.4
323,0.28392,0.0,7.38,0.0,0.493,5.708,74.3,4.7211,5.0,287.0,19.6,391.13,11.74,18.5
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327,0.24103,0.0,7.38,0.0,0.493,6.083,43.7,5.4159,5.0,287.0,19.6,396.9,12.79,22.2
328,0.06617,0.0,3.24,0.0,0.46,5.868,25.8,5.2146,4.0,430.0,16.9,382.44,9.97,19.3
329,0.06724,0.0,3.24,0.0,0.46,6.333,17.2,5.2146,4.0,430.0,16.9,375.21,7.34,22.6
330,0.04544,0.0,3.24,0.0,0.46,6.144,32.2,5.8736,4.0,430.0,16.9,368.57,9.09,19.8
331,0.05023,35.0,6.06,0.0,0.4379,5.706,28.4,6.6407,1.0,304.0,16.9,394.02,12.43,17.1
332,0.03466,35.0,6.06,0.0,0.4379,6.031,23.3,6.6407,1.0,304.0,16.9,362.25,7.83,19.4
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334,0.03738,0.0,5.19,0.0,0.515,6.31,38.5,6.4584,5.0,224.0,20.2,389.4,6.75,20.7
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336,0.03427,0.0,5.19,0.0,0.515,5.869,46.3,5.2311,5.0,224.0,20.2,396.9,9.8,19.5
337,0.03041,0.0,5.19,0.0,0.515,5.895,59.6,5.615,5.0,224.0,20.2,394.81,10.56,18.5
338,0.03306,0.0,5.19,0.0,0.515,6.059,37.3,4.8122,5.0,224.0,20.2,396.14,8.51,20.6
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342,0.02498,0.0,1.89,0.0,0.518,6.54,59.7,6.2669,1.0,422.0,15.9,389.96,8.65,16.5
343,0.02543,55.0,3.78,0.0,0.484,6.696,56.4,5.7321,5.0,370.0,17.6,396.9,7.18,23.9
344,0.03049,55.0,3.78,0.0,0.484,6.874,28.1,6.4654,5.0,370.0,17.6,387.97,4.61,31.2
345,0.03113,0.0,4.39,0.0,0.442,6.014,48.5,8.0136,3.0,352.0,18.8,385.64,10.53,17.5
346,0.06162,0.0,4.39,0.0,0.442,5.898,52.3,8.0136,3.0,352.0,18.8,364.61,12.67,17.2
347,0.0187,85.0,4.15,0.0,0.429,6.516,27.7,8.5353,4.0,351.0,17.9,392.43,6.36,23.1
348,0.01501,80.0,2.01,0.0,0.435,6.635,29.7,8.344,4.0,280.0,17.0,390.94,5.99,24.5
349,0.02899,40.0,1.25,0.0,0.429,6.939,34.5,8.7921,1.0,335.0,19.7,389.85,5.89,26.6
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351,0.0795,60.0,1.69,0.0,0.411,6.579,35.9,10.7103,4.0,411.0,18.3,370.78,5.49,24.1
352,0.07244,60.0,1.69,0.0,0.411,5.884,18.5,10.7103,4.0,411.0,18.3,392.33,7.79,18.6
353,0.01709,90.0,2.02,0.0,0.41,6.728,36.1,12.1265,5.0,187.0,17.0,384.46,4.5,30.1
354,0.04301,80.0,1.91,0.0,0.413,5.663,21.9,10.5857,4.0,334.0,22.0,382.8,8.05,18.2
355,0.10659,80.0,1.91,0.0,0.413,5.936,19.5,10.5857,4.0,334.0,22.0,376.04,5.57,20.6
356,8.98296,0.0,18.1,1.0,0.77,6.212,97.4,2.1222,24.0,666.0,20.2,377.73,17.6,17.8
357,3.8497,0.0,18.1,1.0,0.77,6.395,91.0,2.5052,24.0,666.0,20.2,391.34,13.27,21.7
358,5.20177,0.0,18.1,1.0,0.77,6.127,83.4,2.7227,24.0,666.0,20.2,395.43,11.48,22.7
359,4.26131,0.0,18.1,0.0,0.77,6.112,81.3,2.5091,24.0,666.0,20.2,390.74,12.67,22.6
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361,3.83684,0.0,18.1,0.0,0.77,6.251,91.1,2.2955,24.0,666.0,20.2,350.65,14.19,19.9
362,3.67822,0.0,18.1,0.0,0.77,5.362,96.2,2.1036,24.0,666.0,20.2,380.79,10.19,20.8
363,4.22239,0.0,18.1,1.0,0.77,5.803,89.0,1.9047,24.0,666.0,20.2,353.04,14.64,16.8
364,3.47428,0.0,18.1,1.0,0.718,8.78,82.9,1.9047,24.0,666.0,20.2,354.55,5.29,21.9
365,4.55587,0.0,18.1,0.0,0.718,3.561,87.9,1.6132,24.0,666.0,20.2,354.7,7.12,27.5
366,3.69695,0.0,18.1,0.0,0.718,4.963,91.4,1.7523,24.0,666.0,20.2,316.03,14.0,21.9
367,13.5222,0.0,18.1,0.0,0.631,3.863,100.0,1.5106,24.0,666.0,20.2,131.42,13.33,23.1
368,4.89822,0.0,18.1,0.0,0.631,4.97,100.0,1.3325,24.0,666.0,20.2,375.52,3.26,50.0
369,5.66998,0.0,18.1,1.0,0.631,6.683,96.8,1.3567,24.0,666.0,20.2,375.33,3.73,50.0
370,6.53876,0.0,18.1,1.0,0.631,7.016,97.5,1.2024,24.0,666.0,20.2,392.05,2.96,50.0
371,9.2323,0.0,18.1,0.0,0.631,6.216,100.0,1.1691,24.0,666.0,20.2,366.15,9.53,50.0
372,8.26725,0.0,18.1,1.0,0.668,5.875,89.6,1.1296,24.0,666.0,20.2,347.88,8.88,50.0
373,11.1081,0.0,18.1,0.0,0.668,4.906,100.0,1.1742,24.0,666.0,20.2,396.9,34.77,13.8
374,18.4982,0.0,18.1,0.0,0.668,4.138,100.0,1.137,24.0,666.0,20.2,396.9,37.97,13.8
375,19.6091,0.0,18.1,0.0,0.671,7.313,97.9,1.3163,24.0,666.0,20.2,396.9,13.44,15.0
376,15.288,0.0,18.1,0.0,0.671,6.649,93.3,1.3449,24.0,666.0,20.2,363.02,23.24,13.9
377,9.82349,0.0,18.1,0.0,0.671,6.794,98.8,1.358,24.0,666.0,20.2,396.9,21.24,13.3
378,23.6482,0.0,18.1,0.0,0.671,6.38,96.2,1.3861,24.0,666.0,20.2,396.9,23.69,13.1
379,17.8667,0.0,18.1,0.0,0.671,6.223,100.0,1.3861,24.0,666.0,20.2,393.74,21.78,10.2
380,88.9762,0.0,18.1,0.0,0.671,6.968,91.9,1.4165,24.0,666.0,20.2,396.9,17.21,10.4
381,15.8744,0.0,18.1,0.0,0.671,6.545,99.1,1.5192,24.0,666.0,20.2,396.9,21.08,10.9
382,9.18702,0.0,18.1,0.0,0.7,5.536,100.0,1.5804,24.0,666.0,20.2,396.9,23.6,11.3
383,7.99248,0.0,18.1,0.0,0.7,5.52,100.0,1.5331,24.0,666.0,20.2,396.9,24.56,12.3
384,20.0849,0.0,18.1,0.0,0.7,4.368,91.2,1.4395,24.0,666.0,20.2,285.83,30.63,8.8
385,16.8118,0.0,18.1,0.0,0.7,5.277,98.1,1.4261,24.0,666.0,20.2,396.9,30.81,7.2
386,24.3938,0.0,18.1,0.0,0.7,4.652,100.0,1.4672,24.0,666.0,20.2,396.9,28.28,10.5
387,22.5971,0.0,18.1,0.0,0.7,5.0,89.5,1.5184,24.0,666.0,20.2,396.9,31.99,7.4
388,14.3337,0.0,18.1,0.0,0.7,4.88,100.0,1.5895,24.0,666.0,20.2,372.92,30.62,10.2
389,8.15174,0.0,18.1,0.0,0.7,5.39,98.9,1.7281,24.0,666.0,20.2,396.9,20.85,11.5
390,6.96215,0.0,18.1,0.0,0.7,5.713,97.0,1.9265,24.0,666.0,20.2,394.43,17.11,15.1
391,5.29305,0.0,18.1,0.0,0.7,6.051,82.5,2.1678,24.0,666.0,20.2,378.38,18.76,23.2
392,11.5779,0.0,18.1,0.0,0.7,5.036,97.0,1.77,24.0,666.0,20.2,396.9,25.68,9.7
393,8.64476,0.0,18.1,0.0,0.693,6.193,92.6,1.7912,24.0,666.0,20.2,396.9,15.17,13.8
394,13.3598,0.0,18.1,0.0,0.693,5.887,94.7,1.7821,24.0,666.0,20.2,396.9,16.35,12.7
395,8.71675,0.0,18.1,0.0,0.693,6.471,98.8,1.7257,24.0,666.0,20.2,391.98,17.12,13.1
396,5.87205,0.0,18.1,0.0,0.693,6.405,96.0,1.6768,24.0,666.0,20.2,396.9,19.37,12.5
397,7.67202,0.0,18.1,0.0,0.693,5.747,98.9,1.6334,24.0,666.0,20.2,393.1,19.92,8.5
398,38.3518,0.0,18.1,0.0,0.693,5.453,100.0,1.4896,24.0,666.0,20.2,396.9,30.59,5.0
399,9.91655,0.0,18.1,0.0,0.693,5.852,77.8,1.5004,24.0,666.0,20.2,338.16,29.97,6.3
400,25.0461,0.0,18.1,0.0,0.693,5.987,100.0,1.5888,24.0,666.0,20.2,396.9,26.77,5.6
401,14.2362,0.0,18.1,0.0,0.693,6.343,100.0,1.5741,24.0,666.0,20.2,396.9,20.32,7.2
402,9.59571,0.0,18.1,0.0,0.693,6.404,100.0,1.639,24.0,666.0,20.2,376.11,20.31,12.1
403,24.8017,0.0,18.1,0.0,0.693,5.349,96.0,1.7028,24.0,666.0,20.2,396.9,19.77,8.3
404,41.5292,0.0,18.1,0.0,0.693,5.531,85.4,1.6074,24.0,666.0,20.2,329.46,27.38,8.5
405,67.9208,0.0,18.1,0.0,0.693,5.683,100.0,1.4254,24.0,666.0,20.2,384.97,22.98,5.0
406,20.7162,0.0,18.1,0.0,0.659,4.138,100.0,1.1781,24.0,666.0,20.2,370.22,23.34,11.9
407,11.9511,0.0,18.1,0.0,0.659,5.608,100.0,1.2852,24.0,666.0,20.2,332.09,12.13,27.9
408,7.40389,0.0,18.1,0.0,0.597,5.617,97.9,1.4547,24.0,666.0,20.2,314.64,26.4,17.2
409,14.4383,0.0,18.1,0.0,0.597,6.852,100.0,1.4655,24.0,666.0,20.2,179.36,19.78,27.5
410,51.1358,0.0,18.1,0.0,0.597,5.757,100.0,1.413,24.0,666.0,20.2,2.6,10.11,15.0
411,14.0507,0.0,18.1,0.0,0.597,6.657,100.0,1.5275,24.0,666.0,20.2,35.05,21.22,17.2
412,18.811,0.0,18.1,0.0,0.597,4.628,100.0,1.5539,24.0,666.0,20.2,28.79,34.37,17.9
413,28.6558,0.0,18.1,0.0,0.597,5.155,100.0,1.5894,24.0,666.0,20.2,210.97,20.08,16.3
414,45.7461,0.0,18.1,0.0,0.693,4.519,100.0,1.6582,24.0,666.0,20.2,88.27,36.98,7.0
415,18.0846,0.0,18.1,0.0,0.679,6.434,100.0,1.8347,24.0,666.0,20.2,27.25,29.05,7.2
416,10.8342,0.0,18.1,0.0,0.679,6.782,90.8,1.8195,24.0,666.0,20.2,21.57,25.79,7.5
417,25.9406,0.0,18.1,0.0,0.679,5.304,89.1,1.6475,24.0,666.0,20.2,127.36,26.64,10.4
418,73.5341,0.0,18.1,0.0,0.679,5.957,100.0,1.8026,24.0,666.0,20.2,16.45,20.62,8.8
419,11.8123,0.0,18.1,0.0,0.718,6.824,76.5,1.794,24.0,666.0,20.2,48.45,22.74,8.4
420,11.0874,0.0,18.1,0.0,0.718,6.411,100.0,1.8589,24.0,666.0,20.2,318.75,15.02,16.7
421,7.02259,0.0,18.1,0.0,0.718,6.006,95.3,1.8746,24.0,666.0,20.2,319.98,15.7,14.2
422,12.0482,0.0,18.1,0.0,0.614,5.648,87.6,1.9512,24.0,666.0,20.2,291.55,14.1,20.8
423,7.05042,0.0,18.1,0.0,0.614,6.103,85.1,2.0218,24.0,666.0,20.2,2.52,23.29,13.4
424,8.79212,0.0,18.1,0.0,0.584,5.565,70.6,2.0635,24.0,666.0,20.2,3.65,17.16,11.7
425,15.8603,0.0,18.1,0.0,0.679,5.896,95.4,1.9096,24.0,666.0,20.2,7.68,24.39,8.3
426,12.2472,0.0,18.1,0.0,0.584,5.837,59.7,1.9976,24.0,666.0,20.2,24.65,15.69,10.2
427,37.6619,0.0,18.1,0.0,0.679,6.202,78.7,1.8629,24.0,666.0,20.2,18.82,14.52,10.9
428,7.36711,0.0,18.1,0.0,0.679,6.193,78.1,1.9356,24.0,666.0,20.2,96.73,21.52,11.0
429,9.33889,0.0,18.1,0.0,0.679,6.38,95.6,1.9682,24.0,666.0,20.2,60.72,24.08,9.5
430,8.49213,0.0,18.1,0.0,0.584,6.348,86.1,2.0527,24.0,666.0,20.2,83.45,17.64,14.5
431,10.0623,0.0,18.1,0.0,0.584,6.833,94.3,2.0882,24.0,666.0,20.2,81.33,19.69,14.1
432,6.44405,0.0,18.1,0.0,0.584,6.425,74.8,2.2004,24.0,666.0,20.2,97.95,12.03,16.1
433,5.58107,0.0,18.1,0.0,0.713,6.436,87.9,2.3158,24.0,666.0,20.2,100.19,16.22,14.3
434,13.9134,0.0,18.1,0.0,0.713,6.208,95.0,2.2222,24.0,666.0,20.2,100.63,15.17,11.7
435,11.1604,0.0,18.1,0.0,0.74,6.629,94.6,2.1247,24.0,666.0,20.2,109.85,23.27,13.4
436,14.4208,0.0,18.1,0.0,0.74,6.461,93.3,2.0026,24.0,666.0,20.2,27.49,18.05,9.6
437,15.1772,0.0,18.1,0.0,0.74,6.152,100.0,1.9142,24.0,666.0,20.2,9.32,26.45,8.7
438,13.6781,0.0,18.1,0.0,0.74,5.935,87.9,1.8206,24.0,666.0,20.2,68.95,34.02,8.4
439,9.39063,0.0,18.1,0.0,0.74,5.627,93.9,1.8172,24.0,666.0,20.2,396.9,22.88,12.8
440,22.0511,0.0,18.1,0.0,0.74,5.818,92.4,1.8662,24.0,666.0,20.2,391.45,22.11,10.5
441,9.72418,0.0,18.1,0.0,0.74,6.406,97.2,2.0651,24.0,666.0,20.2,385.96,19.52,17.1
442,5.66637,0.0,18.1,0.0,0.74,6.219,100.0,2.0048,24.0,666.0,20.2,395.69,16.59,18.4
443,9.96654,0.0,18.1,0.0,0.74,6.485,100.0,1.9784,24.0,666.0,20.2,386.73,18.85,15.4
444,12.8023,0.0,18.1,0.0,0.74,5.854,96.6,1.8956,24.0,666.0,20.2,240.52,23.79,10.8
445,10.6718,0.0,18.1,0.0,0.74,6.459,94.8,1.9879,24.0,666.0,20.2,43.06,23.98,11.8
446,6.28807,0.0,18.1,0.0,0.74,6.341,96.4,2.072,24.0,666.0,20.2,318.01,17.79,14.9
447,9.92485,0.0,18.1,0.0,0.74,6.251,96.6,2.198,24.0,666.0,20.2,388.52,16.44,12.6
448,9.32909,0.0,18.1,0.0,0.713,6.185,98.7,2.2616,24.0,666.0,20.2,396.9,18.13,14.1
449,7.52601,0.0,18.1,0.0,0.713,6.417,98.3,2.185,24.0,666.0,20.2,304.21,19.31,13.0
450,6.71772,0.0,18.1,0.0,0.713,6.749,92.6,2.3236,24.0,666.0,20.2,0.32,17.44,13.4
451,5.44114,0.0,18.1,0.0,0.713,6.655,98.2,2.3552,24.0,666.0,20.2,355.29,17.73,15.2
452,5.09017,0.0,18.1,0.0,0.713,6.297,91.8,2.3682,24.0,666.0,20.2,385.09,17.27,16.1
453,8.24809,0.0,18.1,0.0,0.713,7.393,99.3,2.4527,24.0,666.0,20.2,375.87,16.74,17.8
454,9.51363,0.0,18.1,0.0,0.713,6.728,94.1,2.4961,24.0,666.0,20.2,6.68,18.71,14.9
455,4.75237,0.0,18.1,0.0,0.713,6.525,86.5,2.4358,24.0,666.0,20.2,50.92,18.13,14.1
456,4.66883,0.0,18.1,0.0,0.713,5.976,87.9,2.5806,24.0,666.0,20.2,10.48,19.01,12.7
457,8.20058,0.0,18.1,0.0,0.713,5.936,80.3,2.7792,24.0,666.0,20.2,3.5,16.94,13.5
458,7.75223,0.0,18.1,0.0,0.713,6.301,83.7,2.7831,24.0,666.0,20.2,272.21,16.23,14.9
459,6.80117,0.0,18.1,0.0,0.713,6.081,84.4,2.7175,24.0,666.0,20.2,396.9,14.7,20.0
460,4.81213,0.0,18.1,0.0,0.713,6.701,90.0,2.5975,24.0,666.0,20.2,255.23,16.42,16.4
461,3.69311,0.0,18.1,0.0,0.713,6.376,88.4,2.5671,24.0,666.0,20.2,391.43,14.65,17.7
462,6.65492,0.0,18.1,0.0,0.713,6.317,83.0,2.7344,24.0,666.0,20.2,396.9,13.99,19.5
463,5.82115,0.0,18.1,0.0,0.713,6.513,89.9,2.8016,24.0,666.0,20.2,393.82,10.29,20.2
464,7.83932,0.0,18.1,0.0,0.655,6.209,65.4,2.9634,24.0,666.0,20.2,396.9,13.22,21.4
465,3.1636,0.0,18.1,0.0,0.655,5.759,48.2,3.0665,24.0,666.0,20.2,334.4,14.13,19.9
466,3.77498,0.0,18.1,0.0,0.655,5.952,84.7,2.8715,24.0,666.0,20.2,22.01,17.15,19.0
467,4.42228,0.0,18.1,0.0,0.584,6.003,94.5,2.5403,24.0,666.0,20.2,331.29,21.32,19.1
468,15.5757,0.0,18.1,0.0,0.58,5.926,71.0,2.9084,24.0,666.0,20.2,368.74,18.13,19.1
469,13.0751,0.0,18.1,0.0,0.58,5.713,56.7,2.8237,24.0,666.0,20.2,396.9,14.76,20.1
470,4.34879,0.0,18.1,0.0,0.58,6.167,84.0,3.0334,24.0,666.0,20.2,396.9,16.29,19.9
471,4.03841,0.0,18.1,0.0,0.532,6.229,90.7,3.0993,24.0,666.0,20.2,395.33,12.87,19.6
472,3.56868,0.0,18.1,0.0,0.58,6.437,75.0,2.8965,24.0,666.0,20.2,393.37,14.36,23.2
473,4.64689,0.0,18.1,0.0,0.614,6.98,67.6,2.5329,24.0,666.0,20.2,374.68,11.66,29.8
474,8.05579,0.0,18.1,0.0,0.584,5.427,95.4,2.4298,24.0,666.0,20.2,352.58,18.14,13.8
475,6.39312,0.0,18.1,0.0,0.584,6.162,97.4,2.206,24.0,666.0,20.2,302.76,24.1,13.3
476,4.87141,0.0,18.1,0.0,0.614,6.484,93.6,2.3053,24.0,666.0,20.2,396.21,18.68,16.7
477,15.0234,0.0,18.1,0.0,0.614,5.304,97.3,2.1007,24.0,666.0,20.2,349.48,24.91,12.0
478,10.233,0.0,18.1,0.0,0.614,6.185,96.7,2.1705,24.0,666.0,20.2,379.7,18.03,14.6
479,14.3337,0.0,18.1,0.0,0.614,6.229,88.0,1.9512,24.0,666.0,20.2,383.32,13.11,21.4
480,5.82401,0.0,18.1,0.0,0.532,6.242,64.7,3.4242,24.0,666.0,20.2,396.9,10.74,23.0
481,5.70818,0.0,18.1,0.0,0.532,6.75,74.9,3.3317,24.0,666.0,20.2,393.07,7.74,23.7
482,5.73116,0.0,18.1,0.0,0.532,7.061,77.0,3.4106,24.0,666.0,20.2,395.28,7.01,25.0
483,2.81838,0.0,18.1,0.0,0.532,5.762,40.3,4.0983,24.0,666.0,20.2,392.92,10.42,21.8
484,2.37857,0.0,18.1,0.0,0.583,5.871,41.9,3.724,24.0,666.0,20.2,370.73,13.34,20.6
485,3.67367,0.0,18.1,0.0,0.583,6.312,51.9,3.9917,24.0,666.0,20.2,388.62,10.58,21.2
486,5.69175,0.0,18.1,0.0,0.583,6.114,79.8,3.5459,24.0,666.0,20.2,392.68,14.98,19.1
487,4.83567,0.0,18.1,0.0,0.583,5.905,53.2,3.1523,24.0,666.0,20.2,388.22,11.45,20.6
488,0.15086,0.0,27.74,0.0,0.609,5.454,92.7,1.8209,4.0,711.0,20.1,395.09,18.06,15.2
489,0.18337,0.0,27.74,0.0,0.609,5.414,98.3,1.7554,4.0,711.0,20.1,344.05,23.97,7.0
490,0.20746,0.0,27.74,0.0,0.609,5.093,98.0,1.8226,4.0,711.0,20.1,318.43,29.68,8.1
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
#
with open('Xconv.describe.txt', 'w') as f:
print(Xconv.describe(), file=f)

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(type(Xconv.describe()))
#<class 'pandas.core.frame.DataFrame'>
#
#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]
'''
#
#print(Xconv.describe().columns)
'''
Index(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX',
'PTRATIO', 'B', 'LSTAT'],
dtype='object')
'''
#
#print(Xconv.describe()[xname])
'''
count 5.060000e+02
mean -4.563763e-17
std 1.000990e+00
min -3.880249e+00
25% -5.686303e-01
50% -1.084655e-01
75% 4.827678e-01
max 3.555044e+00
Name: RM, dtype: float64
'''
#
#print(Xconv.describe()[xname].loc['mean'])
#-4.563762630870209e-17
#
with open('Xconv.describe.txt', 'w') as f:
print(Xconv.describe(), file=f)

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
#
with open('Xconv.describe.txt', 'w') as f:
print(Xconv.describe(), file=f)

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: All Xs')
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()

othermlr.py

############### Multiple Linear Regression (by selected two dependent variables x1 and x2) ###############

########## Run this script on Terminal of MacOS as follows:
#
#python3 mlrrwstnm.py (csv data file) (clif intercept file) (clif coefficients file) (dependent variable Y) (specified single independent variable x1) (x2)
#
#For instance,
#python3 othermlr.py Xconv_Y_Ypred_YpredSingle.csv clifIntercept.txt clifCoefficients.txt Y RM LSTAT

########## import

import sys
import pandas as pd
import matplotlib.pyplot as plt

########## arguments

dfname = str(sys.argv[1]) # e.g., Xconv_Y_Ypred_YpredSingle.csv
clifI = str(sys.argv[2]) #clifIntercept.txt
clifC = str(sys.argv[3]) #clifCoefficients.txt
yname = str(sys.argv[4]) # e.g., Y (dependent vairible)
xname1 = str(sys.argv[5]) # e.g., RM (one of multiple indepdent variables)
xname2 = str(sys.argv[6]) # e.g., LSAT (one of multiple indepdent variables)

########## data load

df = pd.read_csv(dfname, index_col=0)
#print(df)
'''
CRIM ZN INDUS CHAS ... LSTAT Y Ypred YpredSingle
0 -0.419782 0.284830 -1.287909 -0.272599 ... -1.075562 24.0 30.003843 23.639060
1 -0.417339 -0.487722 -0.593381 -0.272599 ... -0.492439 21.6 25.025562 23.052341
2 -0.417342 -0.487722 -0.593381 -0.272599 ... -1.208727 34.7 30.567597 25.963078
3 -0.416750 -0.487722 -1.306878 -0.272599 ... -1.361517 33.4 28.607036 25.250633
4 -0.412482 -0.487722 -1.306878 -0.272599 ... -1.026501 36.2 27.943524 25.818303
.. ... ... ... ... ... ... ... ... ...
501 -0.413229 -0.487722 0.115738 -0.272599 ... -0.418147 22.4 23.533341 23.707638
502 -0.415249 -0.487722 0.115738 -0.272599 ... -0.500850 20.6 22.375719 21.905571
503 -0.413447 -0.487722 0.115738 -0.272599 ... -0.983048 23.9 27.627426 25.166816
504 -0.407764 -0.487722 0.115738 -0.272599 ... -0.865302 22.0 26.127967 24.473421
505 -0.415000 -0.487722 0.115738 -0.272599 ... -0.669058 11.9 22.344212 21.562684

[506 rows x 16 columns]
'''

##### intercept b0

f0 = open(clifI)
b0 = f0.read()
f0.close()
#print(type(b0))
#<class 'str'>
b0 = float(b0)
#print(b0)
#22.532806324110673

##### coefficients b1 and b2
dfb = pd.read_csv(clifC, delim_whitespace=True)
#
#print(dfb)
'''
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(dfb.columns)
#Index(['Name', 'Coefficients'], dtype='object')
#
#print(dfb.columns[0])
#Name

#print(dfb.columns[1])
#Coefficients
#
#print(dfb['Name'])
#print(dfb['Coefficients'])

#print(float(dfb[dfb.Name == xname1]['Coefficients']))
#print(float(dfb[dfb.eval(dfb.columns[0]) == xname1]['Coefficients']))
#2.67423
#print(type(float(dfb[dfb.eval(dfb.columns[0]) == xname1]['Coefficients'])))
#<class 'float'>
#
#print(float(dfb[dfb.eval(dfb.columns[0]) == xname1]['Coefficients']))
#2.67423
#
#print(float(dfb[dfb.eval(dfb.columns[0]) == xname1][dfb.columns[1]]))
#2.67423
#print(
#type(
#float(dfb[dfb.eval(dfb.columns[0]) == xname1][dfb.columns[1]])
#)
#)
#<class 'float'>

b1 = float(dfb[dfb.eval(dfb.columns[0]) == xname1][dfb.columns[1]])
#print(b1)
#2.67423

b2 = float(dfb[dfb.eval(dfb.columns[0]) == xname2][dfb.columns[1]])
#print(b2)
#-3.7436269999999996

#print(df[xname1])
#print(df[xname2])

Ypred2 = b0 + b1 * df[xname1] + b2 * df[xname2]
#
#print(Ypred2)
#print(type(Ypred2))
#<class 'pandas.core.series.Series'>

Ypred2 = pd.DataFrame(Ypred2)
#print(Ypred2)
Ypred2 = Ypred2.rename(columns={0: 'Ypred2'})
#print(Ypred2)

Xconv_Y_Ypred_YpredSingle_Ypred2 = pd.concat([df, Ypred2], axis=1)
Xconv_Y_Ypred_YpredSingle_Ypred2.to_csv('Xconv_Y_Ypred_YpredSingle_Ypred2.csv', header=True, index=True)

########## Multiple Linear Regeression by using xname1 and xname2: plot xname1

plt.figure(3)

plt.title('Multiple Linear Regression: ' + str(xname1) + ' & ' + str(xname2))
plt.xlabel(xname1, fontsize=14)
plt.ylabel(yname, fontsize=14)

plt.scatter(Xconv_Y_Ypred_YpredSingle_Ypred2.eval(xname1), Xconv_Y_Ypred_YpredSingle_Ypred2.eval(yname), c='blue', label='Y & X1')
plt.scatter(Xconv_Y_Ypred_YpredSingle_Ypred2.eval(xname1), Xconv_Y_Ypred_YpredSingle_Ypred2.Ypred2, c='red', label='Ypred2 (Predicted Y) & X1')

plt.xlim(min(Xconv_Y_Ypred_YpredSingle_Ypred2.eval(xname1)), max(Xconv_Y_Ypred_YpredSingle_Ypred2.eval(xname1)))
plt.ylim(
min(min(Xconv_Y_Ypred_YpredSingle_Ypred2[yname]), min(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred']), min(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred2'])),
max(max(Xconv_Y_Ypred_YpredSingle_Ypred2[yname]), max(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred']), max(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred2']))
)
#print(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred2'])
#print(min(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred2']))
#1.0691449482732711

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_Multiple_Linear_Regression_" + str(xname1) + "_and_" + str(xname2) + "_x-axis_" + str(xname1) + ".png")
plt.show()

########## Multiple Linear Regeression by using xname1 and xname2: plot xname2

plt.figure(4)

plt.title('Multiple Linear Regression: ' + str(xname1) + ' & ' + str(xname2))
plt.xlabel(xname2, fontsize=14)
plt.ylabel(yname, fontsize=14)

plt.scatter(Xconv_Y_Ypred_YpredSingle_Ypred2.eval(xname2), Xconv_Y_Ypred_YpredSingle_Ypred2.Y, c='blue', label='Y & X2')
plt.scatter(Xconv_Y_Ypred_YpredSingle_Ypred2.eval(xname2), Xconv_Y_Ypred_YpredSingle_Ypred2.Ypred2, c='red', label='Ypred2 (Predicted Y) & X2')

plt.xlim(min(Xconv_Y_Ypred_YpredSingle_Ypred2.eval(xname2)), max(Xconv_Y_Ypred_YpredSingle_Ypred2.eval(xname2)))
plt.ylim(
min(min(Xconv_Y_Ypred_YpredSingle_Ypred2[yname]), min(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred']), min(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred2'])),
max(max(Xconv_Y_Ypred_YpredSingle_Ypred2[yname]), max(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred']), max(Xconv_Y_Ypred_YpredSingle_Ypred2['Ypred2']))
)

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_Multiple_Linear_Regression_" + str(xname1) + "_and_" + str(xname2) + "_x-axis_" + str(xname2) + ".png")
plt.show()

Output Files

**Xconv.describe.txt**
CRIM ZN ... B LSTAT count 5.060000e+02 5.060000e+02 ... 5.060000e+02 5.060000e+02 mean -1.123388e-16 7.898820e-17 ... -7.442444e-16 -3.089316e-16 std 1.000990e+00 1.000990e+00 ... 1.000990e+00 1.000990e+00 min -4.197819e-01 -4.877224e-01 ... -3.907193e+00 -1.531127e+00 25% -4.109696e-01 -4.877224e-01 ... 2.050715e-01 -7.994200e-01 50% -3.906665e-01 -4.877224e-01 ... 3.811865e-01 -1.812536e-01 75% 7.396560e-03 4.877224e-02 ... 4.336510e-01 6.030188e-01 max 9.933931e+00 3.804234e+00 ... 4.410519e-01 3.548771e+00 [8 rows x 13 columns]

**estXfit.summary.txt**
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.

**clifCoefficients.txt**
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

**clifIntercept.txt**
22.532806324110673

**cliffR2.txt**
0.7406426641094094

**X_Y.csv**
,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 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**Xconv_Y_Ypred_YpredSingle.csv**
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**Xconv_Y_Ypred_YpredSingle_Ypred2.csv**
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Figures

Figure_Multiple_Linear_Regression_s.png

Figure_Single_Linear_Regression_s.png

Figure_Multiple_Linear_Regression_RM_and_LSTAT_x-axis_RM.png

Figure_Multiple_Linear_Regression_RM_and_LSTAT_x-axis_LSTAT.png

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Tuesday, July 14, 2020

Package: Data Generation, Data Loading and Standardization, Initial Data Analysis, Multiple Linear Regression, Polynominal Liner Regression in Python

Tuesday, June 9, 2020

Multiple Linear Regression of Raw Data, Standardized Data, and Normalized Data, Single Linear Regression), plus Multiple Linear Regression by two selected independent variables x1 and x2

Deep Learning (Regression, Multiple Features/Explanatory Variables, Supervised Learning): Impelementation and Showing Biases and Weights

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