# Simple linear regression of two variables

This is the code I built to implement a simple linear regression to check the impact of variable A on B. I am not interested in predicting that's why the statistical approach is important for me to focus on the descriptive analytics such as the statsmodels summary and comparing RMSE of training set and test set to see if the model did a good job or not (I'm not looking to compare Dependent variable and RMSE to check prediction quality for example). Is there anything fundamentally wrong with this approach to a simple Linear Regression?

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import statsmodels.api as sm
from scipy import stats

# Import Excel File
data = pd.read_excel("C:\\Users\\AchourAh\\Desktop\\Simple_Linear_Regression\\SP Level Simple Linear Regression\\PL32_PMM_03_09_2018_SP_Level.xlsx",'Sheet1') #Import Excel file

# Replace null values of the whole dataset with 0
data1 = data.fillna(0)
print(data1)

# Extraction of the independent and dependent variable
X = data1.iloc[0:len(data1),1].values.reshape(-1, 1) #Extract the column of  the COPCOR SP we are going to check its impact
Y = data1.iloc[0:len(data1),2].values.reshape(-1, 1) #Extract the column of the PAUS SP

# Data Splitting to train and test set
from sklearn.model_selection import train_test_split
X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size =0.25,random_state=42)

# Training the model and Evaluation of the Model
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
import math
from sklearn import model_selection
from sklearn.model_selection import KFold
lm = LinearRegression() #create an lm object of LinearRegression Class
lm.fit(X_train, Y_train)  #train our LinearRegression model using the   training set of data - dependent and independent variables as parameters.  Teaching lm that Y_train values are all corresponding to X_train.
kf = KFold(n_splits=6, random_state=None)
for train_index, test_index in kf.split(X_train):
print("Train:", train_index, "Validation:",test_index)
X_train1, X_test1 = X[train_index], X[test_index]
Y_train1, Y_test1 = Y[train_index], Y[test_index]
results = -1 * model_selection.cross_val_score(lm, X_train1,  Y_train1,scoring='neg_mean_squared_error', cv=kf)
print(results)
print(results.mean())
mse_test = mean_squared_error(X_test, Y_test)
print(mse_test)

#RMSE values interpretation test and train are similar no overfitting or underfitting the model performed well
print(math.sqrt(mse_test))
print(math.sqrt(results.mean()))

# Graph of the Training model
plt.scatter(X_train, Y_train, color = 'red')#plots scatter graph of COP COR  against PAUS for values in X_train and y_train
plt.plot(X_train, lm.predict(X_train), color = 'blue')#plots the graph of predicted PAUS against COP COR.
plt.title('SP000905974')
plt.xlabel('COP COR Quantity')
plt.ylabel('PAUS Quantity')
plt.show()#Show the graph

# Statistical Analysis of the training set with Statsmodels
X2 = sm.add_constant(X_train) # add a constant to the model
est = sm.OLS(Y_train, X2).fit()
print(est.summary()) # print the results