Below is the linear regression result, in which the estimated coefficients are->:
b_0 = 2.055980432211423
b_1 = 0.27828827666358774
A Python program written to obtain the above regression is
import numpy as npimport matplotlib.pyplot as pltimport pandas as pdimport numpy as npdef estimate_coefficients(x, y):# number of observations/pointsno_observation = np.size(x)# mean of x and y vectorslope_x = np.mean(x)slope_y = np.mean(y)# calculating cross-deviation and deviation about xS_xy = np.sum(y*x) - no_observation*slope_y*slope_xS_xx = np.sum(x*x) - no_observation*slope_x*slope_x# calculating regression coefficientsb_1 = S_xy / S_xxb_0 = slope_y - b_1*slope_xreturn (b_0, b_1)def plot_regression(x, y, b):# plotting the actual points as scatter plotplt.scatter(x, y, color="m",marker="o",s=30)# predicted response vectordiabetes_pred = b[0] + b[1]*x# plotting the regression lineplt.plot(x, diabetes_pred, color="g")# putting labelsplt.xlabel('x')plt.ylabel('y')# function to show plotplt.show()def main():# observations / datadiabt = pd.read_excel('diabetes.xlsx')diabArray = np.array(diabt)diabetesList = list(diabArray)obses = pd.read_excel('obesity.xlsx')obsArray = np.array(obses)obesityList = list(obsArray)obesityArray = []diabetesArray = []for fpsObesity in obesityList:for fpsDiabetes in diabetesList:if fpsDiabetes[1] == fpsObesity[1]:obesityArray.append(fpsObesity[4])diabetesArray.append(fpsDiabetes[4])obesityOnX = np.array(obesityArray)diabetesOnY = np.array(diabetesArray)# estimating coefficientscoefficient = estimate_coefficients(obesityOnX, diabetesOnY)print("coefficients are->:\nb_0 = {}\\nb_1 = {}".format(coefficient[0], coefficient[1]))# plotting regression lineplot_regression(obesityOnX, diabetesOnY, coefficient)if __name__ == "__main__":main()Currently, I will read more about residuals and how to minimize error with respect to coefficients i.e. changing b_0 and b_1.
Also will study if the error with current coefficients is minimum or not. As the shape of the graph obtained is fanning out.