import numpy as np
import matplotlib.pyplot as plt

X=[]
Y=[]
# load the data
for line in open("1d_Linear_regression.csv"):
	x,y= line.split(',')#line data has 2 column seperated by comma so take seperate input use split() function
	X.append(float(x));
	Y.append(float(y));
# let's turn X and Y into numpy arrays since that will be useful later
X=np.array(X)
Y=np.array(Y)
#plot only the each point
plt.scatter(X,Y)
#plt.plot(X,Y)
plt.show();
# now apply linear regression formula
deno= X.dot(X)-X.mean()*X.sum()
a=(X.dot(Y)-Y.mean()*X.sum())/deno
b=(Y.mean()*X.dot(X)-X.mean()*X.dot(Y))/deno

Yhat= a*X+b

#ploting the value
plt.scatter(X,Y)
plt.plot(X,Yhat)
plt.show()

#R squared code
d1= Y-Yhat
d2= Y-Y.mean()

r2=1-((d1.dot(d1))/(d2.dot(d2)))
print "The value of the R squared model",r2