Linear Regression Proof

#1
Hello! Can anyone help me in writing a proof regarding linear regression? I do not know how to go about it. I have attached the document containing the problem, and I hope you guys can help me figure things out.

Thanks for your time and help! :)
 

Dragan

Super Moderator
#2
Hello! Can anyone help me in writing a proof regarding linear regression? I do not know how to go about it. I have attached the document containing the problem, and I hope you guys can help me figure things out.

Thanks for your time and help! :)

Simply substitute for Yhat_i:

Yhat_i = Ybar + r*(Sy/Sx)*(X_i – Xbar)

and simplify while using the fact that Sum(X_i - Xbar)=0.