Regression model: = + + .

Suppose that and are random variables, and parameters and are constants.

1. If and are negatively correlated i.e., (,) < 0, how does it impact the estimation of parameter in the linear regression model?

2. Suppose that the i.i.d samples (1,,) are realizations of the random variable , and suppose that and are independent. Given that

()=[()]2= 1()2=1

(,)= [(())(())]=1()()=1,

consider the expression for the Least Square Estimator in Page 42 of Lecture 8s slides Inventory Management III and Forecasting. Try to establish the expression for the estimator from the hints given above.