Question

In some instances, we would rather to centralize the covariate before running the regres-sion analysis. Write down the simple linear regression and find the OLS estimators of the beta0 and beta1for this model

Answer 1

Linear Regression Model is given by:

                               (1)
So,\we can write for each observation as follows:

                           (2)                  

                               i = 1,2,..., n

To minimize the Sum of Squares:

                 (3)

From (3), we get:

                                 (4)

and

                             (5)

Equating (4) and (5) to 0, we get the Ordinary Least Squares (OLS) estimators of and as follows:

                (6)

and

              (7)

From (6), we get:

                                    (8)

and

                                          (9)

where

Thus, equations (8) and (9) give the OLS estimators o0f and .