Question

1. Consider the following linear regression model which estimates only a constant:
Yi = β1 + ui
What will the value of ˆβ1 be? Remember we are minimizing the sum of the squared residuals.
2. Consider the following regression model with K parameters:
Yi = β1 + β2X2i + β3X3i + ... + βKXKi + ui
Now consider the F-test of the null hypothesis that all slope parameters (β2,β3,...,βK) are equal to zero. Using the equation from class:
F =（(RSSk −RSSm)/(m−k)） RSSm/(N −m)

Prove that the F statistic for this test is equivalent to the following expression:
F =（ESSm/(m−1) RSSm）/(N −m)

Hint: Your answer from question one will be helpful, make sure you correctly identify the restricted and unrestricted models, and make sure that you remember all of the relevant equations relating to RSS and R2.

Answer 1