2. (12' 3'+2' +2' +2+3) Consider the model Yt= a + x + t, t= 1,..., T where xt is kx 1. Let x = (,,T)' (hence r is the giant matrix without the column of 1's), e = (1,,ET)'. Assume E[ex] = 0, and E[|r] =o1. Let 3 be the OLS estimate of 3. Suppose we now multiply all the observation values (yt, t) by X>0 and estimate the model again by OLS. Let 3 be the new OLS estimate after multiplying all the observations by A. Answer the questions below and show your work. a). How much is compared with ? (Hint: the partial regression formulas would be helpful, for 3 here does not include the intercept.) b). How much is a compared with ? (Hint: use the fact that y = a + ' in both old and new data.) c). Does the R change (and if so, by how much)? d). Does the vector of estimated residuals & = yt--x change (and if so, by how much)? e). Does the value of t statistic for Ho : 3 = 0 change (and if so, by how much)?