OLS Regression - Scale

HPW1

New Member
#1
Can anyone help me out with these questions?

Consider the simple linear regression model y = β0 + β1x + u

Suppose you first use a sample of n observations {xi, yi}ni=1 to estimate this model by OLS and obtain βˆ0, βˆ1 and R2. Then you scale {xi}ni=1 by a factor of 8 and obtain a new sample {8xi, yi}ni=1, and you re-estimate the model by OLS and obtain β ̃0, β ̃1 and R 2 .

(a) Give the expression of β ̃1 in terms of βˆ1, and justify your answer. (b) Give the expression of β ̃0 in terms of βˆ0, and justify your answer. (c) Give the expression of R ̃2 in terms of R2, and justify your answer. (d) Suppose n = 2, give the numerical value of R2, and justify your answer.