Hello! I need help solving the following question. I'll include a screenshot at the end and the text here in case it doesn't upload.

1.Consider fitting a simple linear regression model, Yi = beta0 + beta1xi + epsilon_i with epsilon_i independent N(0, sigma^2), i = 1, 2, ..., n.

For variables x and y, let y_i_star = 2y_i and

x_i_star = 2_x_i + 5,

i = 1, ...,n

Now consider two simple linear regression models:

Model A: Yi = beta0 + beta1xi + epsilon_i

Model B: Yi_star = beta0_star + beta1_star(x_i_star) + epsilon_i

Let beta0_star_hat and beta1_star_hat be the least squares estimates for the data y_i_star, x_i_star, i = 1, ..., n

i. How are x_bar_star, y_bar_star related to x_bar, y_bar?

ii. How are sx?, sy? related to sx, sy?

iii. How are ??0?, ??1? related to ??0 , ??1 ? (beta-hat-0-star, etc.)

iv. How are SS(Res) for Model A related to SS(Res) for Model B?

v. How are R2 for Model A related to R2 for Model B?

(e) For variables x and y, let y* = 2y and x; =2x;+5, i=1,...,n. Now consider the two simple linear regression models, Model A:Y, = Bo+ Bi; +e; and Model B: Y* =8; + 8;x* +e; and, let ; and 8; be the least squares estimates for the data y; ,r; , i=1,...,n. i. [1 mark] How are i*, y* related to i, y? ii. [1 mark] How are S,+, sy- related to $1, Sy? iii. [2 marks] How are ;, ; related to Bo, B,? iv. [1 mark] How are SS(Res) for Model A related to SS(Res) for Model B? v. [1 mark] How are R" for Model A related to R' for Model B