Using the data on two variables x and y, a statistician regressed y on x and obtained the equation y = a+bx. A second statistician regressed x on y and obtained the equation x = 2+ 0.5y.

(i) Given that the R2 of the second regression is 0.8 and the sample mean of the y values ( ) = 10 find the values of a and b in the first regression.

(ii) Show that the two regression equations are identical if and only if R2 is equal to 1.

(iii) Show that the R2 values of the two regression models are identical to one another.

(iv) Show that the F-statistic (used for test

Question

Using the data on two variables x and y, a statistician regressed y on x and obtained the equation y = a+bx. A second statistician regressed x on y and obtained the equation x = 2+ 0.5y. 

(i)	Given that the R2 of the second regression is 0.8 and the sample mean of the y values ( ) = 10 find the values of a and b in the first regression. 

(ii)	Show that the two regression equations are identical if and only if R2 is equal to 1. 

(iii)	Show that the R2 values of the two regression models are identical to one another. 

(iv)	Show that the F-statistic (used for test