Suppose that a linear regression model with k = 2 regressors has been fit to n = 25 observations and R 2 = 0.90. a. Test for significance of regression at a = 0.05. Use the results of the Exercise...

Suppose that a linear regression model with k = 2 regressors has been fit to n = 25 observations and R²
= 0.90.

a. Test for significance of regression at a = 0.05. Use the results of the Exercise 3.14.

b. What is the smallest value of R²
that would lead to the conclusion of a significant regression if λ = 0.05? Are you surprised at how small this value of R²
is?

Exercise 3.14
Show that an equivalent way to perform the test for significance of regression in multiple linear regression is to base the test on R
²
as follows. To test H₀
: B₁
= B₂
= · · · = B_k

 versus H₁: at least one B_j
= 0, calculate

and reject H₀
if the computed value of F₀
exceeds F_a.k.n-p•
where p = k + 1.