Show that an equivalent way to perform the test for signifi cance of regression in multiple linear regression is to base the test on R2 as follows To test H0 1 2 k versus H1 at least one j 0, calculate F Rn p k R 0 2 2 1 ( ) ( ) and to reject H0 if the computed value of F0 exceeds F ,k,np , where p k 1

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Question: Show that an equivalent way to perform the test for signifi cance of regression in multiple linear regression is to base the test on R2

Show that an equivalent way to perform the test for signifi cance of regression in multiple linear regression is to base the test on R2 as follows: To test H0 :

β1 = β2 = . . . = βk versus H1 : at least one βj ≠ 0, calculate F Rn p k R 0 2

2 1 = ( ) −

( ) −

and to reject H0 if the computed value of F0 exceeds F α,k,n−p , where p = k + 1.

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