7 Consider the straight line, Y Bo Bixi i, (i 1, 2, n) Using results for matrix forms of Y XB , and direct minimization of sums of squares (both methods), show that (yi y)(xi 7) , o y , ( ) Derive the F test for H Bo 0 For testing H Bi c, show that F test is F (1 c)2 S2 (Xi )2 where (n 2)S2 (yi y)2 ( i u) Let r be the sample correlation between y and x Show that RSS (1 12) (9i ) when c 0, show that the F test for H B1 0, is r2n 2) F 1 2 show that when c 0, for testing B1 0), F test is equivalent to T test where T (1 2) (n 2) 7 Consider the straight line, Y Bo Bixi i, (i 1, 2, n) Using results for matrix forms of Y XB , and direct minimization of sums of squares (both methods), show that (yi y)(xi 7) , o y , ( ) Derive the F test for H Bo 0 For testing H Bi c, show that F test is F (1 c)2 S2 (Xi )2 where (n 2)S2 (yi y)2 ( i u) Let r be the sample correlation between y and x Show that RSS (1 12) (9i ) when c 0, show that the F test for H B1 0, is r2n 2) F 1 2 show that when c 0, for testing B1 0), F test is equivalent to T test where T (1 2) (n 2)

Question

7  Consider the straight line, Y    Bo   Bixi   i, (i   1, 2,    n) Using results for matrix forms of Y   XB , and direct minimization of sums of squares (both methods), show that (yi   y)(xi 7)  , o   y   , (  )  Derive the F test for H  Bo   0  For testing H  Bi   c, show that F test is F  (1  c)2 S2 (Xi )2 where (n 2)S2   (yi y)2   ( i u)  Let r be the sample correlation between y and x  Show that RSS   (1 12) (9i )    when c   0, show that the F test for H   B1   0, is r2n   2) F  1   2 show that when c   0, for testing B1   0), F test is equivalent to T test where T  (1 2) (n 2) 7  Consider the straight line, Y    Bo   Bixi   i, (i   1, 2,    n) Using results for matrix forms of Y   XB , and direct minimization of sums of squares (both methods), show that (yi   y)(xi 7)  , o   y   , (  )  Derive the F test for H  Bo   0  For testing H  Bi   c, show that F test is F  (1  c)2 S2 (Xi )2 where (n 2)S2   (yi y)2   ( i u)  Let r be the sample correlation between y and x  Show that RSS   (1 12) (9i )    when c   0, show that the F test for H   B1   0, is r2n   2) F  1   2 show that when c   0, for testing B1   0), F test is equivalent to T test where T  (1 2) (n 2)

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7. Consider the straight line, Y; = Bo + Bixi + i, (i = 1, 2, ...n) Using results for matrix forms of Y =

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