4.41. The estimates of .... and l: in Problem 3.1 are

(a) Find the estimates of the parameters of the conditional distribution of (X3,X 4) given (xl,xz); that is, find SZISIII and S22'1 =S2Z -SZISI;ISIZ'

(b) Find the partial correlation r~4'12'

(e) Use Fisher's Z to find a confidence interval for P34'IZ with confidence 0.95.

(d) Find the sample multiple correlation coefficients between x:, and (XI' xz)
and between X4 and (XI' X2~'

(e) Test the hypotheses that X3 is independent of (XI' x2 ) and x4 is inJependent of (XI' X2) at significance levels 0.05.

Transcribed Image Text:

= (185.72 151.12 183.84 149.24)', 95.2903 52.8683 69.6617 46.1117' 52.8683 54.3600 51.3117 35.0533 S == 69.6617 51.3117 100.8067 56.5400 46.1117 35.0533 56.5400 45.0233,