Problems 431
x 1 x 2 x 3 x 4 y
11116 4275
2 10 9 3 183
3 9 4 2 140
48 1 1 82
57 2 1 97
66 1−1 122
75 4−2 146
84 9−3 246
9316 −4 359
10225 −5 48246.The following data refer to Stanford heart transplants. It relates the survival time
of patients that have received heart transplants to their age when the transplant
occurred and to a so-called mismatch score that is supposed to be an indicator of
how well the transplanted heart should fit the recipient.Survival Time (in days) Mismatch Score Age
624 1.32 51.0
46 .61 42.5
64 1.89 54.6
1,350 .87 54.1
280 1.12 49.5
10 2.76 55.3
1,024 1.13 43.4
39 1.38 42.8
730 .96 58.4
136 1.62 52.0
836 1.58 45.0
60 .69 64.5(a) Letting the dependent variable be the logarithm of the survival time, fit
a regression on the independent variables mismatch score and age.
(b) Estimate the variance of the error term.
47.(a) Fit a multiple linear regression equation to the following data set.
(b) Test the hypothesis thatβ 0 =0.
(c) Test the hypothesis thatβ 3 =0.
(d) Test the hypothesis that the mean response at the input levelsx 1 =x 2 =
x 3 =1 is 8.5.