(a) Fit the multiple regression model to obtain estimates of individual
regression coe‰cients and their standard errors. Draw your conclu-
sion concerning the conditional contribution of each factor.
(b)Within the context of the multiple regression model in part (a), does
gender alter the e¤ect of height on weight?
(c) Taken collectively, do the three independent variables contribute
significantly to the variation in weights?
(d) Calculate the coe‰cient of multiple determination and provide your
interpretation.8.7 In an assay of heparin, a standard preparation is compared with a test
preparation by observing the log clotting times (y, in seconds) of blood
containing di¤erent doses of heparin (xis the log dose) (Table E8.7).
Replicate readings are made at each dose level). Separately for each
preparation, standard and test:
TABLE E8.7
Log Clotting Times
Standard Test Log Dose
1.806 1.756 1.799 1.763 0.72
1.851 1.785 1.826 1.832 0.87
1.954 1.929 1.898 1.875 1.02
2.124 1.996 1.973 1.982 1.17
2.262 2.161 2.140 2.100 1.32(a) Draw a scatter diagram to show a possible association between the
log clotting time (used as the dependent variable) and the log dose
and check to see if a linear model is justified.
(b)Estimate the regression parameters, the log clotting time for a log
dose of 1.0 (are estimates for di¤erent preparations di¤erent?), and
draw the regression line on the same graph with the scatter diagram.
(c) Test to see if the two factors are independent; state your hypotheses
and choice of test size.
(d) Calculate the coe‰cient of determination and provide your inter-
pretation.
(e) Is there evidence of an e¤ect modification? (Compare the two
coe‰cients of determination/correlation informally.)8.8 Refer to the data in Exercise 8.7, but in the context of a multiple regres-
sion problem with three independent variables: log dose, preparation,
and product log dose by preparation.
(a) Fit the multiple regression model to obtain estimates of individual
regression coe‰cients and their standard errors. Draw your conclu-
sion concerning the conditional contribution of each factor.
EXERCISES 309