(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.
8.4 Refer to the data in Exercise 8.3, but in the context of a multiple regres-
sion problem with two independent variables: the net food supply
(x 1 ¼x) and its square (x 2 ¼x^2 ).
(a)Taken collectively, do the two independent variables contribute sig-
nificantly to the variation in the number of infant deaths?
(b)Calculate the coe‰cient of multiple determination and provide your
interpretation.
(c)Fit the multiple regression model to obtain estimates of individual
regression coe‰cients and their standard errors, and draw your con-
clusions: especially, the conditional contribution of the quadratic
term.
8.5 The following are the heights (measured to the nearest 2 cm) and the
weights (measured to the nearest kilogram) of 10 men:Height 162 168 174 176 180 180 182 184 186 186
Weight 65 65 84 63 75 76 82 65 80 81and 10 women:Height 152 156 158 160 162 162 164 164 166 166
Weight 52 50 47 48 52 55 55 56 60 60Separately for each group, men and women:
(a)Draw a scatter diagram to show a possible association between the
weight (used as the dependent variable) and the height and check to
see if a linear model is justified.
(b)Estimate the regression parameters, the weight for a subject who is
160 cm (does gender have an e¤ect on this estimate?), 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.)
8.6 Refer to the data in Exercise 8.5, but in the context of a multiple regres-
sion problem with three independent variables: height, gender, and
product height by gender.308 CORRELATION AND REGRESSION