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, 81
For 10 women:
Height: 152, 156, 158, 160, 162, 162, 164, 164, 166, 166
Weight: 52, 50, 47, 48, 52, 55, 55, 56, 60, 60
Separately 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. Check to see if a linear model is justified.
b) Estimate the regression parameters , the weight for a subject who is 160cm (does gender have an effect on this estimate? ). Draw the regression line
c) Test to see if the two factors are independent ; state your hypothesis and choice of test size.
d) Calculate the coefficient of determination and provide your interpretation
e) Is there evidence of an effect modification? ( Compare the two coefficients of determination/correlation informally).