8.38 Husbands and wives, Part III. Exercise 8.6 presents a scatterplot displaying the rela-tionship between husbands' and wives' ages in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. Given below is summary output of the least squares tfor predicting wife's age from husband's age. (a) (b) (d) (9) (f) \".0 I I. g :3 3.3 l ': 9. - . 0-. I: lg 920:! In. 9 ' I." .3 , - 3 g 6;?! m 20 . IIII . I I re . : -:.!"" - ' a U ... _ 0 I O T I 20 40 60 Husband's age (in years) Estimate Std. Error tvalue P >' Intercept 1.5740 1.1501 1.37 0.1730 age husband 0.9112 0.0259 35.25 0.0000 Elf = 168 We might wonder, is the age di erence between husbands and wives consistent across ages? If this were the casel then the slope parameter would be 1 = 1. Use the information above to evaluate if there is strong evidence that the di erence in husband and wife ages di ers for di erent ages. Write the equation of the regression line for predicting wife's age from husband's age. Interpret the slope and intercept in context. Given that R2 = 0:38, what is the correlation of ages in this data set? You meet a married man from Britain who is 55 years old. What would you predict his wife's age to be? How reliable is this prediction? You meet another married man from Britain who is 85 years old. Would it be wise to use the same linear model to predict his wife's age? Explain