Exercise 8.33 presents a scatterplot displaying the relationship 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 fit for predicting wife's age from husband's age.

(a) We might wonder, is the age difference between husbands and wives consistent across ages? If this were the case, then the slope parameter would be β₁ = 1. Use the information above to evaluate if there is strong evidence that the difference in husband and wife ages differs for different ages.

(b) Write the equation of the regression line for predicting wife's age from husband's age.

(c) Interpret the slope and intercept in context.

(d) Given that R² = 0:88, what is the correlation of ages in this data set?

(e) 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?

(f) 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.

Data from Exercise 8.33

The scatterplot below summarizes husbands' and wives' heights in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. Summary output of the least squares fit for predicting wife's height from husband's height is also provided in the table.

Transcribed Image Text:

Wife's age (in years) 60- 20- 20 40 Husband's age (in years) 60 (Intercept) age_husband. Estimate Std. Error 1.5740 1.1501 0.9112 0.0259 t value 1.37 35.25 Pr(>|t|) 0.1730 0.0000 df 168