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.

library(tidyverse)
## -- Attaching packages --------------------------------------- tidyverse 1.3.0 --
## v ggplot2 3.3.2     v purrr   0.3.4
## v tibble  3.0.3     v dplyr   1.0.2
## v tidyr   1.1.2     v stringr 1.4.0
## v readr   1.4.0     v forcats 0.5.0
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
tribble(
  ~x,~Estimate,~StdError,~tvalue,~pvalue,
        "(Intercept)",1.5740,1.1501,1.37,.1730,
        "age_husband",.9112,.0259,35.25,.0000
  )
  1. 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 B_1 = 1. Use the information above to evaluate if there is strong evidence that the difference in husband and wife ages differs for different ages

No the difference in age is not consistent with the age of the husband as the slope of the linear regression is .9

Write the equation of the regression line for predicting wife’s age from husband’s age.

**wifes_age=.9*husbands_age+1.574**

Interpret the slope and intercept in context.

The slope is the rate at which the wifes age decreases in comparison to the husband. The intercept sets the initial conditions of this dynamic.

Given that R^2 = 0.88, what is the correlation of ages in this data set?

The corellation is the square root of R^2, so .94

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?

husbands_age<-55
(wifes_age=.9*husbands_age+1.574)
## [1] 51.074

**Since the R^2 is so high, I would find this value reliable.

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.

No, you should not use the same linear model to predict his wife’s age. 85 is outside of the scope of our model, meaning our data doesn’t reach to 85 years old so our model should not be used for predictions.