Chapter 12, Problem 100CP

True or false The variables y = annual income (thousands of dollars), x₁ = number of years of education, and x₂ = number of years experience in job are measured for all the employees having city-funded jobs in Knoxville, Tennessee. Suppose that the following regression equations and correlations apply:

1. i) $\hat{y}=10+1.0x_1,r=\mathrm{0.30.}$
2. ii) $\hat{y}=14+0.4x_2,r=\mathrm{0.60.}$

The correlation is −0.40 between x₁ and x₂. Which of the following statements are true and which are false?

1. a. The strongest sample association is between y and x₂.
2. b. A standard deviation increase in education corresponds to a predicted increase of 0.3 standard deviations in income.
3. c. There is a 30% reduction in error in using education, instead of $\bar{y}$, to predict y.
4. d. When x₁ is the predictor of y, the sum of squared residuals is larger than when x₂ is the predictor of y.
5. e. If s = 8 for the model using x₁ to predict y, then it is not unusual to observe an income of $100,000 for an employee who has 10 years of education.