Consider the following regression output:

Ŷ_i = 0.2033 + 0.6560X_t

se = (0.0976) (0.1961)

r² = 0.397 RSS = 0.0544 ESS = 0.0358

where Y = labor force participation rate (LFPR) of women in 1972 and X = LFPR of women in 1968. The regression results were obtained from a sample of 19 cities in the United States.

a. How do you interpret this regression?

b. Test the hypothesis: H₀: β₂ = 1 against H₁: β₂ > 1. Which test do you use? And why? What are the underlying assumptions of the test(s) you use?

c. Suppose that the LFPR in 1968 was 0.58 (or 58 percent). On the basis of the regression results given above, what is the mean LFPR in 1972? Establish a 95 percent confidence interval for the mean prediction.

d. How would you test the hypothesis that the error term in the population regression is normally distributed? Show the necessary calculations.