Suppose that your client suspects that the relationship between wages and health LO4 insurance likely varies by firm size. In particular, your client suspects that firms that employ at least 20 workers have a positive relationship between wages and health insurance (holding all other variables constant), whereas firms that employ fewer than 20 workers have a negative relationship (again holding all other variables constant).

(a) Explain how you would evaluate your client’s hunch by estimating a particular regression twice. Write down the regression equation that you would estimate (twice) and state which two samples you would use to estimate it.

Explain how you would use the parameter estimates from both estimations to measure the relationship between wages and health insurance and how that relationship varies with firm size.

(b) Explain how you would evaluate your client’s hunch by estimating a particular regression that includes an interaction term. Write down the regression equation that you would estimate and state which sample you would use to estimate it. Explain how you would use the parameter estimates to measure the relationship between wages and health insurance and how that relationship varies with firm size.

(c) Suppose that your client’s hunch is correct. Could the estimates of β1 that are reported in the preceding table still occur or do those estimates contradict your client’s hunch?