The data in 401K. RAW are a subset of data analyzed by Papke (1995) to study the relationship between participation in a 401(k) pension plan and the generosity of the plan. The variable prate is the percentage of eligible workers with an active account; this is the variable we would like to explain. The measure of generosity is the plan match rate, mrate. This variable gives the average amount the firm contributes to each worker’s plan for each $1 contribution by the worker. For example, if mrate 5 0.50, then a $1 contribution by the worker is matched by a 50¢ contribution by the firm. (i) Find the average participation rate and the average match rate in the sample of plans. (ii) Now, estimate the simple regression equation prate 5 bˆ 0 1 bˆ 1 mrate, and report the results along with the sample size and R-squared. (iii) Interpret the intercept in your equation. Interpret the coefficient on mrate. (iv) Find the predicted prate when mrate 5 3.5. Is this a reasonable prediction? Explain what is happening here. (v) How much of the variation in prate is explained by mrate? Is this a lot in your opinion?