The project manager at a construction company is evaluating how crew size affects the productivity of framing jobs. He has experimented with varying crew size on a weekly basis over the past 27 weeks and has recorded weekly productivity (in jobs completed). A portion of the data is shown in the accompanying table.

Crew SizeProductivity

(#workers) (jobs/week)

2.......................................10

3.......................................12

⋮..........................................⋮

10......................................12

a. Create a scatterplot of the data. Based on the scatterplot alone, what crew size(s) seems optimal?

b. Estimate the linear and the quadratic regression models. Evaluate the two models in terms of variable significance and adjusted R 2. Which model provides the best fit? Provide an intuitive justification for the chosen model.

c. Use the best-fitting model to predict how many jobs a crew of 5 could be expected to complete in a week.

d. Estimate the cubic regression model. Would it improve the fit as compared to the quadratic regression model?