Question: A naval base is considering modifying or adding to its fleet of 48 standard aircraft. The final decision regarding the number of aircraft to be added depends on a comparison of cost versus effectiveness of the modified fleet. Consequently, the naval base would like to model the projected percentage increase, y, in fleet effectiveness by the end of the decade as a function of the cost, x (in millions of dollars), of modifying the fleet. A first proposal is to build a simple regression model based on the experience of ten naval bases of similar size that expanded their fleets.

(a) Develop an estimated regression model to predict fleet effectiveness based on the cost of modifications.

(b) Is the model developed in (a) useful for predicting effectiveness? Test at a 5% significance level.

(c) Interpret the estimated coefficients found in part (a), i.e. what do they mean for this particular application?

(d) Interpret the R² value.

(e) Conduct a residual analysis and comment on the results.

(f) Estimate the effectiveness of a $100,000,000 modification to an existing naval base.

(g) Develop and interpret a 95% confidence interval and a 95% prediction interval for the modification described in part (f) above.