A naval base is considering modifying or adding to its fleet of 48 standard aircraft. The final decision regarding the type and number of aircraft to be added depends on a comparison of cost versus...

A naval base is considering modifying or adding to its fleet of 48 standard aircraft. The final decision regarding the type and 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 of modifying the fleet. A first proposal is the quadratic model E(y)=β0+β1x+β2x2

The data provided in the accompanying table were collected on 10 naval bases of a similar size that recently expanded their fleets.

a. Fit the model to the data, then construct a residual plot versus x. Do you detect any trends? Any outliers?

b. Obtain influence diagnostics for the model. Are there any observations that have large influence on the analysis?