1. (Problems 1.20 and 1.24 in KNN)

The Tri-City Office Equipment Corporation sells an imported copier on a franchise basis and performs preventive maintenance and repair service on this copier. The data in copier_maintainenance.txt were collected from 45 recent calls on users to perform routine preventive maintenance service; for the ith call let xi denote the number of copiers serviced and yi the total number of minutes spent by the service person, for i = 1, 2, . . . , n = 45.

(a) Plot the data and overlay a lowess smoother. Does it seem that the simple linear regression model

yi = β0 + β1xi + εi

is appropriate? Explain.

(b) Obtain the least squares estimated linear regression function, and overlay it on a scatterplot of the data. How well does the estimated regression function fit the data?

(c) Interpret b1 in your estimated regression function.

(d) Interpret b0 in your estimated regression function. Does b0 provide any relevant information here? Explain.

(e) Obtain a point estimate of the mean service time for calls on which x = 5 copiers are serviced.

(f) Obtain a point prediction for the service time of a single call on which x = 5 copiers are to be serviced.

(g) Obtain the residuals ei = yi − (b0 + b1xi) and confirm that they sum to zero. Explain the relation between the sum of squared residuals and the quantity

(h) Obtain point estimates of σ 2 = var(εi) and σ. In what units is σ expressed?