Estimating repair and replacement costs of water pipes.

Refer to the IHS Journal of Hydraulic Engineering (Sept.

2012) study of the repair and replacement of water pipes, Exercise 11.28

(p. 628). Recall that a team of civil engineers used regression analysis to model y = the ratio of repair to replacement cost of commercial pipe as a function of x = the diameter (in millimeters) of the pipe. Data for a sample of 13 different pipe sizes are reproduced in the accompanying table. In Exercise 11.28, you fit a straightline model to the data. Now consider the quadratic model E1y2 = b0 + b1x + b2x2. A MINITAB printout of the analysis follows in the next column.

a. Give the least squares prediction equation relating ratio of repair to replacement cost (y) to pipe diameter (x).

b. Conduct a global F-test for the model using a = .01.
What do you conclude about overall model adequacy?

c. Evaluate the adjusted coefficient of determination, R2a, for the model.

d. Give the null and alternative hypotheses for testing if the rate of increase of ratio (y) with diameter (x) is slower for larger pipe sizes.

e. Carry out the test, part

d, using a = .01.

f. Locate on the printout a 95% prediction interval for the ratio of repair to replacement cost for a pipe with a diameter of 250 millimeters. Interpret the result.

Transcribed Image Text:

Diameter Ratio 80 6.58 100 6.97 125 7.39 150 7.61 200 7.78 250 7.92 300 8.20 350 8.42 400 8.60 450 8.97 500 9.31 600 9.47 700 9.72