Refer to the IHS Journal of Hydraulic Engineering (September 2012) study of water pipes, Exercise 11.12. Recall that a team of civil engineers used regression analysis to estimate y = the ratio of repair to replacement cost of commercial pipe. The independent variable in the regression analysis was x = the diameter (in millimeters) of the pipe. Data for a sample of 13 different pipe sizes are provided in the table, followed by a Minitab simple linear regression printout.

Diameter (mm) 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

a. Find the least squares line relating ratio of repair to replacement cost (y) to pipe diameter (x) on the printout.

b. Locate the value of SSE on the printout. Is there another line with an average error of 0 that has a smaller SSE than the line, part a? Explain.

c. Interpret, practically, the values β0 and β1.

d. Use the regression line to predict the ratio of repair to replacement cost of pipe with a diameter of 800 millimeters.

e. Comment on the reliability of the prediction, part d.

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Regression Analysis: RATIO versus DIAMETER Analysis of Variance DF Adj sa adj NE F-Value p-value 0.000 0.000 Source Regresaion i 10.5067 10.8067 221.20 DIAMETER 1 10.8067 10.8067 221.20 11 0.5374 0.0489 12 11.3441 Error Total Model Summazy R-aq (adj) R-aq (pred) 94.83 1 R-aq 0.221034 95.26 92.09 Coefficients Coef ar coef -value -Value 6.678 Tecm VIr Constant DIAMETER 0.004786 0.000322 0.121 55.29 0.000 14.87 0.000 1.00 segression Equation HATIO - 6.678 + 0.004786 DIANETER 0.004786 DIAMETER