Solved: Exercise 16 of Section 12.2 gave data on x =

Chapter 12, Problem 32E

(choose chapter or problem)

Problem 32E

Exercise 16 of Section 12.2 gave data on x = rainfall volume and y = runoff volume (both in m3). Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff, and then calculate a confidence interval for the true average change in runoff volume associated with a 1 m3 increase in rainfall volume.

Reference exercise 16

p>The article “Characterization of Highway Runoff in Austin, Texas, Area” (J. of Envir. Engr., 1998: 131–137) gave a scatter plot, along with the least squares line, of x = rainfull volume (m3) and y = runoff volume (m3 ) for a particular location. The accompanying values were read from the plot.

a. Does a scatter plot of the data support the use of the simple linear regression model?

b. Calculate point estimates of the slope and intercept of the population regression line.

c. Calculate a point estimate of the true average runoff volume when rainfall volume is 50.

d. Calculate a point estimate of the standard deviation σ.

e. What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall?