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

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x L5 1214 17 23 30 40 47 y 40 3 15 5 25 2746 x 55 67 72 81 96 112 127 y 38 46 5370 82 9900