Data on the actual cost (Y) and the estimated cost (X),in millions of dollars, for n = 26 construction projects are given in Table 2-8 in the context of Example 2.13.Figure 2-17 shows the fitted line plot for these data.
a. Reanalyze the cost data using a simple linear regression model. Construct a plot of the residuals versus the fitted values.
b. Is the regression of actual cost on estimated cost significant? Justify your answer.
c. Identify and interpret r2.
d. What are the appropriate values for the slope and intercept coefficients in the population regression function if estimated cost is a perfect predictor of expected actual cost? Are the estimated coefficients in the equation for your fitted straight line consistent with these values? Discuss.
e. Consider the plot of the residuals versus the fitted values. Does it appear as if estimated costs are, in general, more accurate predictors of actual costs for relatively inexpensive projects than for expensive projects? Why or why not?