1. HW 18
Key

2. 22:42
Leases. This data table gives annual costs of 223 commercial leases. All of these leases provide office space in a Midwestern city in the United States. For the response, use the cost of the lease per sq ft. As the explanatory variable, use the reciprocal of the number of sq ft.

3. 22:42 a
a. Identify the leases whose values lie outside the 95% prediction intervals for leases of their size. Does the location of these data indicate a problem with the fitted model? (Are residuals on the same side?)

4. 22:42 a
a. Most of the points outside of the prediction interval are above the regression, which indicates that the regression underestimates.

5. 22:42 b
b. Given the context of the problem, list several possible lurking variables that might be responsible for the size and position of leases with large residual costs. The large residuals are typically smaller homes. Some lurking variables could be location, luxuriousness, or age.

6. 22:42 c
c. The leases with the four largest residuals have something in common. What is it, and does it help you identify a lurking variable? years old City, very close to the city center

7. 22:43
R&D Expenses. This table contains accounting and financial data that describe 324 companies operating in the information sector in The largest of these provide telephone services. One column gives the expenses on research and development (R&D), and another gives the total assets of the companies. Both columns are reported in millions of dollars. Use the logs of both variables rather than the originals. (That is, set Y to the natural log of R&D expenses, and set X to the natural log of assets. Note that the variables are recorded in millions, so 1,000=1 billion)

8. 22:43 a
a. What problem with the use of the SRM is evident in the scatterplot of y on x as well as in the plot of the residuals from the fitted equation on x?

9. 22:43 a
a. There seems to be a bulge below the line, the regression doesn’t seem to do a very good job of explaining the variation.

10. 22:43 b
b. If the residuals are nearly normal, of the values that lie outside the 95% prediction interval, what proportion should be above the fitted equation? The same amount that would be below, ½ above and ½ below.

11. 22:43 c
c. Based on the property of residuals identified in part b, can you anticipate that these residuals are not nearly normal – without needing the normal quantile plot?

12. 22:43 c
c. All the points (18) that are outside of the prediction interval are below the line. This is enough to anticipate that the residuals are not normal without a normal quantile plot. The probability of this occurring is ½ ^18 =