Problem: Research and Development. A company is interested in the relationship between profit (PROFIT) on a number of projects and two explanatory variables. These variables are the expenditure on research and development for the project (RD) and a measure of risk assigned at the outset of the project (RISK). PROFIT is measured in thousands of dollars and RD is measured in hundreds of dollars. The scatterplots of PROFIT versus RISK and PROFIT versus RD are shown in Figures 6.17 and 6.18, respectively. The regression results are in Figure 6.19. The residual plots of the standardized residuals versus the fitted values, RISK, and RD are shown in Figures 6.20, 6.21, and 6.22, respectively. Using any of the given outputs, does the linearity assumption appear to be violated? Justify your answer. If you answered yes, state how the violation might be corrected. Then try your correction using a computer regression routine. Does your model appear to be an improvement over the original model? Justify your answer. These data are available in a file named RD6 on the CD.

Problem: Petroleum Imports. The data for U.S. monthly petroleum imports from 1991 through 1997 appear in Table 6.4. Figure 6.54 shows the regression results for the regression of monthly petroleum imports (in millions of barrels) on the one-period lagged imports. Figure $6.55$ is a time-series plot of the standardized residuals from this regression. Figure 6.56 shows the plot of the standardized residuals versus the fitted values. Figures 6.57 and 6.58 show, respectively, plots of the DFITS and Cook's D statistics. These data are available in a file named PETRO6 on the CD. Are there any unusual observations that should be checked before accepting these regression results? If so, which observations? Can you determine what might be causing certain observations to appear unusual? Justify your answers.

6. Major League Baseball Salaries. The owners of Major League Baseball (MLB) teams are concerned with rising salaries (as are owners of all professional sports teams). Table 3.9 provides the average salary (AVESAL) of the \(30 \mathrm{MLB}\) teams for the 2002 season. Also provided is the number of wins (WINS) for each team during the 2002 season. In Chapter 3 you were asked to run the regression of WINS on AVESAL to determine whether there is evidence that teams with higher total payrolls tend to be more successful. Rerun this regression now. The data are in the file BBALL6 on the CD. Examine the standardized residuals. Are there any teams that appear to be winning more games than expected given the size of their payroll? Justify your answer. Which team or teams, if any, did you identify?

Solution: The following regression results are obtained:

The following residual plots are obtained:

Problem: Coal Mining Fatalities. The file CUTTING6 on the CD contains data on the following two variables:

FATALS: the annual number of fatalities from gas and dust explosions in coal mines for the years 1915 to 1978

CUTTING: the number of cutting machines in use

Run the regression using FATALS as the dependent variable and CUTTING as the independent variable.

Based on an examination of scatterplots and residual plots, do any assumptions of the linear regression model appear to be violated? If so, which one (or ones)? If any violations are detected, suggest possible corrections. Rerun the regression with the suggested corrections and compare your results to the original results. Be sure to do residual plots for the model using the suggested correction. Which model do you prefer and why?

Problem: Computer Repair. A computer repair service is examining the time taken on service calls. The data obtained for 30 service calls are in the file named COMPREP6 on the CD. Information obtained includes:

number of machines to be repaired (NUMBER)

years of experience of service person (EXPER)

time taken (in minutes) to provide service (TIME)

Develop a model to predict average time on the service calls using EXPER and NUMBER as explanatory variables. Use scatterplots and residual plots to determine whether any of the assumptions of the linear regression model have been violated. If any of the assumptions have been violated, state which one or ones and suggest possible corrections. Try the new model to see if it is an improvement over the original one. Be sure to examine residual plots from the corrected model (or models) that you try. Indicate your choice for the best model.

Price: $28.21

Solution: The downloadable solution consists of 17 pages, 1121 words and 26 charts.
Deliverable: Word Document