Problem: Byron Nelson Donations. Since 1982 , the year that PGA Tour officials began tracking charitable donations from its tournaments on an annual basis, no event has contributed more to charities in its community than the Byron Nelson tournament. The amount donated each year from 1982 through 2002 (in millions of dollars) is provided in the file named DONATIONS6 on the CD. Fit a linear trend to these data.

1. What is the resulting regression equation?
2. What percentage of the variation in \(y\) has been explained by the regression?
3. Test to see whether the disturbances are positively autocorrelated. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a 0.05 level of significance. On the basis of the test result, what action should be taken?
4. Add a lagged value of the dependent variable to the equation. Your equation will now have a term for linear trend as well as the lagged dependent variable. What is the resulting regression equation?
5. Test to see whether the disturbances are positively autocorrelated. (What test should you use for this model?) State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a 0.05 level of significance. On the basis of the test result, what action should be taken?
6. Use your choice of the "best" model to predict donations for 2003. Find a point prediction and a 95% prediction interval.

Solution: (a) We get

Problem: Estimating Residential Real Estate Values. The Tarrant County Appraisal District must appraise properties for the entire county. The appraisal district uses data such as square footage of the individual houses as well as location, depreciation, and physical condition of an entire neighborhood to derive individual appraisal values on each house. This avoids labor-intensive reinspection each year.

Regression can be used to establish the weight assigned to various factors used in assessing values. For example, the file REALEST6 on the CD contains the value (VALUE), size in square feet (SIZE), a physical condition index (CONDITION), and a depreciation factor (DEPRECIATION) for a sample of 100 Tarrant County houses (in 1990). Using these data, develop an equation that might be useful to the appraisal district in assessing values.

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.

Discuss how the equation developed here could be used to value houses. What would be the value assigned to a 1400 -square-foot house with physical condition index 0.70 and depreciation factor 0.02?

Problem: Salaries. A large state university is interested in comparing salaries of its graduates (BA or BS) in the following areas: business, education, engineering, and liberal arts. Five graduates in each major are randomly selected and their starting salaries recorded. These data are available in a file named SALMAJ9 on the CD. In he MINITAB file, the variable SALARY will be one column. The variable MAJOR is a second column coded as \(1=\) business, \(2=\) education, \(3=\) engineering, and \(4=\) liberal arts. The salary data are in four separate columns in the Excel spreadsheet.

1. The university wants to know if there is a difference in the population average salaries for the four majors. Use a \(5 \%\) level of significance in making the decision. State any hypotheses to be tested, the decision rule, the test statistic, and your decision.
2. Find a \(95 \%\) interval estimate for the difference between the business and engineering mean salaries.
3. Use the Tukey or Bonferroni method to compare all possible pairs of means with a familywise confidence level of \(90 \%\). Use the familywise comparisons to determine if there is a significant difference in the population mean salaries for

1. business and education majors
2. business and engineering majors
3. education and liberal arts majors

If so, which major has a higher mean salary in each comparison?

Price: $27.84

Solution: The downloadable solution consists of 16 pages, 1184 words and 17 charts.
Deliverable: Word Document