# Develop the estimated regression equation that could be used to predict the percentage of games won, given the average number of passing yards per attempt. What proportion of variation in the sample values of proportion of games won does this model explain?

**There are 3 questions. **

**The assignment must be posted in an excel file with the formulas. **

- The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for the 2011 season (NFL web site, February 12, 2012)

- Develop the estimated regression equation that could be used to predict the percentage of games won, given the average number of passing yards per attempt. What proportion of variation in the sample values of proportion of games won does this model explain?
- Develop the estimated regression equation that could be used to predict the percentage of games won, given the number of interceptions thrown per attempt. What proportion of variation in the sample values of proportion of games won does this model explain?
- Develop the estimated regression equation that could be used to predict the percentage of games won, given the average number of passing yards per attempt and the number of interceptions thrown per attempt. What proportion of variation in the sample values of proportion of games won does this model explain?
- The average number of passing yards per attempt for the Kansas City Chiefs during the 2011 season was 6.2, and the team’s number of interceptions thrown per attempt was 0.036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs during the 2011 season. Compare your prediction to the actual percentage of games won by the Kansas City Chiefs. (
*Note*: For the 2011 season, the Kansas City Chiefs’ record was 7 wins and 9 losses.) - Did the estimated regression equation that uses only the average number of passing yards per attempt as the independent variable to predict the percentage of games won provide a good fit?

- A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk

is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicat- ing a smoker and 0 indicating a nonsmoker. - Develop an estimated multiple regression equation that relates risk of a stroke to the person’s age, systolic blood pressure, and whether the person is a smoker.
- Is smoking a significant factor in the risk of a stroke? Explain. Use a 0.05 level of significance.
- What is the probability of a stroke over the next 10 years for Art Speen, a 68-year old smoker who has a systolic blood pressure of 175? What action might the physician recommend for this patient?
- An insurance company will only sell its Select policy to people for whom the probability of a stroke in the next 10 years is less than 0.01. If a smoker with a systolic blood pressure of 230 applies for a Select policy, under what condition will the company sell him the policy if it adheres to this standard?
- What other factors could be included in the model as independent variables?
- Alumni donations are an important source of revenue for colleges and universities. If administrators could determine the factors that could lead to increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues. Research shows that students who are more satisfied with their contact with teachers are more likely to graduate. As a result, one might suspect that smaller class sizes and lower student/faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. The following table shows data for 48 national universities. The Graduation Rate column is the percentage of students who initially enrolled at the university and graduated. The % of Classes Under 20 column shows the percentages of classes with fewer than 20 students that are offered. The Student/Faculty Ratio column is the number of students enrolled divided by the total number of faculty. Finally, the Alumni Giving Rate column is the percentage of alumni who made a donation to the university.

**Managerial Report **

- Use methods of descriptive statistics to summarize the data.
- Develop an estimated simple linear regression model that can be used to predict the alumni giving rate, given the graduation rate. Discuss your findings.
- Develop an estimated multiple linear regression model that could be used to predict the alumni giving rate using Graduation Rate, % of Classes Under 20, and Student/ Faculty Ratio as independent variables. Discuss your findings.
- Based on the results in parts (2) and (3), do you believe another regression model may be more appropriate? Estimate this model and discuss your results.
- What conclusions and recommendations can you derive from your analysis? What universities are achieving a substantially higher alumni giving rate than would be expected, given their Graduation Rate, % of Classes Under 20, and Student/Faculty Ratio? What universities are achieving a substantially lower alumni giving rate than would be expected, given their Graduation Rate, % of Classes Under 20, and Student/ Faculty Ratio? What other independent variables could be included in the model?

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