The following table gives a football team\'s season-ticket sales, percentage of
ID: 1210035 • Letter: T
Question
The following table gives a football team's season-ticket sales, percentage of games won, and number of active alumni for the years 1998-2007. 1. Compute a correlation matrix for the variables. A software statistical package is recommended. Interpret the correlation between each pair of variables. 2. Estimate a regression model for sales and Percentage of games won 3. Estimate a regression model for sales and Number of active alumni 4. If sales is the dependent variable, which of the two independent variables do you think explains sales better? Explain.Explanation / Answer
1. The Correlation Numbers are as follows
- Between Sales and No of Games: .170 : This means that for a 1 unit change in one variable the other variable changes by .170 (positive impact)
- Between Games won and No of Alumni Active Years: -.070 : This means that for a 1 unit change in no of years active for alumni, the games won % goes down by .070 units
- Between Sales of Tickets and Year of active alumni: .98: Very close positive correlation between years of active alumni and sales of tickets - higher th no of years - higher is the sales of tickets.
2. Assuming Sales are Y variable , and No of Games won as X variable, the regression equation is as follows
- Sales = 4344.28+1.22 (% of games won). This means that if % of games won increased by 1 unit, the sales of tickets will increase by 1.22. Further for both the intercept and the X variable, P - values are less than .05, and hence they are statistically significant at 95% CI. Also R-square is at .98 which is a very good value, indicating that 98% of variation in Y and explained by the X variable.
3. Assuming Sales are Y variable , and No of years of alumni active won as X variable, the regression equation is as follows
- Sales = 12244.13-6.69 (No of year active for alumni). This means that if % of games won increased by 1 unit, the sales of tickets will decrease by 6.69. Also R-square is only at .03, which is ver very bad value, indicating that only 3% of variation in Y and explained by the X variable. Hence this model should not be adopted.
4. From the above regression equations it is clear that no of games won explains sales better since the model throws up significant P-values and a much higher R-Square value.
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