Packers University\'s athletic department wants to develop its budget for the co

Question

Packers University's athletic department wants to develop its budget for the coming year, using a forecast for football attendance. Football attendance accounts for the largest portion of its revenue, and the athletic director believes attendance is directly related to the number of wins by the team as well as the money spent on promotion and advertising. The business manager has accumulated the total annual attendance figures for the past 8 years. Data is shown below. Wins Promotion (S) Attendance 29500 55700 71300 87000 75000 72000 55300 81600 36300 40100 41200 53000 44000 45600 39000 47500 1. The manager wants to develop a regression equation for this data to forecast attendance for this level of success using the number wins and promotion expenses. Use Minitab to conduct regression analysis and copy and paste the output here 2. Does the regression p value indicate a good or bad regression equation? 3. Other than the regression p value, what is an indicator of how good the equation is? Evaluate that indicator based on the value the output shows 4. What do the VIF values measure? Interpret their meaning based on the value shown. Is there a reason for concern? 5. If your answer for question 4 shows concern, use the Stepwise method to deal with it. Paste the output here. 6. Use the regression equation given to you in the output of question 5 to predict attendance if the team wins 8 games next season.

Explanation / Answer

Here dependent variable is attendance and independent variable is promotion.

We have to fit regression of attendance on promotion.

We can fit regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : attendance --> Predictors : promotion --> Results : select second option --> ok --> ok

The output is,

Regression Analysis: attendance versus promotion

Analysis of Variance

Model Summary

Coefficients

Regression Equation

26382 + 0.2572 promotion

This is the regression equation.

Now we have to test the hypothesis that,

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for independent variable.

Assume alpha = =level of significance = 0.05

Test statistic follows t-distribution.

Test statistic = 4.74

P-value = 0.003

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Promotion is significant variable.

VIF = 1.00

It indicates that multicollinearity is less.

= sqrt(VIF) = sqrt(1.00) = 1 this means that the standard error for the coefficient of that predictor variable is 1 times as large as it would be if that predictor variable were uncorrelated with the other predictor variables.

R-sq = 78.93%

It expresses the proportion of variation in attendace which is expressed by variation in promotion.

r = sqrt(R sq) = sqrt(78.93%) = 0.8884

It indicates that there is positive relationship between two variables.

ANother method to verify model is good or not :

Calculate correlation coefficient between independent and dependent variables.

Take absolute value of correlation coefficient.

Calculate critical value using Pearson correlation coefficient table with df = n-2 and alpha value (0.05,0.01,0.1,….)

If | r | > Critical value model fits well or good.

And if | r | < Critical value model doesn’t fits good.

Critical value = 0.707

Here |r| > critical value

Therefore model fits well or good.

Source DF Adj SS Adj MS F-Value P-Value Regression 1 157574650 157574650 22.48 0.003 promotion 1 157574650 157574650 22.48 0.003 Error 6 42064100 7010683 Total 7 199638750

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