1. /30 points): The athletic director of university is interested in developing a multiple regression model that could be used to explain the variation in attendance at soccer games at his school. A sample of 16 games was selected from home games played during the past ten seasons. Data for the following factors were determined: y = Game attendance x1 = Team win/loss percentage to date x2 = Opponent win/loss percentage to date x3 = Games played this season x4 = Temperature at game time Using the information provided in the excel output, answer the following questions: a. /5 points): What percentage of the total variation in the dependent variable is explained by the four independent variables in the model? b. /5 points): Test to determine whether the overall model is statistically significant. Write your hypothesis testing. Use a = 0.05. c. /5 points): Which, if any, of the independent variables is statistically significant? Use a significance level of a = 0.08 and the p-value approach to conduct these tests. d. (5 points): Define the term collinearity and indicate the potential problems that collinearity can cause for this model. Indicate what, if any, evidence there is of collinearity problems with this regression model. Use the variance inflation factor to assist you in this analysis. Define the VIF. The VIF for the variables in this problem are: VIF Team Win/Loss % 1.509 Opponent Win/Loss % 1.570 Games Played 1.964 Temperature 1.314 e. [10 points): Develop a 95% confidence interval estimate for each of the regression slope coefficients and interpret each estimate. Are the variables statistically significant?SUMMARY OUTPUT Regression Statistics Multiple R 0.880534596 R Square 0.775341175 Adjusted R Square 0.693647057 Standard Error 1184.124723 Observations 16 ANOVA of 5S MS F Significance F Regression 4 53230058.97 13307514.74 9.490783318 0.001427993 Residual 11 15423664.97 1402151.361 Total 15 68653723.94 Coefficients Standard Error t Stat P-value Intercept 14122.24086 4335.791765 3.25713079 0.007637823 Team Win/Loss % 63.15325348 14.93880137 4.227464568 0.001418453 Opponent Win/Loss % 10.09582009 14.31396102 0.705312811 0.49528028 Games Played 31.50621796 177.129782 0.177870811 0.862057676 Temperature -55.4609057 62.09372861 -0.89318047 0.390882768