A college football team has developed a multiple regression model to predict attendance (y) at its outdoor football games based upon three variables:
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A local state university 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 revenues, and the athletic director believes attendance is directly related to the number of wins by the team. The business manager has accumulated total annual attendance figures for the past 8 years: Attendance Wins Advertising 36,300 4 $29,500 40,100 6 $55,700 41,200 6 $71,300 53,000 8 $87,000 44,000 6 $75,000 45,600 7 $72,000 39,000 5 $55,300 47,500 7 $81,600 Given the number of returning starters and the strength of the schedule, the athletic director believes the team will win at least seven games next year. Develop a simple regression equation for these data to forecast attendance for this level of success. What is Total Sum of Squares (TSS)? What is the coefficient of determination, r2? Interpret r2. If there were 8 wins, what would you predict the attendance to be? Use a 95.44% confidence interval. Please interpret. Instead of predicting attendance based only on wins, include a second variable – advertising. What is the multiple regression equation? What is the coefficient of determination, r2? Interpret r2. What is the partial r2y2.1? Interpret your result. Provide your spreadsheet results. Interpret your results. What would you advise the business manager? Please answer the last 2 questions.
Breanna O.
The following is a set of data for $y,$ the amount of money (thousands of dollars) contributed to the alumni association at Virginia Tech by the Class of $1960,$ and $x,$ the number of years following graduation: $$ \begin{array}{rr|rl} y & \multicolumn{1}{c|} {X} & \multicolumn{1}{c} {y} & \multicolumn{1}{c} {X} \\ \hline 812.52 & 1 & 2755.00 & 11 \\ 822.50 & 2 & 4390.50 & 12 \\ 1211.50 & 3 & 5581.50 & 13 \\ 1348.00 & 4 & 5548.00 & 14 \\ 1301.00 & 8 & 6086.00 & 15 \\ 2567.50 & 9 & 5764.00 & 16 \\ 2526.50 & 10 & 8903.00 & 17 \end{array} $$ (a) Fit a regression model of the type $$ \mu_{Y \mid x}=00+O L X $$ (b) Fit a quadratic model of the type $$ \mu_{Y \mid x}=\beta_{0}+\beta_{1} x+\beta_{11} x^{2} $$ (c) Determine which of the models in (a) or (b) is preferable. Use $s^{2}, R^{2},$ and the PRESS residuals to support your decision.
Multiple Linear Regression and Certain Nonlinear Regression Models
Cross Validation, C;), and Other Criteria for Model Selection
Team Rank based on several factors Regression Statistics Multiple R: 0.894 R Square: 0.799 Adjusted R Square: 0.745 Standard Error: 89.008 Observations: 20 ANOVA SS MS F Significance F 471595.683 117898.921 14.882 4.19593E-05 118835.219 7922.348 590430.902 Regression Residual Total 4 15 19 Coefficients Standard Error Intercept 5381.214 2346.661 Winning Percentage 14.471 7.719 Total Yards 15.181 8.319 Allowed Points 8.545 6.53 Scored Points 0.352 5.765 t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 2.293 0.037 379.424 10383.004 379.424 10383.004 1.875 0.013 -1.982 30.925 -1.982 30.925 1.825 0.088 -2.55 32.911 -2.551 32.911 1.309 0.021 -5.373 22.464 -5.373 22.464 0.052 0.959 -11.988 12.588 -11.988 12.588
Rachel G.
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