Multiple Regression

Topic 8: Multiple Regression Answer
a.
Scatterplot
120 Game Attendance 100 80 60 40 20 0 0 5,000 10,000 15,000 20,000 25,000 Team Win/Loss %

There appears to be a positive linear relationship between team win/loss percentage and

game attendance. There appears to be a positive linear relationship between opponent win/loss percentage and game attendance.

There appears to be a positive linear relationship between games played and game

attendance. There does not appear to be any relationship between temperature and game attendance.

b. Game Attendance Game Attendance Team Win/Loss % Opponent Win/Loss % Games Played Temperature Team Win/Loss % Opponent Win/Loss % Games Played Temperature

1 0.848748849 1 0.414250332 0.286749997 1 0.599214835 0.577958172 0.403593506 1 -0.476186226 -0.330096097 -0.446949168 -0.550083219

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No alpha level was specified. Students will select their own. We have selected .05. Critical t = + 2.1448 t for game attendance and team win/loss % = 0.8487/ (1 − 0.84872) /(16 − 2) = 6.0043 t for game attendance and opponent win/loss % = 0.4143/ (1 − 0.41432) /(16 − 2) = 1.7032 t for game attendance and games played = 0.5992/ (1 − 0.59922) /(16 − 2) = 2.8004 t for game attendance and temperature = -0.4762/ (1 − ( − 0.4762 ) ) /(16 − 2) = -2.0263 There is a significant relationship between game attendance and team win/loss % and games played. Therefore a multiple regression model could be effective. Multiple regression equation using x1, x2, x3, x4 as independent variables to predict y
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c.

Regression Analysis Regression Statistics Multiple R 0.880534596 R Square 0.775341175 Adjusted R Square 0.693647057 Standard Error 1184.124723 Observations 16 ANOVA df Regression Residual Total Significance SS MS F F 4 53230058.9713307514.749.4907833180.001427993 11 15423664.971402151.361 15 68653723.94

Standard Coefficients t Stat P-value Lower 95% Error Intercept 14122.24086 4335.791765 3.257130790.0076378234579.222699 Team