In: Statistics and Probability
complete a multiple regression and select the best mix of IV to explain game attendance. Once you have the best mix of variables, accept or reject the nulls, create the formula for predicting the regression, lower 95% Confidence Interval and upper 95% Confidence Interval
Game Number | Game Attendance | Team Win/Loss Percentage | Opponent Win/Loss Percentage | Games Played | Temperature |
1 | 14,502 | 33.3 | 80 | 6 | 47 |
2 | 12,459 | 25 | 50 | 4 | 56 |
3 | 15,600 | 80 | 66.6 | 5 | 55 |
4 | 16,780 | 75 | 100 | 8 | 60 |
5 | 14,600 | 60 | 80 | 10 | 55 |
6 | 19,300 | 100 | 60 | 10 | 49 |
7 | 14,603 | 66.6 | 25 | 3 | 67 |
8 | 15,789 | 50 | 50 | 6 | 55 |
9 | 17,800 | 80 | 40 | 10 | 53 |
10 | 19,450 | 75 | 100 | 8 | 48 |
11 | 13,890 | 20 | 75 | 5 | 65 |
12 | 15,097 | 70 | 70 | 10 | 56 |
13 | 17,666 | 83.3 | 66.6 | 6 | 60 |
14 | 12,500 | 20 | 20 | 5 | 59 |
15 | 16,780 | 80 | 100 | 8 | 46 |
16 | 17,543 | 80 | 70 | 10 | 50 |
Football Attendance at State University | ||||||
File: Football.xlsx | ||||||
Column A: Game Number | ||||||
Column B: Game Attendance | ||||||
Column C: Win/Loss Percentage | ||||||
Column D: Opponent Win/Loss Percentage | ||||||
Column E: Games Played | ||||||
Column F: Temperature |
The best model is:
r² | 0.720 | |||||
r | 0.849 | |||||
Std. Error | 1170.998 | |||||
n | 16 | |||||
k | 1 | |||||
Dep. Var. | Game Attendance | |||||
ANOVA table | ||||||
Source | SS | df | MS | F | p-value | |
Regression | 4,94,56,399.4686 | 1 | 4,94,56,399.4686 | 36.07 | 3.22E-05 | |
Residual | 1,91,97,324.4689 | 14 | 13,71,237.4621 | |||
Total | 6,86,53,723.9375 | 15 | ||||
Regression output | confidence interval | |||||
variables | coefficients | std. error | t (df=14) | p-value | 95% lower | 95% upper |
Intercept | 11,392.0432 | |||||
Team Win/Loss Percentage | 72.2163 | 12.0249 | 6.006 | 3.22E-05 | 46.4255 | 98.0071 |
The regression equation is:
Game Attendance = 11,392.0432 + 72.2163*Team Win/Loss Percentage
lower 95% Confidence Interval = 46.4255
upper 95% Confidence Interval = 98.0071