Regression Analysis of Each Division
Six Year Results
Each of the tables below are the result of a
regression analysis run on each division.
A brief description of each statistic can be found below.
To the bottom of each table is my interpretation of what the results indicate.
Division I 

Rsquare  .134912 
Regression F  8.49936 
Significance F  0.000371 
Students:  
Coefficient  1.6E05 
tStat  2.74039 
Private:  
Coefficient  0.013564 
tStat  3.416551 
Since the Regression F is greater than the Significance F, we know that the regression is significant.
The tstat for students shows that it is statistically significant. More student generally mean lower pts per student reults.
The tstat for private shows that this is significant. The coefficient shows that for two schools (one public, one private) of the same enrollment, the private schools should have a points per student value .013564 greater.
Division II 

Rsquare  0.188620161 
Regression F  13.01823 
Significance F  8.25E06 
Students:  
Coefficient  6.86044E05 
tStat  2.67274 
Private:  
Coefficient  0.020650821 
tStat  3.901928 
ince the Regression F is greater than the Significance F, we know that the regression is significant.
Both students and private are significant predictors. The # of students actually has a negative effect. Private schools have an advantage of .02065 points per student.
Division III 

Rsquare  0.173982938 
Regression F  12.00584 
Significance F  1.86E05 
Students:  
Coefficient  0.000161466 
tStat  2.60446 
Private:  
Coefficient  0.024872558 
tStat  4.194438 
Since the Regression F is greater than the Significance F, we know that the regression is significant.
Number of Students is a significant variable. Private is significant. Private schools have an advantage of .02487 points per student over identically sized pubic schools.
Division IV 

Rsquare  0.053664887 
Regression F  3.260717 
Significance F  0.041936 
Students:  
Coefficient  0.000139784 
tStat  2.18736 
Private:  
Coefficient  0.009591398 
tStat  1.165233 
The rsquare value is fairly low, so we don't have a perfect predictor with only the two variables tested. However, since the Regression F is greater than the Significance F, we know that the regression is significant.
The number of students is significant and is a negative indicator as in the other regressions.
The Public/Private variable is not a statistically significant predictor with 95% certainty.
Division V 

Rsquare  0.048547131 
Regression F  2.857356 
Significance F  0.061615 
Students:  
Coefficient  0.000164398 
tStat  1.10149 
Private:  
Coefficient  0.017881956 
tStat  2.127166 
The rsquare value is fairly low, so we don't have a perfect predictor with only the two variables tested. However, since the Regression F is greater than the Significance F, we know that the regression is significant.
Number of students is not a good predictor, but private school is a good predictor. In this division, private schools have an advantage of .01788 points per student over equalsized public schools
Division VI 

Rsquare  0.076873891 
Regression F  4.871623 
Significance F  0.009285 
Students:  
Coefficient  0.000450864 
tStat  2.10796 
Private:  
Coefficient  0.019933557 
tStat  1.624769 
The rsquare value is fairly low, so we don't have a perfect predictor with only the two variables tested. However, since the Regression F is greater than the Significance F, we know that the regression is significant.
The number of students is significant and is a negative indicator as in the other regressions.
The Public/Private variable is not a statistically significant predictor with 95% certainty.
Discussion of Regression Statistics
Rsquare: An overall measure of how well the predictive variables (in this case enrollment and whether public/private) predict the independent variable (in this case points per student). This value is between 0 and 1. The closer to 1, the better the predictive power.
Regression F and Significance F: The Regression F value must be higher than the significance F value for the regression to have any statistically significant predictive power.
Coefficient: The value that is placed on a particular variable. For example if the Coefficient of private is .01, then a private school would have an advantage of .01 points per student if the enrollment variable is equal. Likewise, if the Coefficient for students is .0001, then for every additional student enrolled, the points per student should increase by .0001.
tStat: This shows statistical significance of a predictive variable. Simply put, a tstat of less than 2 or greater than 2 is required in order to say that any variable has any predictive power.
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