Statistical Results of Public vs. Private for 2005

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
R-square	.094613
Regression F	5.904225
Significance F	0.00364

Students:
Coefficient	-.000012
t-Stat	-1.7064

Private:
Coefficient	0.016158
t-Stat	3.189482

The r-square 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 t-stat 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 .016158 greater.

Division II
R-square	0.07571192
Regression F	4.750999
Significance F	0.010395

Students:
Coefficient	-.000075
t-Stat	-2.05926

Private:
Coefficient	0.017949904
t-Stat	2.064172

Both students and private are significant predictors. The # of students actually has a negative effect. Private schools have an advantage of .01794 points per student.

Division III
R-square	0.0814
Regression F	5.095273
Significance F	0.007582

Students:
Coefficient	-0.00015
t-Stat	-1.80494

Private:
Coefficient	0.021318
t-Stat	2.655351

Students is not a significant variable. Private is significant. Private schools have an advantage of .0213 points per student over identically sized pubic schools.

Division IV
R-square	0.047733693
Regression F	2.932395
Significance F	0.057196

Students:
Coefficient	-0.000238238
t-Stat	-1.60397

Private:
Coefficient	0.019292166
t-Stat	1.623957

Neither of our predictive variables are statistically significant predictors with 95% certainty.

Division V
R-square	0.045210849
Regression F	2.746396
Significance F	0.068333

Students:
Coefficient	-.000069
t-Stat	-0.33744

Private:
Coefficient	0.025497976
t-Stat	2.322016

Number of students is not a good predictor, but private school is a good predictor. In this division, private schools have an advantage of .02549 points per student over equal-sized public schools

Division VI
R-square	0.005139709
Regression F	0.312559
Significance F	0.732161

Students:
Coefficient	-.000086
t-Stat	-0.33938

Private:
Coefficient	0.008383307
t-Stat	0.559203

This regression does not have reliable predictive power. The regression F is less than the significance F.

R-square: 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.

t-Stat: This shows statistical significance of a predictive variable. Simply put, a t-stat of less than -2 or greater than 2 is required in order to say that any variable has any predictive power.