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	.134912
Regression F	8.49936
Significance F	0.000371

Students:
Coefficient	-1.6E-05
t-Stat	-2.74039

Private:
Coefficient	0.013564
t-Stat	3.416551

Since the Regression F is greater than the Significance F, we know that the regression is significant.

The t-stat for students shows that it is statistically significant. More student generally mean lower pts per student reults.

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 .013564 greater.

Division II
R-square	0.188620161
Regression F	13.01823
Significance F	8.25E-06

Students:
Coefficient	-6.86044E-05
t-Stat	-2.67274

Private:
Coefficient	0.020650821
t-Stat	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
R-square	0.173982938
Regression F	12.00584
Significance F	1.86E-05

Students:
Coefficient	-0.000161466
t-Stat	-2.60446

Private:
Coefficient	0.024872558
t-Stat	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
R-square	0.053664887
Regression F	3.260717
Significance F	0.041936

Students:
Coefficient	-0.000139784
t-Stat	-2.18736

Private:
Coefficient	0.009591398
t-Stat	1.165233

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 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
R-square	0.048547131
Regression F	2.857356
Significance F	0.061615

Students:
Coefficient	-0.000164398
t-Stat	-1.10149

Private:
Coefficient	0.017881956
t-Stat	2.127166

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 equal-sized public schools

Division VI
R-square	0.076873891
Regression F	4.871623
Significance F	0.009285

Students:
Coefficient	-0.000450864
t-Stat	-2.10796

Private:
Coefficient	0.019933557
t-Stat	1.624769

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.

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.