Regression Analysis Essay

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Regression Analysis of Graduation %

Dependent Variable: Graduation %

The Graduation percentage is the dependent variable that the independent variable will influence. In this scenario the independent variables will be SAT math (SATM) scores, SAT vocabulary (SATV) scores, percentage of the faculty that have a PHD (%FacPhD), and percentage of high school graduates who graduated in the top 20% of their class (%Top20%), which will help to determine the most logical forecast of a colleges graduation percentage.

Independent Variables:
SATM: this variable represents each students score on the math portion of the SAT exam. I believe that the SATM variable is going to directly influence the percentages of students who graduate from college.
SATV: this variable represents each students score on the vocabulary portion of the SAT exam. I believe the SATV variable is going to directly influence the percentages of students who graduate from college.
%FacPhD: this variable represents the percentage of faculty who has a PHD at a particular college. I believe that the %FacPhD variable is going to directly influence the percentages of students who graduate from college.
%Top20%: this variable represents students that who are currently enrolled that graduated in the top 20% of their high school class. I believe the %Top20% variable is going to directly influence the percentages of students who graduate from college.

All four variables will directly influence the percentage of students who graduate from college because they will have either helped them be more prepared for college before starting their college career or will significantly increase the percentage of graduating throughout their college career. SATM score gauges a student’s ability to comprehend college level mathematics, the higher a student scores on that portion of the exam, the higher their percentage of graduating will be. SATV score gauges a student’s ability to comprehend college level vocabulary & grammar. The higher a student scores on that portion of the exam, the higher their percentage of graduating will be. The percentage of faculty who has a PHD will give students an enhanced learning environment with innovative teaching methods that will increase their graduation percentage during their college career. Lastly, students who graduated in the top 20% of their high school gives us a good barometer that these students in particular are more college ready then those outside of the 20% range which increases their graduation percentage. In conclusion I believe that all coefficients of the independent variables will be positive

Regression Run # 1

Independent variables being tested: SATM, SATV, %FacPhD

Regression Analysis: Graduation % versus, SATM, SATV, %FacPhD

Regression Equation:
%Graduate = -28.9 + 0.0962 SATV + 0.0756 SATM + 0.001 %FacPhD

T Stat Analysis:

Term Coef SE Coef T-Value P-Value
Constant -28.9 13.4 -2.15 0.040
SATV 0.0962 0.0704 1.37 0.183
SATM 0.0756 0.0753 1.00 0.324
%FacPhD 0.001 0.205 0.01 0.996

The t-stats for all three independent variables are less than two, so all three variables are not acceptable or significant at the 5% level. This means that multicollinearity exists and to fix this we’ll need to eliminate 1 of the independent variables and or replace it with another and rerun the regression.

Durban Watson Statistic:

Durbin-Watson Statistic = 1.37233

The Durbin-Watson is 1.37233 so the regression equation is not positively or negatively auto correlated. No action is necessary.

R Squared Analysis:

S = 10.8044 R Squared = 69.06% R Squared (adj.) = 65.62%

The R-squared is less than 80% & the data is in levels so we cannot accept our R Squared.
Graph Analysis:

The relationship on the scatterplot graph between Graduation % and SATM indicates that there is a chance for hetroskedacity to occur meaning we may be unable to trust our confidence intervals. We can
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