1. Determining Factors of GPA Natalie Arndt Allison Mucha MA 331 12/6/07

2. Objectives Determine important factors related to a Stevens student’s GPA Make use of methods and analytic techniques discussed in class Observe differences between (or lack thereof) engineering and science students

3. Initial Variable Ideas Years at school Hours work / week Hours sleep / night Cleanliness rating Which SAT score was higher Number of siblings Expected graduation year

4. Final Variable Ideas Gender (Primary) major # Semesters # Credits / semester GPA each semester Cumulative # credits Cumulative GPA Gender: ____________Major: ____________ SemesterCreditsGPA for Semester 1 2 3 4 5 6 7 8 9 10 Total credits earned: ______Cumulative GPA: ____

5. Data Collection Method Voluntary Survey Anonymous Sent out to several subsets of general student body Only full-time (≥12 credits), undergraduate Stevens students considered Alumni who satisfied these conditions during their time at Stevens also considered

6. Lurking Variables Influence of extracurricular activities Changes in curriculum from year to year certainly a factor Personal issues, medical problems, stressful situations unaccounted for Differences between same course as time passes (professor, size, textbook, etc.) Large variability to begin with

7. Data Collected 28 students participated in the survey Combined 154 semesters worth of data 18 males, 10 females 19 engineering, 8 science, 1 art GPA ranged from 2.317 to 4.000 Credits ranged from 12.0 (imposed) to 25.5 Cumulative credits ranged from 33.0 to 177.0

8. After Data Was Collected … All names removed, obs category created for relating information for one individual Semester 0 refers to cumulative data Primary major used to create categorical school column Number of credits per semester used to create load category

9. Data Compilation obsgendermajorschoolsemcreditsloadGPA 2MaleEngineering ManagementE117.0b3.938 2MaleEngineering ManagementE417.5b4.000 2MaleEngineering ManagementE218.0c4.000 2MaleEngineering ManagementE318.5c3.829 2MaleEngineering ManagementE520.0c4.000 2MaleEngineering ManagementE0101.0N/A3.947 … 20MaleComputer ScienceS313.0a3.769 20MaleComputer ScienceS413.0a3.845 20MaleComputer ScienceS115.0b3.866 20MaleComputer ScienceS219.0c3.948 20MaleComputer ScienceS069.0N/A3.884 … 26FemaleElectrical EngineeringE115.0b3.222 26FemaleElectrical EngineeringE214.0a3.668 26FemaleElectrical EngineeringE320.0c3.651 26FemaleElectrical EngineeringE420.0c3.773 26FemaleElectrical EngineeringE069.0N/A3.592

10. Preliminary Analysis somewhat normalskewed, left-tailed (by semester)

11. Initial Regressions GPA = 0.01799*credits + 3.21493 R 2 = 0.01623 GPA = -0.0002035*credits + 3.5644477 R 2 = 0.0005585 semester datacumulative data

12. Residual Plots semester datacumulative data

13. Comparisons by Gender semester data cumulative data MaleFemale MaleFemale

14. Comparisons by School semester datacumulative data EngineeringScience Engineering

15. Comparisons by Load Load ALoad BLoad CLoad DLoad E

16. Stepwise Regression > stepwise = step(lm(gpa~credits+school+gender+sem),direction="both") Start: AIC=-217.77 gpa ~ credits + school + gender + sem Df Sum of Sq RSS AIC - gender 1 0.017 20.359 -219.667 - sem 1 0.198 20.541 -218.549 20.342 -217.772 - credits 1 0.524 20.866 -216.568 - school 2 0.907 21.250 -216.273 Step: AIC=-219.67 gpa ~ credits + school + sem Df Sum of Sq RSS AIC - sem 1 0.194 20.553 -220.472 20.359 -219.667 - credits 1 0.530 20.889 -218.427 - school 2 0.905 21.264 -218.189 + gender 1 0.017 20.342 -217.772 Step: AIC=-220.47 gpa ~ credits + school Df Sum of Sq RSS AIC 20.553 -220.472 + sem 1 0.194 20.359 -219.667 - school 2 0.872 21.425 -219.238 - credits 1 0.556 21.109 -219.108 + gender 1 0.013 20.541 -218.549 Call: lm(formula = gpa ~ credits + school) Coefficients: (Intercept) credits schoolE schoolS 2.95972 0.02407 0.09478 0.27379 > summary(stepwise) Call: lm(formula = gpa ~ credits + school) Residuals: Min 1Q Median 3Q Max -1.2119 -0.2735 0.0806 0.3038 0.6567 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.95972 0.28566 10.361 <2e-16 *** credits 0.02407 0.01325 1.817 0.0717. schoolE 0.09478 0.21630 0.438 0.6620 schoolS 0.27379 0.21774 1.257 0.2110 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.4104 on 122 degrees of freedom Multiple R-Squared: 0.05626, Adjusted R-squared: 0.03305 F-statistic: 2.424 on 3 and 122 DF, p-value: 0.06899 > anova(stepwise) Analysis of Variance Table Response: gpa Df Sum Sq Mean Sq F value Pr(>F) credits 1 0.3536 0.3536 2.0987 0.14999 school 2 0.8717 0.4359 2.5872 0.07936. Residuals 122 20.5532 0.1685 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

17. Important Variables Both forward and stepwise regression return credits and school as most important variables Gender and semester deemed insignificant using AIC Summary returns that credits is marginally significant (10%) Anova returns that school is marginally significant (10%)

18. Observations & Conclusions Intercept: 2.96 Engineering majors: add 0.09 Science majors: add 0.27 Add 0.02 to GPA per credit Allows us to conclude that the science majors represented by our study average a GPA 0.18 points higher than engineering majors.

19. Recommendations Create a more refined study that allows us to focus on a specific area, rather than manipulating several variables at once Draw data from a significantly larger sample Find appropriate methodology to remove effect of lurking variables

20. Questions?