Determining Factors of GPA

Natalie ArndtAllison Mucha

MA 33112/6/07

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

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

Final Variable Ideas

• Gender• (Primary) major• # Semesters• # Credits / semester• GPA each semester• Cumulative # credits• Cumulative GPA

Gender: ____________ Major: ____________

Semester Credits GPA for Semester

1    

2    

3    

4    

5    

6    

7    

8    

9    

10    

Total credits earned: ______ Cumulative GPA: ____

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

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

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

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

Data Compilationobs gender major school sem credits load GPA

2 Male Engineering Management E 1 17.0 b 3.938

2 Male Engineering Management E 4 17.5 b 4.000

2 Male Engineering Management E 2 18.0 c 4.000

2 Male Engineering Management E 3 18.5 c 3.829

2 Male Engineering Management E 5 20.0 c 4.000

2 Male Engineering Management E 0 101.0 N/A 3.947

…20 Male Computer Science S 3 13.0 a 3.769

20 Male Computer Science S 4 13.0 a 3.845

20 Male Computer Science S 1 15.0 b 3.866

20 Male Computer Science S 2 19.0 c 3.948

20 Male Computer Science S 0 69.0 N/A 3.884

…26 Female Electrical Engineering E 1 15.0 b 3.222

26 Female Electrical Engineering E 2 14.0 a 3.668

26 Female Electrical Engineering E 3 20.0 c 3.651

26 Female Electrical Engineering E 4 20.0 c 3.773

26 Female Electrical Engineering E 0 69.0 N/A 3.592

Preliminary Analysis

somewhat normal skewed, left-tailed

(by semester)

Initial Regressions

GPA = 0.01799*credits + 3.21493R2 = 0.01623

GPA = -0.0002035*credits + 3.5644477R2 = 0.0005585

semester data cumulative data

Residual Plotssemester data cumulative data

Comparisons by Gender

semester data cumulative data

Male Female Male Female

Comparisons by School

semester data cumulative data

EngineeringScience Science Engineering

Comparisons by Load

Load A Load B Load C Load D Load E

Stepwise Regression> stepwise = step(lm(gpa~credits+school+gender+sem),direction="both")Start: AIC=-217.77gpa ~ 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<none> 20.342 -217.772- credits 1 0.524 20.866 -216.568- school 2 0.907 21.250 -216.273Step: AIC=-219.67gpa ~ credits + school + sem Df Sum of Sq RSS AIC- sem 1 0.194 20.553 -220.472<none> 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 -217.772Step: AIC=-220.47gpa ~ credits + school Df Sum of Sq RSS AIC<none> 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 -218.549Call: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 freedomMultiple 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 TableResponse: 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

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%)

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.

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

Questions?