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