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Determining Factors of GPA
Natalie ArndtAllison Mucha
MA 33112/6/07
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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
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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
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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: ____
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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
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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
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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
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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
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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
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Preliminary Analysis
somewhat normal skewed, left-tailed
(by semester)
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Initial Regressions
GPA = 0.01799*credits + 3.21493R2 = 0.01623
GPA = -0.0002035*credits + 3.5644477R2 = 0.0005585
semester data cumulative data
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Residual Plotssemester data cumulative data
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Comparisons by Gender
semester data cumulative data
Male Female Male Female
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Comparisons by School
semester data cumulative data
EngineeringScience Science Engineering
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Comparisons by Load
Load A Load B Load C Load D Load E
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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
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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%)
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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.
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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
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Questions?