Regression Analysis of Work Hours in Relation to GPA

This research investigated the affects of working extra hours in a labor position on students’ GPAs each semester at Berea College. It was my belief that students who worked more hours were more likely to have lower GPAs due to their studying abilities and opportunities being compromised as a result of working too long (a negative correlation or trend between GPAs and hours worked each week).

For each hour a student worked it was my belief that he or she became more fatigued, more stressed, and lost an hour in which to study. Each student must work at least ten hours here on campus as required by the Berea College Labor Program. Students may select to work more to make more money or to gain experience in a chosen field, or they may have to work more to meet work requirements for state assistance programs which help them financially but require that certain number of hours (usually 20) be worked by the student each week.

In order to test this hypothesis it was important that I collect unbiased samples. I did so by placing a survey in the labor program office where any random student was just as likely as any other to come in during this time of year when all students were turning in forms for their labor positions for the next year.

I asked the students to record their classification (freshman, sophomore, etc.), whether or not they were recent transfer students, the number of hours they worked, and their semester GPA. I specifically asked that all of this information be in regards to the last full term, fall semester of 2011, so as not to get incomplete data for the current semester which is not finished. I only asked for their semester GPA and their number of hours they worked each week during that same semester and not for their entire college career.

This was so that I would not need to account for the fact that students can work a different number of hours each semester. Out of 40 surveys I had to exclude six that were completed by freshmen or recent transfers who are all only allowed to work ten hours in their first semester. Had they been included there would have been a large number of students who worked 10 hours which would have shifted the mean and median calculations for hours and would not have given a more accurate view of the entire Berea population.

Also, freshmen and transfers are new to their positions and are placed by the program which may put them at a disadvantage in jobs they may not like that stress them out and cause them to experience more fatigue as opposed to upper-classmen who get to pick their positions and work in places they feel more comfortable and are, therefore, less stressed and fatigued before studying.

Having eliminated the freshmen and recent transfers the end result was a sample of 34 students. The minimum semester GPA for the sample was 1.95 while the maximum was a 4.0. I contemplated eliminating to samples that had GPAs of 4.0 to keep them from raising the average too high but the next high GPA was 3.81 which meant that the two numbers did not seem to be outliers and were consistent with the other data.

The obvious minimum numbers of hours one can work is the 10 hours required by the college while the maximum in our samples is 20. This could vary in the population but it is very rare that any student would work more than 20 hours because it requires special permission. (Working between 15 and 20 hours requires special permission but is not as hard to get approved and occurs quite frequently.) More of the descriptive statistics are shown in the table 1.

Table 1: Descriptive Statistics

| |Hours Worked Each Week |Semester GPA | |Mean |12.82352941 |2.982647059 | |Standard Deviation |3.468215752 |0.547890217 | |Minimum |10 |1.95 | |Median |12 |3.115
| |Maximum |20 |4 |

It is important to note that the two students in the sample who held the maximum GPA’s of 4.0 also worked the minimum amount of hours each week (10 hours). Also, the student who held the minimum GPA of 1.95 worked the maximum amount of hours each week (20 hours). So as the number of hours increased from the minimum to the maximum, the GPA decreased from maximum to the minimum, thus supporting my hypothesis. With this preliminary information in support of my hypothesis it was time to further analyze the data.

Using a simple linear regression model to analyze the sample data I tested the model

Semester GPA=β0+β1 Work Hours +ε

Where β0 is the intercept and β1 is the marginal effect of an additional hour of work each week. The results are show in table 2.

Table 2: Regression Statistics

|Regression Statistics | | | | | | | |Multiple R |0.557 | | | | | | |R Square |0.311 | | | | | | |Adjusted R Square |0.289 | | | | | | |Standard Error |0.462 | | | | | | |Observations |34 | | | | | | | | | | | | | | |Coefficients |Standard Error |t Stat |P-value
|Lower 95% |Upper 95% | |Intercept |4.11 |0.31 |13.36 |1.2E-14 |3.48 |4.74 | |Hours |-0.09 |0.02 |-3.80 |0.00 |-0.14 |-0.04 |

Using the data in table two the estimated relationship between the number of hours worked each week and the semester GPA is understood to be the following:

Semester GPA=4.11-0.09 *Hours

The equation shows that for every extra hour of work a student loses .09 from their semester GPA. Obviously the equation is limited in its ability to perfectly grasp the situation as a perfect GPA is considered a 4.0 and working zero hours could not get you a GPA of 4.11. But if you insert the desired 4.0 into the equation you get the following:

4.0 = 4.11-0.09*Hours

4.0-4.11 = 4.11-0.09*Hours-4.11

-0.11 = -0.09*Hours

-0.11/-0.09 = (-0.09*ours)/-0.09

1.22 = Hours

This would mean that at 1.22 hours of work each weak are beneficial or have no affect on a student’s ability to study. This is a fact that would require more developed methods to research which will not be used in the paper. A regular student at Berea College who studies 10 hours a week will earn a GPA of 3.21 on average with this equation. The marginal effect on GPA is rather large (t=-3.80 or 3.80, p=0.00) and this model explains 31.1% of the variation in GPAs. Graph 1 shows the data plots.

Graph 1

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The research in this paper supports the hypothesis that working more hours cause a students GPA to go down. With this in mind, students should not put more of a burden on themselves to work than absolutely necessary. Also, the labor program should think about reducing its requirement for students to work at least 10 hours each week which may have a negative affect on the students’ GPAs each semester.

In order to really see how much each hour of work effects a students GPA it would be necessary for additional research to study things like personal motivation and factors of whether or not a student chose to work extra hours or was required to do so. One would also need to find a way of measuring the amount of stress put on each individual by there job as some may be more physically stressful than others. Lastly it would be necessary to measure the difficulty of different majors and courses taken by each individual student in comparison to others.