GPA of College Students Vs. Time Spent During Day

Van Buskirk, Orban, Lopez 1

Everett Van Buskirk, George Lopez, Matthew Orban

STAT402_01

Professor Weinstein

4 December 2014

GPA of College Students Vs. Time Spent During Day

This study is designed to analyze the effect that different hobbies or responsibilities had

on college student’s grade point average (GPA). Participants’ GPA’s are measured alongside

four different possible aspects of their day: exercise, video game usage, internet usage, and

work. Responses were taken by survey using Google Forms, and links to the survey were

posted to the Facebook pages of Everett Van Buskirk, George Lopez, and Matthew Orban to

gain publicity.

The survey used in the study.

In total there are 38 responses over the course of 6 days (See page 10 for raw response

data). The target population of this study is college students, but with lack of resources, the

population the data represents is that of Facebookusing college students who were befriended

by Everett Van Buskirk, Matthew Orban, and George Lopez. This topic is interesting because it

gave insight to how certain; hobbies could affect academic performance.


It is important to note that there are limits to the regression since there are only 24

hours to a day, which wouldn’t all be spent doing one task. Also, there is a limit of 4 on the

response variable because a 4.0 GPA is the highest one can achieve.

Because Facebook is not the most formal website to conduct a study, there are a few

occurrences in which participants entered unrealistic responses (i.e playing video games for 22

hours a day while maintaining a 4.0 GPA). . These cases were easily taken care of by diligently

sifting through data and deleting duplicates and/or responses deemed unrealistic. This also

brings up the possibility of a duplicate response that was indeed factual. Another issue is that

the survey is not restricted to one response per participant. Last, it is likely that people who were

not in college responded to the survey, but there was an attempt to combat this by stating in the

Facebook posts that the study was intended for college students.

The four explanatory variables (work, video games, exercise, and internet usage) is

measured in hours per day, whereas the response variable , GPA, is measured on 4.0

scale.The following section shows the distribution of each explanatory variable. Note that all

distributions are right skewed.


To begin, subjects worked on an average of 5.13 hours per day, which is the highest of any

explanatory variable. A standard deviation of 3.68 shows that the data has the largest span of

any of the variables. The lowest response is 0 hours working, while the largest response is 12

hours working. This is also the only variable to not have outlier present.

Next, subjects played video games on an average of .68 hours per day, which is the

lowest amount of time spent compared to any variable. The standard deviation of .98 shows that

this data was relatively condense. The minimum value of this variable is 0 while the largest is

3.There is also an outlier that lies at 3 hours of playing video games.

The next variable, time spent using the internet, has a mean of 4.32 and standard

deviation 2.67. This variable has similar data to that of work time. Though it is slightly more

condense, with the lowest value being 1, and the highest being 12 hours per day. Also, there

are two outliers in this data at 10 and 12 hours.

Last, hours per day exercising is similar to the data recorded in hours per day spent

playing video games. The average time spent .88 hours and the standard deviation is .86. The

maximum response is 3 hours while the lowest is 0. 3 hours is also an outlier in this data.



The first scatterplot representation (top left) shows the correlation between Internet

usage per hours of the day in hours and college GPA. The direction of the line is going in a

positive direction which could indicate positive correlation(i.e the more internet use, the higher a

GPA.) The form of the graph is very weakly linear and most just scattered with no form. The

strength of the graph is between weak and moderate positive correlation because the value of

R is 0.311. There is only one outlier from the graph which lies at a GPA of 2.0. Consequently,

there is the same outlier for all variables graphs.

The second scatterplot representation (top right) shows the correlation between work

and GPA. The direction of the line of fit is going in a negative direction which could indicate

negative correlation(i.e the more subjects work, the less the subject’s GPA.) The form of the

graph shows that there is presumably no association between work and GPA. However, with an

R value of 0.335, shows that there is a slight negative correlation between work and GPA.

The third scatterplot representation(bottom left) shows the correlation between video

games and GPA. The direction of the line of fit is going in a slightly positive direction which

could indicate positive correlation(i.e the more subjects play video games, the higher the

subject’s GPA.) The form of the graph are all straight lines going vertical which indicates that

there is probably no correlation between time spent on video games and GPA. The R value in

this case is less than 0.01 so there is no correlation between video games and GPA.

The final scatterplot shows the relation between GPA and exercise time. The regression

line of the plot goes in a negative direction. The line is almost completely horizontal, so if there

is a relation it is at most, very slight. Looking at the individual data points, it is evident that the

form shows no association between GPA and exercise. To prove this we can see that the

strength of this graph is extremely weak with an R less than .01.


One condition that was not met for inference was that the data was not taken as a simple

random sample, due to the fact it was taken using a survey posted to Facebook. Much of the

expected values for the explanatory variables are less than 5. Last, certain inputs could give

impossible outputs, such as a GPA above 4.0.

Given that we have a multiple regression, we’d need to perform a confidence interval

and a significance test for all , which correspond to intercept, working, video games, internet,βj

and exercise respectively.The multiple regression model is:

3.53106 0.0395(working) .0427(video games) + 0.0603(internet) 0.1199(exercise)GPA =

95% Confidence Interval: ± t*βj SEj

t(n p 1), n = 38, p = 4 → DF(33)

Conservative t* = 2.042

Actual t* = 2.0345

Significance Test: t statistic→ t = βjSEj

α = 0.05

:β0

3.5308 ± (2.0345)(0.1776)→(3.1695, 3.8921)

We are 95% confident that the slope lies in this interval.

: : There is no relationship.H0 β0 = 0

≠ : There is a relationshipHa : β0 0

t = =19.88060.17763.5308

tCdf(19.8806,∞,33) * 2 < 0.0001


:β1

0.0395 ± (2.0345)(0.0185)→(0.0771, 0.0019)



≠ : There is a relationship.Ha : β1 0

t = = 2.13510.0185−0.0395

tCdf(∞,2.1351,33) * 2 = 0.0403

:β2

0.0427 ± (2.0345)(0.0700)→(0.1851, 0.0997)




t = = 0.60990.0700−0.0427

tCdf(∞,0.6099,33) * 2 = 0.5461

:β3

0.0603 ± (2.0345)(0.0273)→(0.0048, 0.1158)




t = = 2.20880.02730.0603

tCdf(2.2088,∞,33) * 2 = 0.0342


:β4

0.1199 ± (2.0345)(0.0838)→(0.2904, 0.0506)


: : There is a relationship.H0 β4 = 0


t = = 1.43080.0838−0.1199

tCdf(∞,1.4308,33) * 2 = 0.1619


The null hypotheses for can all be rejected because their pvaules are less than, , β0 β1 β3

0.05, the value of alpha. This means that their tests are significant. can fail to be rejected,, β2 β4

meaning it’s test is not significant.

The meaning of these tests confirm that there is indeed an effect to GPA when

measured against work and internet use and that there is not an effect on GPA when compared

to time spent playing video games and exercising. It can now be said that work negatively

affects college student’s GPA, while internet use positively affects GPA. This project was

interesting to see how college students spend their time and how certain activities can harm or

help how well they do in school. More questions arise, though, such as: Does internet help GPA

because students are using it for school work? In future projects it would likely be useful to

collect data from a source other than Facebook. It would be interesting to see what social

networking sites would give the most honest responses when taking a survey.


Documents

GPA of College Students Vs. Time Spent During Day