More Related Content Similar to GPA of College Students Vs. Time Spent During Day Similar to GPA of College Students Vs. Time Spent During Day (20) 1.
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.
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Van Buskirk, Orban, Lopez 2
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.
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Van Buskirk, Orban, Lopez 3
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.
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Van Buskirk, Orban, Lopez 5
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.
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Van Buskirk, Orban, Lopez 6
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 =
βj
SEj
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 = =19.88060.1776
3.5308
tCdf(19.8806,∞,33) * 2 < 0.0001
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Van Buskirk, Orban, Lopez 7
:β1
0.0395 ± (2.0345)(0.0185)→(0.0771, 0.0019)
We are 95% confident that the slope lies in this interval.
: : There is no relationship.H0 β1 = 0
≠ : 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)
We are 95% confident that the slope lies in this interval.
: : There is no relationship.H0 β2 = 0
≠ : There is a relationship.Ha : β2 0
t = = 0.60990.0700
−0.0427
tCdf(∞,0.6099,33) * 2 = 0.5461
:β3
0.0603 ± (2.0345)(0.0273)→(0.0048, 0.1158)
We are 95% confident that the slope lies in this interval.
: : There is no relationship.H0 β3 = 0
≠ : There is a relationship.Ha : β3 0
t = = 2.20880.0273
0.0603
tCdf(2.2088,∞,33) * 2 = 0.0342
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Van Buskirk, Orban, Lopez 9
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.
