Phone Contacts Vs GPA
Is there a Correlation between the number of Contacts in someone's phone and their G.P.A?
IntroIntro
We felt that the number of phone We felt that the number of phone contacts vs. GPA was a unique contacts vs. GPA was a unique comparisoncomparison
We felt that any correlation would be We felt that any correlation would be interesting to see; even if there was no interesting to see; even if there was no correlationcorrelation
Univariate Analysis of Univariate Analysis of GPAGPA
Mean X= 3.45 Mean X= 3.45 SX= .476SX= .476
Outlier test=Outlier test=Q3-Q1 * 1.5= .7125Q3-Q1 * 1.5= .7125 Outlier=Outlier=2.74 <X<4.162.74 <X<4.16 Outliers are 1.8, 2.5, Outliers are 1.8, 2.5,
2.72.7
Min xMin x 1.81.8
Q1Q1 3.2253.225
Q2Q2 3.523.52
Q3Q3 3.73.7
Max xMax x 4.044.04
Univariate Analysis of Univariate Analysis of ContactsContacts
Mean X= 93.576 Mean X= 93.576 SX= 60.597SX= 60.597
Outlier test=Outlier test=
Q3-Q1 * 1.5= 158.25Q3-Q1 * 1.5= 158.25
Outlier=Outlier=
-64.674<X<251.826-64.674<X<251.826
No Outliers.No Outliers.
Min xMin x 2020
Q1Q1 34.534.5
Q2Q2 9090
Q3Q3 140140
Max xMax x 228228
Explanatory & Response VariableExplanatory & Response Variable
Explanatory = GPAExplanatory = GPA Response= # of Phone ContactsResponse= # of Phone Contacts
The GPA of a student affects the amount The GPA of a student affects the amount of contacts they have in their phone of contacts they have in their phone because people with higher GPA’s spend because people with higher GPA’s spend more time studying, and therefore less more time studying, and therefore less time with friendstime with friends
DataData
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Series1
•Form: Linear
•Direction: Negative
•Strength: Moderate
3.95 55
3.7 60
3.7 102
3.7 30
4.04 60
3 205
3.33 30
3.64 111
3.5 104
3.7 155
3.7 114
3.6 70
3.5 90
3.25 140
3.2 28
3.67 187
4 100
3.52 116
3.84 31
3.7 37
3.5 32
3.5 177
3.7 44
3.5 83
3 27
2.5 228
3 20
3 100
3.9 41
2.7 140
4 21
3.4 160
1.8 190
GPA Contacts GPA Contacts
Raw Data
VariationVariation
Explained variation = sum (ŷ – y-mean)Explained variation = sum (ŷ – y-mean)22
= 25453.37673= 25453.37673
Unexplained variation = sum (y – ŷ)Unexplained variation = sum (y – ŷ)22
=92048.68388=92048.68388
Total variation = sum (y – y-mean)Total variation = sum (y – y-mean)22
=117502.0606=117502.0606
r = -.4654, r2= .2166 or 21.7% c.v=.335 so r>c.v Regression line – Y= 297.9936 + -59.309xRegression line – Y= 297.9936 + -59.309x
There is a Negative correlation between the GPA and number of contacts. The lower the GPA= More contacts; Higher GPA= Less contacts.
XY
GPA
# of contacts
Histogram cont’dHistogram cont’d
Both histograms have an equal Both histograms have an equal distributiondistribution
For GPA: Outliers are 1.8, 2.5, 2.7For GPA: Outliers are 1.8, 2.5, 2.7
For Contacts: No OutliersFor Contacts: No Outliers Conforms with Empirical Rule TestConforms with Empirical Rule Test
Empirical Rule Test
Empirical Rule Test for GPA: 68% of the data falls between
the values 3.591 – 0.3445 = 3.2465 3.591 + 0.3445 = 3.9355 95% of the data falls between
the values 3.591 – 2(0.3445) = 2.902 3.591 + 2(3.445) = 4.28 99.7% of the data falls
between the values 3.591 – 3(0.3445) = 2.5575 3.591 + 3(0.3445) = 4.6245
Empirical Rule Test for Current Events Scores:
68% of the data falls between the values
0.6445 – 0.2896 = 0.3549 0.6445 + 0.2896 = 0.9341 95% of the data falls between
the values 0.6445 – 2(0.2896) = 0.0653 0.6445 + 2(0.2896) = 1.2237 99.7% of the data falls
between the values 0.6445 – 3(0.2896) = -0.2243 0.6445 + 3(0.2896) = 1.5133
Standard ErrorStandard Error
se = (y – y)2
n – 2
^
se =
31
se =
E = t2 se n(x2) – (x)2
n(x0 – x)2
1 + +1n
E = 2.0433() – (
33 (3.7 – 93.5758)2
1.03 +
E = 68.19
95% Prediction Interval (X95% Prediction Interval (X00 = = 3.7)3.7)
95% Prediction Interval (cont’d)95% Prediction Interval (cont’d)
y - E < y < y + E^ ^
78.551 – 68.19 < y < 78.511 + 68.19
10.361 < y < 146.741
There is a very large prediction interval, due in part to the small r and r2 values.
ResidualsResiduals
This shows linear correlation because the plots are randomly scattered and there is no patter on the residual graph
ConclusionConclusion
In conclusion we found out that there was In conclusion we found out that there was a weak correlation on students GPA and a weak correlation on students GPA and the amount of contacts they have in their the amount of contacts they have in their phone. Since it was so weak it is only phone. Since it was so weak it is only true a very little % of the time.true a very little % of the time.
4.9 GPA- 4 contacts
(Mom, Dad, Home, and Steve)