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)