Phone Contacts Vs GPA

1. Phone Contacts Vs GPA Is there a Correlation between the number of Contacts in someone's phone and their G.P.A?

2. Intro • We felt that the number of phone contacts vs. GPA was a unique comparison • We felt that any correlation would be interesting to see; even if there was no correlation

3. Univariate Analysis of GPA • Mean X= 3.45 • SX= .476 Outlier test= Q3-Q1 * 1.5= .7125 Outlier= 2.74 <X<4.16 Outliers are 1.8, 2.5, 2.7

4. Univariate Analysis of Contacts • Mean X= 93.576 • SX= 60.597 Outlier test= Q3-Q1 * 1.5= 158.25 Outlier= -64.674<X<251.826 No Outliers.

5. Explanatory & Response Variable • Explanatory = GPA • Response= # of Phone Contacts The GPA of a student affects the amount of contacts they have in their phone because people with higher GPA’s spend more time studying, and therefore less time with friends

6. Data • Form: Linear • Direction: Negative • Strength: Moderate

7. Raw Data GPA Contacts GPA Contacts

8. Variation • Explained variation = sum (ŷ – y-mean)2 • = 25453.37673 • Unexplained variation = sum (y – ŷ)2 • =92048.68388 • Total variation = sum (y – y-mean)2 • =117502.0606

9. r = -.4654, r2= .2166 or 21.7% • c.v=.335 so r>c.v • Regression 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.

10. GPA X Y # of contacts

11. Histogram cont’d • Both histograms have an equal distribution For GPA: Outliers are 1.8, 2.5, 2.7 For Contacts: No Outliers • Conforms with Empirical Rule Test

12. 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 Empirical Rule Test

13. (y – y)2 ^ 92048.68 n –2 31 Standard Error se = se = se = 54.49

14. 33 (3.7 – 93.5758)2 n(x0–x)2 1 1 + + 1.03 + E = t2se E = 2.04 n n(x2) – (x)2 33(399.26) – (12936.79) 95% Prediction Interval (X0 = 3.7) E = 68.19

15. ^ ^ 78.551 – 68.19 < y < 78.511 + 68.19 y - E < y < y + E 95% Prediction Interval (cont’d) 10.361 < y < 146.741 There is a very large prediction interval, due in part to the small r and r2 values.

16. Residuals This shows linear correlation because the plots are randomly scattered and there is no patter on the residual graph

17. Conclusion • In conclusion we found out that there was a weak correlation on students GPA and the amount of contacts they have in their phone. Since it was so weak it is only true a very little % of the time. 4.9 GPA- 4 contacts (Mom, Dad, Home, and Steve)