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= Outlier= 2.74 <X<4.16 Outliers are 1.8, 2.5, 2.7 Outliers are 1.8, 2.5, 2.7 Min x 1.8 Q13.225 Q23.52 Q33.7 Max x 4.04

4. Univariate Analysis of Contacts  Mean X= 93.576  SX= 60.597 Outlier test= Q3-Q1 * 1.5= 158.25 Outlier= Outlier=-64.674<X<251.826 No Outliers. No Outliers. Min x 20 Q134.5 Q290 Q3140 Max x 228

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 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. 3.9555 3.760 3.7102 3.730 4.0460 3205 3.3330 3.64111 3.5104 3.7155 3.7114 3.670 3.590 3.25140 3.228 3.67187 4100 3.52116 3.8431 3.737 3.532 3.5177 3.744 3.583 327 2.5228 320 3100 3.941 2.7140 421 3.4160 1.8190 GPA Contacts GPA Contacts Raw Data

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, r 2 =.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. X Y GPA # of contacts

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

12. 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

13. Standard Error s e =  ( y – y ) 2 n – 2 ^ s e =  31 s e = 

14. E = t   2 s e n(x2)n(x2) – (  x) 2 n(x0 – x)2n(x0 – x)2 1 + + 1 n E = 2.04 33(  ) – (  33 (3.7 – 93.5758) 2 1.03 + E = 68.19 95% Prediction Interval (X 0 = 3.7)

15. 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 r 2 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)