Data were collected on GPA and number of Facebook friends for students in a small statistics class. Some summary statistics, partial output from the regression analysis are provided. Assume that the students in this class are typical of all students at a university.
| Variable |
Mean |
St Dev |
Minimum |
Maximum |
| GPA |
3.2067 |
0.4118 |
2.4000 |
3.9500 |
| Facebook Friends |
677.9 |
307.2 |
185.0 |
1500.0
|
The regression equation is GPA = 3.830 - 0.000919 Facebook Friends
| Source |
DF |
SS |
MS |
F |
P |
| Regression |
1 |
2.31193 |
2.31193 |
24.85 |
0.000 |
| Error |
28 |
2.60534 |
0.09305 |
|
|
| Total |
29 |
4.91727 |
|
|
|
a) Determine whether we should have any strong concerns about the conditions being met for using a linear model with these data. Explain.
b) Write down the equation of the least squares line and use it to predict the GPA for someone with 800 Facebook friends.
c) The correlation between GPA and number of Facebook friends is -0.686. Use the correlation and signficance level of 5% to test for a negative linear association between GPA and number of Facebook friends. Include all details of the test.