Facebook vs GPA - Clustering: You will need to
use software to answer these questions.
Below is the scatterplot, regression line, and corresponding data
for the weekly Facebook hours and College GPA's of 8 randomly
selected students. You should notice something odd about the
scatterplot.
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You should be able to copy and paste the data by highlighting
the entire table.
Answer the following questions regarding the relationship. Test at
a 0.05 significance level.
(a) Using all 8 data pairs for Facebook hours and GPA, calculate
the correlation coefficient. Round your answer to 3 decimal
places.
r =
(b) Is there a significant linear correlation between these 8 data
pairs?
YesNo
(c) Using only the first 4 data pairs for Facebook
hours and GPA, calculate the correlation coefficient. Round
your answer to 3 decimal places.
r =
(d) Is there a significant linear correlation between these first 4
data pairs?
YesNo
(e) Using only the last 4 data pairs for Facebook
hours and GPA, calculate the correlation coefficient. Round
your answer to 3 decimal places.
r =
(f) Is there a significant linear correlation between these last 4
data pairs?
YesNo
(g) Which statement explains this situation?
The data seems to be divided into two 'clusters'; those who spend a lot of time on Facebook and those who don't.The clustering of the data creates a significant correlation. Within each cluster there is not a significant correlation.It appears that the students who spend a lot of time on Facebook have a lower GPA than those students who do not.All of these are valid statements.
a)
| S.No | X | Y | (x-x̅)2 | (y-y̅)2 | (x-x̅)(y-y̅) |
| 1 | 1 | 3.3 | 8.0514 | 0.46 | -1.9153 |
| 2 | 1.5 | 3 | 5.4639 | 0.14 | -0.8766 |
| 3 | 2 | 3.2 | 3.3764 | 0.33 | -1.0566 |
| 4 | 2.2 | 2.9 | 2.6814 | 0.08 | -0.4503 |
| 5 | 5 | 2.3 | 1.3514 | 0.11 | -0.3778 |
| 6 | 5.5 | 2 | 2.7639 | 0.39 | -1.0391 |
| 7 | 6 | 2.2 | 4.6764 | 0.18 | -0.9191 |
| 8 | 7.5 | 2.1 | 13.4139 | 0.28 | -1.9228 |
| Total | 30.7 | 21 | 41.7788 | 1.96 | -8.5575 |
| Mean | 3.838 | 2.63 | SSX | SSY | SXY |
| correlation coefficient r= | Sxy/(√Sxx*Syy) = | -0.947 | |
b)Yes
c)
| correlation coefficient r= | Sxy/(√Sxx*Syy) = | -0.645 | |
d)No
e)
| correlation coefficient r= | Sxy/(√Sxx*Syy) = | -0.359 | |
f)
No
g)
All of these are valid statements.
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