As a sociologist, you are interested in better understanding what factors impact personal annual income. To explore this topic, you asked participants to report how many years of education they have attained as well as their salaries. What is the correlation between education and income in the sample below?
Case |
Education (X) |
Salary (in thousands) (Y) |
1 |
14 |
46 |
2 |
16 |
85 |
3 |
15 |
51 |
4 |
13 |
69 |
5 |
15 |
64 |
6 |
16 |
71 |
7 |
14 |
61 |
8 |
13 |
54 |
9 |
16 |
45 |
10 |
12 |
45 |
Use this table to help you calculate the correlation coefficient.
Case |
X |
Y |
XY |
X^{2} |
Y^{2} |
1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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10 |
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∑ |
5. SPxy:
6. SSx:
7. SSy:
8. r:
Part 3.
For each of the scatterplots below, identify the direction of the relationship between two variables
Figure 1. (see attachment)
9. Is the direction of the correlation in Figure 1 positive, negative, or zero (null)
Figure 2. (see attachment)
10. Is the direction of the correlation in Figure 2 positive, negative, or zero (null)
Part 4.
In the following scenarios, determine how the correlation coefficient has been distorted.
11. Educational researchers believe a null correlation in their study was due to the fact that their participants came from two very different demographic groups.
a. Confounding variable
b. Outliers
c. Range restriction
d. Subsamples
12. Doctors suspect a very strong, positive correlation in their study was due to the fact that one participant scored much higher on their tests than the rest of the sample.
a. Confounding variable
b. Outliers
c. Range restriction
d. Subsamples
CASE | X | Y | XY | X^2 | Y^2 |
1 | 14 | 46 | 644 | 196 | 2116 |
2 | 16 | 85 | 1360 | 256 | 7225 |
3 | 15 | 51 | 765 | 225 | 2601 |
4 | 13 | 69 | 897 | 169 | 4761 |
5 | 15 | 64 | 960 | 225 | 4096 |
6 | 16 | 71 | 1136 | 256 | 5041 |
7 | 14 | 61 | 854 | 196 | 3721 |
8 | 13 | 54 | 702 | 169 | 2916 |
9 | 16 | 45 | 720 | 256 | 2025 |
10 | 12 | 45 | 540 | 144 | 2025 |
SUM | 144 | 591 | 8578 | 2092 | 36527 |
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