Question

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	X2	Y2
1
2
3
4
5
6
7
8
9
10
∑

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

Answer 1

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