Question

Instructions: Please apply what you know about correlations (from class and from our text) to complete the following questions, after reading the scenario below.

Scenario: A social worker is interested in studying the relationship between participating in a housing program and ability to obtain employment. To complete this study, the social worker obtains the data from seven (7) housing programs around California and how many were subsequently able to get employment within a 12-month period. Below are the results of the social worker’s study.

The social worker found the following number of participants for each of the housing programs, respectively: 20, 12, 8, 15, 10, 17, 11. (Hint: these are marked as the “X” values).

From the same programs, respectively, the social worker discovered the following number of participants also successfully found employment: 12, 7, 4, 10, 6, 10, 7. (Hint: these are marked as the “Y” values).

To set up this information conveniently, you may choose to make a table like this:

	Participated in program (X)	Found employment (Y)
Program 1	20	12
Program 2	12	7

And so on….. to program 7.

Now, please set up the columns and row for X, Y, XY, X², and Y² from the data collected. And do not forget your N value as well. (3 points).

Answer 1

Participarion in program (x)	Found Employment(Y)	XY	X^2	Y^2
20	12	240	400	144
12	7	84	144	49
8	4	32	64	16
15	10	150	225	100
10	6	60	100	36
17	10	170	289	100
11	7	77	121	49

• COV(X,Y)= (X-Xbar)(Y-Ybar) =   - Xbar Ybar = 116.1428571- (13.2857)(8) = 9.8571
• VAR(X) = - Xbar = 15.3469387755102
• SD(X) = = 3.9175169
• VAR(Y) = - Ybar = 6.571428571
• SD(Y) = 2.563479778

CORRELATION = = 0.981545

There is a high correlation in the relationship between participating in a housing program and ability to obtain employment.