Question

A psychologist was interested in whether a sense of "Job Autonomy" (a measure of how much freedom and discretion employees have over their job -higher scores on this measure correspond to more autonomy) could predict levels of Burnout among social workers. To study this, she collected data from five social workers, and conducted a regression analysis to predict levels of Burnout from Job Autonomy. Burnout was measured with a standard scale, where 1- low burnout and 10 high burnout (so, higher scores- more burnout). The table below presents the results for the sample of the five social workers. Product of Deviation Deviation Deviation Squared Deviation Squared Deviation Scores Job Burnout Autonomy 3 5 1. Which variable is "X" or the Predictor? 2. Which variable is "Y or the Criterion?

Answer 1

Job Autonomy	Deviation	Deviation Squared	Burnout	Deviation	Deviation Squared	Product of deviation scores
1	-3.4	11.56	6	1.2	1.44	-4.08
3	-1.4	1.96	8	3.2	10.24	-4.48
5	0.6	0.36	5	0.2	0.04	0.12
6	1.6	2.56	3	-1.8	3.24	-2.88
7	2.6	6.76	2	-2.8	7.84	-7.28
Mx = 4.4		SSxx = 23.2	My= 4.8		SSyy = 22.8	$\Sigma$ xy= -18.6

1) The predictor variable = Job Autonomy

2) The criterion variable is Burnout.

3)

i) regression coefficient b = ($\Sigma$ xy)/(SSxx) = -18.6/23.2 = -0.802

b = -0.802 which mean with every one unit increase in job autonomy the burnout decrease by 0.802 units.

ii) regression constatnt a = My - b*Mx = 4.8 - (-0.807)*4.4 = 8.328

iii) Burnout = 8.328 - 0.802*Jubautonomy

Y = 8.328 - 0.802*X

4) predicted scores

Job Autonomy	Burnout	predicted scores $\hat{Y}$
1	6	7.526
3	8	5.922
5	5	4.318
6	3	3.516
7	2	2.714

5)

Burnout vs Job autonomy 0.8017x + 8.3276 y- R20.654 6 Burnout 闷 Linear (Burnout) _ 0 0 4 Job Autonomy

6)

Burnout Y	predicted scores $\hat{Y}$	deviation in Y
6	7.526	-1.526	2.328676
8	5.922	2.078	4.318084
5	4.318	0.682	0.465124
3	3.516	-0.516	0.266256
2	2.714	-0.714	0.509796
			$\Sigma$ = 7.887936

SS_Error = 7.89

r² = (1 - SS_Error/SS_y) = (1- 7.89/22.8) = 0.654