Question

PREDICTION (REGRESSION) – Chapter 12

3. A researcher was interested in whether there was a relationship between stress and depression scores obtained from emergency health care providers. The data from 10 emergency workers are below. This is the same data you calculated a correlation on in Question 1. We are trying to use stress scores (IV or Predictor) to predict depression scores (DV or outcome). Using SPSS, calculate a linear regression model:

Y = a+b1X1      where Y is Depression and X₁ is stress.

We actually could rewrite the equation as:    Depression = a+b1Stress

Stress	Depression
38	26
28	16
42	34
18	22
26	15
45	24
32	18
26	18
22	12
33	15

Using the output:

1. What is the value of b₁? _______
   standard Error of b₁? ___________

Significance Level of b₁ (i.e. “p-value”)? ___________

2. Write a sentence that describes the interpretation of b₁.

3. What is the standardized value of b₁? Notice this is the same as the correlation coefficient from Question 1! The correlation coefficient and the standardized regression coefficient are the same in a one predictor regression.

4. What is the value of a? _______
   standard Error of a? ___________

Significance Level of a (i.e. “p-value”)? ___________

5. Write a sentence that describes the interpretation of a.

6. What is the predicted value of Depression, for someone with a score of 30 on stress?

Answer 1

Answer:

Given that,

$\rightarrow$  A researcher was interested in whether there was a relationship between stress and depression scores obtained from emergency health care providers.

$\rightarrow$ The data from 10 emergency workers are below. This is the same data you calculated a correlation on in Question 1.

$\rightarrow$ We are trying to use stress scores (IV or Predictor) to predict depression scores (DV or outcome).

Calculate a linear regression model:

Y = a+b1X1      where Y is Depression and X₁ is stress.

We actually could rewrite the equation as:    

Depression = a+b1Stress

Stress	Depression
38	26
28	16
42	34
18	22
26	15
45	24
32	18
26	18
22	12
33	15

Using SPSS, go to Data, select Data analysis, Choose regression. Put stress in X input range and depression in Y input range.

Summary Output
Regression Statistics
Multiple R	0.647
R-square	0.418
Adjusted R square	0.345
Standard error	5.326
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	163.072	163.072	5.749	0.043
Residual	8	226.928	28.366
Total	9	390.000
	Coefficients	Standard Error	t stat	P-value	Lower 95%	Upper 95%
Intercept	4.819	6.552	0.736	0.483	-10.289	19.927
Stress	0.490	0.204	2.398	0.043	0019	0.961

(a).

b1=0.49

Standard error of b1=0.204

The p-value of b1=0.043

(b).

With one unit increase in stress, depression increases by 0.49 units.

(c).

Standardized value of b1 (Multiple R)=0.647

(d).

a=4.819

Standard error of a=6.552

The p-value of a=0.483

(e).

If there is no stress, the depression score will be 4.819.

(f).

y=4.819+0.49x

Stress=30

Depression=4.819+0.49(30)

=4.819+14.7

=19.519