Question

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: Ý a + b X where Y is Depression and X, is stress. We actually could rewrite the equation as: Depression = a + b Stress Stress 38 28 Depression 26 16 34 22 15 24 18 18 12 15 42 18 26 45 32 26 22 33 I Using the output: a. What is the value of bi? standard Error of bi? Significance Level of bi (i.e. "p-value")? b. Write a sentence that describes the interpretation of b. What is the standardized value of bi? 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 d. What is the value of a? standard Frror of a?

Answer 1

Using Excel, 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	0.019	0.961

a. b₁ = 0.49

Standard error of b₁ = 0.204

p-value of b₁ = 0.043

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

c. Standardised value of b₁ (Multiple R) = 0.647

d. a = 4.819

Standard error of a = 6.552

p-value of a = 0.483

e. If there is no stress, 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