Question

A psychologist employed at a large engineering company is asked to investigate the relationship between job satisfaction (Y) and productivity (X₁) and perseverance (X₂). Higher scores indicate greater levels of these constructs. Data are collected from 100 employees and summarized as follows:

	PROD	PERS	JOB (Y)	Mean	SD
PROD	------	.23	.77	8.60	1.40
PERS		------	.67	7.30	1.70
JOB (y)			------	20.50	5.30

Step	Variable entered	R	R2	SE	Partial r's
0				5.30
1				5.21
2		.85	.72	4.98

1. In a stepwise multiple regression, what variable would be entered at step 1, and why?
2. The partial r for the remaining variable is .64 and is significant. Explain to me what this means. Would you proceed with Step 2?
3. The multiple R and R2 st step 2 have been provided to you. Explain what each of these values are telling us.
4. Why are the SE values decreasing at each step?  

Answer 1

a. The variable with maximum correlation with y (jobs satisfaction) will be entered first because it will be able to explain maximum variability possible in y i.e., X1 i.e, productivity will be entered first as it as 0.77 correlation

b. This means that perseverence has correlation with y in presence of productivity = 0.67 and in absense of X1 or the correlation of X2 alone with y is 0.64 which means that the variables X1 and X2 are negligibly correlated and explain different variabilities in y and both are important and significant. In step 2, we will include X2 also in the model

c. R is the multiple correlation of y with X1 and X2 = 0.85 (strong and positive) i.e., as X1 and X2 increase, y increases.

R-sq = 0.72 ie., X1 and X2 together explain 72% variabillity in y(chol)

d. The SE or standard error is the residual or unexplained variation that remains in y.

Since, we are adding significant variables at each step that are explaining some part of variability in Y and hence, unexplained variability reduces at each step.

Therefore, SE reduces at each step

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