Hypothesis Test for Slope of Regression Line
The district manager of Jasons, a large discount electronics chain, is investigating why certain stores in her region are performing better than others. She believes that three factors are linked to total sales: the number of competitors in the region, population in the surrounding area, and the amount spent on advertising. From her district, consisting of some hundred stores, she selects a random sample of 30 stores. For each store she gathered the following information.
Y =

total sales last year (in $ thousands).

X_{1} =

number of competitors in the region.

X_{2} =

population of the region (in millions).

X_{3} =

advertising expense (in $ thousands).

The sample data were run on MINITAB, with the following results.
Analysis of variance

SOURCE

DF

SS

MS

Regression

3

3050.00

1016.67

Error

26

2200.00

84.62

Total

29

5250.00

Â

Predictor

Coef

StDev

tratio

Constant

14.00

7.00

2.00

X 1

1.00

0.70

1.43

X 2

30.00

5.20

5.77

X 3

0.20

0.08


a) Perform a global test of hypothesis to determine whether any of regression coefficients are not equal to zero. Use the .05 level of significance.
b) Conduct tests of hypotheses to conclude which of the independent variables have significant regression coefficients. Which variables would you consider eliminating? Use the .05 significance level.