The district manager of Jason’s, a large discount electronics chain, is investigating why certain stores in her region are
performing better than others. She believes that three factors are related to total sales: the number of competitors in
the region, the population in the surrounding area, and the amount spent on advertising. From her district, consisting
of several 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).
X1 =
number of competitors in the region.
X2 =
population of the region (in millions).
X3 =
advertising expense (in $ thousands).
The sample data were run on MINITAB, with the following results.
Analysis of variance
SOURCE
DF
Regression
SS
3
MS
3050.00
Error
26
2200.00
Total
29
5250.00
Predictor
Coef
Constant
14.00
84.62
StDev
7.00
X1
-1.00
0.70
-1.43
X2
30.00
5.20
5.77
X3
0.20
1.
0.08
1016.67
t-ratio
2.00
2.50
What are the estimated sales for the Bryne store, which has four competitors, a regional population of 0.4
(400,000), and advertising expense of 30 ($30,000)?
2.
Compute the R2 value.
3.
Compute the multiple standard error of estimate.
4.
Conduct a global test of hypothesis to determine whether any of the regression coefficients are not equal to
zero. Use the .05 level of significance.
5.
Conduct tests of hypotheses to determine which of the independent variables have significant regression
coefficients. Which variables would you consider eliminating? Use the .05 significance level.
a) What are the estimated sales for the Bryne store, which has four competitors, a regional population of 0.4
(400,000), and advertising expense of 30 ($30,000)?
The estimated regression equation is
Sales = 14 - 1 * Number of competitors + 30 * Population + 0.20 * Advertising expense
The estimated value is Sales = 14 -1 * 4 + 30 * 0.4 + 0.20 * 30 =$28000
b) Compute the R2 value.
R^2 = SSR/SST =3050/5250 = 0.58095
c) Compute the multiple standard error of estimate.
Standard error of estimate =
MSE = 84.62 = 9.1989
d) Conduct a global test of hypothesis to determine whether any of the regression coefficients are not equal
to zero. Use the .05 level of significance.
ANOVA (F test ) is used to determine if any of the regression coefficients are not 0.
F = 1016.67/84.62 = 12.0145
Critical value of F with (3,26) = 2.975
Since 12.0145 > 2.975, we reject the null hypothesis that all variables are insignificant
e) Conduct tests of hypotheses to determine which of the independent variables have significant regression
coefficients. Which variables would you consider eliminating? Use the .05 significance level.
The null hypothesis that the regression coefficients are 0s. We have the following results:
Critical value =2.056
Variable
Test t- score
Decision
X1 = number of competitors in the region.
-1.43
Fails to reject
X2 = population of the region (in millions).
5.77
Reject
X3 = advertising expense (in $ thousands).
2.50
Reject
The significance test suggests that the variable X1 = number of competitors in the region has an
insignificant regression coefficient in the model. This variable can be removed from the model.