1
Regression
39472730.773
2
19736365.387
48.477
.000
b
Residual
12620946.668
31
407127.312
Total
52093677.441
33
a. Dependent Variable: Bars
b. Predictors: (Constant), Promotion, Price
p-value = 0.000
Since the p-value =0.000 < 0.05, we rejected the null hypothesis. We have enough evidence to
conclude that
at least one
of the independent variables (price and/or promotional expenditures) is
related to sales.

9
Tests of Hypothesis
To determine whether variable X
2
(amount of promotional expenditures) has a significant effect on
sales, taking into account the price of OmniPower bars, the null and alternative hypotheses are
H
0
:
β
2
= 0
H
1
:
β
2
≠ 0
Coefficients
a
Model
Unstandardized
Coefficients
Standardized
Coefficients
t
Sig.
95.0% Confidence Interval
for B
Collinearity
Statistics
B
Std. Error
Beta
Lower
Bound
Upper
Bound
Tolerance
VIF
1
(Constant)
5837.521
628.150
9.293
.000
4556.400
7118.642
Price
-53.217
6.852
-.690
-7.766
.000
-67.193
-39.242
.991
1.009
Promotion
3.613
.685
.468
5.273
.000
2.216
5.011
.991
1.009
a. Dependent Variable: Bars
The p-value = 0.000
Since the p-value =0.000 < 0.05, we rejected the null hypothesis. We have enough evidence to
conclude that there is a significant relationship between the variable X
2
(promotional expenditures)
and sales, taking into account the price, X
1
At the 0.05 level of significance, is there evidence that the slope of sales with price
is different from zero?
H
0
:
β
1
= 0
H
1
:
β
1
≠ 0
The p-value = 0.000
Since the p-value =0.000 < 0.05, we rejected the null hypothesis. We have enough evidence to
conclude that there is a significant relationship between the variable X
1
(price) and sales, taking into
account the promotional expenditures, X
2

10
Confidence Interval Estimation
Instead of testing the significance of a population slope, you may want to estimate the value of a
population slope.
To construct a 95% confidence interval estimate of the population slope,
β
1
(the effect of price, X
1
,
on sales, Y, holding constant the effect of promotional expenditures, X
2
),
Coefficients
a
Model
Unstandardized
Coefficients
Standardized
Coefficients
t
Sig.
95.0% Confidence Interval
for B
Collinearity
Statistics
B
Std. Error
Beta
Lower
Bound
Upper
Bound
Tolerance
VIF
1
(Constant)
5837.521
628.150
9.293
.000
4556.400
7118.642
Price
-53.217
6.852
-.690
-7.766
.000
-67.193
-39.242
.991
1.009
Promotion
3.613
.685
.468
5.273
.000
2.216
5.011
.991
1.009
a. Dependent Variable: Bars
Taking into account the effect of promotional expenditures, the estimated effect of a 1-cent increase
in price is to reduce mean sales by approximately 39.242 to 67.193 bars.
−67.193 ≤ β
1
≤ −39.242
You have 95% confidence that this interval correctly estimates the relationship between these
variables.
More example
Construct a 95% confidence interval estimate of the population slope of sales with promotional
expenditures.
2.216 ≤ β
1
≤ 5.011
Thus, taking into account the effect of price, the estimated effect of each additional dollar of
promotional expenditures is to increase mean sales by approximately 2.2 to 5.0 bars. You have 95%
confidence that this interval correctly estimates the relationship between these variables.

11
Exercises
Q1
A mail-order catalog business selling personal computer supplies, software, and hardware maintains
a centralized warehouse. Management is currently examining the process of distribution from the
warehouse and wants to study the factors that affect warehouse distribution costs. Currently, a small

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