Management of a fastfood chain proposed the following regression model to predict sales at outlets:
y = β_{0} + β_{1}x_{1} + β_{2}x_{2} + β_{3}x_{3} + ε, where
y = sales ($1000s)
x_{1}= number of competitors within one mile
x_{2}= population (in 1000s) within one mile
x_{3}is 1 if a driveup window
is present, 0 otherwise
Multiple regression analysis was performed on a random sample of
data collected from 25 outlets.
Given the following portion of an output of the regression software
tool, answer the question:
Which of the independent variables are significant at α
= 2.5%?
Coefficients 
Standard Error 
t Statistic 
Pvalue 

Intercept 
39.223 
5.942 
6.601 
0.0000 
Competitors 
3.556 
2.115 
1.681 
0.1076 
Population 
7.314 
2.189 
3.341 
0.0031 
Driveup 
9.065 
3.814 
2.377 
0.0270 
Select one:
Population only
Competitors only
Both Population and Driveup
Driveup only
Both Population and Competitors
All three variables
Answer: Population Only
Explanation: We have the Null Hypothesis that the coefficients are not significant vs the alternative Hypothesis that the Coefficients are significant.
We reject the null hypothesis to conclude that the coefficients are significant if pvalue < 0.025.
So, All those variables are significant for which pvalue < 0.025
Pvalue for Population = 0.0031 < 0.025 > Significant
Pvalue for Competitors = 0.1076 > 0.025 > Insignificant
Pvalue for Drive up = 0.0270 > 0.025 > Insignificant
Thus, only Population is significant.
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