Question

Management of a fast-food chain proposed the following regression model to predict sales at outlets:

y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε, where

y = sales ($1000s)

x₁= number of competitors within one mile

x₂= population (in 1000s) within one mile

x₃is 1 if a drive-up 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	P-value
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
Drive-up	9.065	3.814	2.377	0.0270

Select one:

Population only

Competitors only

Both Population and Drive-up

Drive-up only

Both Population and Competitors

All three variables

Answer 1

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 p-value < 0.025.

So, All those variables are significant for which p-value < 0.025

P-value for Population = 0.0031 < 0.025 ------> Significant

P-value for Competitors = 0.1076 > 0.025 ------> Insignificant

P-value for Drive up = 0.0270 > 0.025 ------> Insignificant

Thus, only Population is significant.