Question

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

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

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.

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