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Lenny's, a national restaurant chain, conducted a study of the factors affecting demand (sales).

Lenny's, a national restaurant chain, conducted a study of the factors affecting demand (sales). The following variables were defined and measured for a random sample of 30 of its restaurants:
(NOTE: This question and the 3 that follow it, may require the use of statistical tables.)
---Y = Annual restautant sales ($000)
---X1 = Disposable personal income (per capita) of residents within a 5 mile radius
---X2 = License to sell beer/wine (0=No, 1=Yes)
---X3 = Location (within one-half mile of interstate highway; 0 = No, 1 = Yes)
---X4 = Population (within a 5 mile radius)
---X5 = Number of competing restaurants within a 2 mile radius.

The data were entered into a computerized regression program and the following results were obtained:

MULTIPLE R ----------------------------.889
R-SQUARE ------------------------------.79
STD. ERROR OF EST. --------------.40

ANALYSIS OF VARIANCE

------------------------------DF--------------Sum of Squares--------------Mean Sqr.--------------F-Stat.
Regression --------------5--------------------326.13--------------------------65.226-----------------18.17
Error ----------------------24 --------------------86.17---------------------------3.590
Total ----------------------29 ------------------412.30

Variable--------------Coefficient--------------Std. Error--------------t-value
Constant__________.363____________.196___________1.852
__X-1____________.00275___________.00104_________2.644
__X-2 ____________76.65 ___________93.70 _________.818
__X-3 ____________164.3 ___________235.4_________ .698
__X-4 ____________.00331 __________.00126 ________2.627
__X-5 ____________-46.2 ____________12.1 _________-3.818

Based on the information presented above, which of the coefficients are statistically significantly different from zero at the .05 level of significance?

a. Constant, X-2 and X-3
b. X-1, X-4 and X-5
c. All except X-2 and X-3
d. None are significant

Solution Summary

This solution examines the t-value of a coefficient: if t-value of a coefficient is external to the critical value of t we reject Ho - ie. that particular coefficient if statistically significant. Calculations and answer are provided.

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