# 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

https://brainmass.com/economics/regression/lenny-s-a-national-restaurant-chain-conducted-a-study-of-the-factors-affecting-demand-sales-69317

#### 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.