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

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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

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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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Lenny's, a national restaurant chain...

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.
Y = Annual restaurant sales ($000)
X1 = Disposable personal income per capita of residents within 5 miles radius
X2 = License to sell beer / wine (0= Yes, 1 = No)
X3 - Location (Within ½ mile of interstate highway (0 = No, 1 = Yes)
X4 = Population (within 5 miles radius)
X5 - Number of competing restaurants within 2 miles radius

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

Multiple R .889
R-Square .79
Standard Error of Estimate .40
F-Stat 18.17

Variable Constant Standard Error T-Values
Constant .363 .196 1.852
X1 .00275 .00104 2.644
X2 76.65 93.70 .818
X3 164.3 235.4 .698
X4 .00331 .00126 2.627
X5 46.2 12.1 3.818

Question

A. Write the regression equation for predicting restaurant sales.
B. Give the interpretation of each of the estimated regression coefficients
C. Which of the independent variables (if any) are statistically significant at the .05 significance level in "explaining" restaurant sales? Why?
D. What proportion of the variation in restaurant sales is "explained" by the regression equation?
E. Perform an F-Test (at .05 significance level) of the overall explanatory power of the regression model.

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