Question Details

Give the regression equation for predicting restaurant sales


2.	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 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 5 mile radius)
X5	= Number of competing restaurants within 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 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  

Questions:

(a)	Give the regression equation for predicting restaurant sales.
(b)	Give an interpretation of each of the estimated regression coefficients.
(c)	Which of the independent variables (if any) are statistically significant at the .05 level in "explaining" restaurant sales?
(d)	What proportion of the variation in restaurant sales is "explained" by the regression equation?
(e)	Perform an F-test (at the .05 significance level) of the overall explanatory power of the regression model.




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