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# Regression Model

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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.
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.

##### Solution Summary

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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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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