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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.

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    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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