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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


    ------------------------------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
    __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.