Lenny's,a National Restaurant Chain,conducted a Study of the Factors Affecting

Essay

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: $$\begin{array} { l l } \mathrm { Y } & = \text { Annual restaurant sales ( } \$ 000 ) \\\mathrm { X } _ { 1 } & = \text { Disposable personal income (per capita) of residents within } 5 \text { mile radius } \\\mathrm { X } _ { 2 } & = \text { License to sell beer/wine } ( 0 = \text { No, } 1 = \mathrm { Yes } ) \\\mathrm { X } _ { 3 } & = \text { Location (within one-half mile of interstate highway- } 0 = \text { No, } 1 = \text { Yes) } \\\mathrm { X } _ { 4 } & = \text { Population (within } 5 \text { mile radius) } \\\mathrm { X } _ { 5 } & = \text { Number of competing restaurants within } 2 \text { mile radius }\end{array}$$ The data were entered into a computerized regression program and the following results were obtained: $$\begin{array} { l l } \text { MULTIPLE R } & .889 \\\text { R-SQUARE } & .79 \\\text { STD. ERROR OF EST. } & .40\end{array}$$ ANALYSIS OF VARIANCE
$\begin{array}{lrrrr} & \text { DF } & \text { Sum Squares } & \text { Mean Sqr. } & \text { F-Stat } \\\hline \text { Regression } & 5 & 326.13 & 65.226 & 18.17 \\\text { Error } & 24 & 86.17 & 3.590 & \\\text { Total } & 29 & 412.30 & &\end{array}$

$\begin{array}{lccr}\text { Variable } & \text { Coefficient } & \text { Std. Error } & \text { T-Value } \\\text { Constant } & .363 & .196 & 1.852 \\\mathrm{X}-1 & .00275 & .00104 & 2.644 \\\mathrm{X}-2 & 76.65 & 93.70 & .818 \\\mathrm{X}-3 & 164.3 & 235.4 & .698 \\\mathrm{X}-4 & .00331 & .00126 & 2.627 \\\mathrm{X}-5 & 46.2 & 12.1 & -3.818\end{array}$ 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
(c) "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.