Question

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) X 1 = Disposable personal income (per capita) of residents within 5 mile radius X 2 = License to sell beer/wine (0 = No, 1 = Yes) X 3 = Location (within one-half mile of interstate highway-- 0 = No, 1 = Yes) X 4 = Population (within 5 mile radius) X 5 = 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. (fill the blanks using the information given from the above tables, do not round) Y = .363 + [ ] X 1 + [ ] X 2 + [ ] X 3 + [ ] X 4 - [ ] X 5 (b) True or False: (fill either T or F in each of the blanks in this question) X 1 is statistically significant at the .05 level in "explaining" restaurant sales. [ ] Each of X 2 and X 3 is statistically significant at the .05 level in "explaining" restaurant sales. [ ] Each of X 4 and X 5 is statistically significant at the .05 level in "explaining" restaurant sales. [ ] (c) [ ] % of the variation in restaurant sales is "explained" by the regression equation. (fill the blanks using the number given from the above tables, do not round) (d) True or False: "The result of the F-test (at the .05 significance level) of the overall explanatory power of the regression model is that we reject the null hypothesis (at the .05 significance level) and conclude that the five independent variables "explain" a significant proportion of the variation in restaurant sales." [ ] (fill either T or F in the blank)

          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)
X 1 = Disposable personal income (per capita) of residents within 5 mile radius
X 2 = License to sell beer/wine (0 = No, 1 = Yes)
X 3 = Location (within one-half mile of interstate highway-- 0 = No, 1 = Yes)
X 4 = Population (within 5 mile radius)
X 5 = 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. (fill the blanks using the information given from the above tables, do not round)
Y = .363 + [ ] X 1 + [ ] X 2 + [ ] X 3 + [ ] X 4 - [ ] X 5
(b) True or False: (fill either T or F in each of the blanks in this question)
X 1 is statistically significant at the .05 level in "explaining" restaurant sales. [ ]
Each of X 2 and X 3 is statistically significant at the .05 level in "explaining" restaurant sales. [ ]
Each of X 4 and X 5 is statistically significant at the .05 level in "explaining" restaurant sales. [ ]
(c) [ ] % of the variation in restaurant sales is "explained" by the regression equation. (fill the blanks using the number given from the above tables, do not round)
(d) True or False: "The result of the F-test (at the .05 significance level) of the overall explanatory power of the regression model is that we reject
the null hypothesis (at the .05 significance level) and conclude that the five independent variables "explain" a significant proportion of the variation in restaurant sales." [ ] (fill either T or F in the blank)

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)
X 1 = Disposable personal income (per capita) of residents within 5 mile radius
X 2 = License to sell beer/wine (0 = No, 1 = Yes)
X 3 = Location (within one-half mile of interstate highway– 0 = No, 1 = Yes)
X 4 = Population (within 5 mile radius)
X 5 = 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. (fill the blanks using the information given from the above tables, do not round)
Y = .363 + [ ] X 1 + [ ] X 2 + [ ] X 3 + [ ] X 4 - [ ] X 5
(b) True or False: (fill either T or F in each of the blanks in this question)
X 1 is statistically significant at the .05 level in "explaining" restaurant sales. [ ]
Each of X 2 and X 3 is statistically significant at the .05 level in "explaining" restaurant sales. [ ]
Each of X 4 and X 5 is statistically significant at the .05 level in "explaining" restaurant sales. [ ]
(c) [ ] % of the variation in restaurant sales is "explained" by the regression equation. (fill the blanks using the number given from the above tables, do not round)
(d) True or False: "The result of the F-test (at the .05 significance level) of the overall explanatory power of the regression model is that we reject
the null hypothesis (at the .05 significance level) and conclude that the five independent variables "explain" a significant proportion of the variation in restaurant sales." [ ] (fill either T or F in the blank)

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