Western Steakhouses, a fast-food franchiser, opened 15 years ago. Each year sinc
ID: 403513 • Letter: W
Question
Western Steakhouses, a fast-food franchiser, opened 15 years ago. Each year since then, the number of restaurants in operation was recorded. An analyst for the firm wishes to use these data to predict the number of restaurants that will be in operation next year. The data that was collected is in the following table:
Year-t
#Restaurants
Year-t
#Restaurants
Year-t
#Restaurants
0
11
5
36
10
119
1
14
6
46
11
156
2
16
7
67
12
257
3
22
8
82
13
284
4
28
9
99
14
403
Excel was used to perform a Regression Analysis and the output is as follows:
Regression Statistics
Multiple R
0.88
R Square
0.77
ANOVA
df
SS
MS
F
Significance F
Regression
1
152755.7143
152755.7
47.49001
1.1E-05
Residual
13
41815.61905
3216.586
Total
14
194571.3333
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-54
27.88084712
-1.94279
0.074019
-114.4
6.06623
-114.4
6.06623
Year-t
23
3.389366819
6.8913
1.1E-05
16.03486
30.67942
16.03486
30.67942
Year-t
#Restaurants
Year-t
#Restaurants
Year-t
#Restaurants
0
11
5
36
10
119
1
14
6
46
11
156
2
16
7
67
12
257
3
22
8
82
13
284
4
28
9
99
14
403
Explanation / Answer
(1)
R Square = 0.77
Thus, 77% of the data is explained by the regression line. Hence, It is significant.
(2)
Restaurants =-54+23*year-t
(3)
next year=15
Restaurants =-54+23*15 =291
(4)
No, as the R^2 value is only 77%. It is not that strong.
(5)
No.
AS R^2 value is only 77%. It is not that strong..Even Regression is not significant.
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