Lebanese American University
Business School
ECO811
Spring 2022
1. 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 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 5 mile radius)
X5 = 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
R-SQUARE
STD. ERROR OF EST
.889
.79
.40
ANALYSIS OF VARIANCE
Regression
Error
Total
DF
5
24
29
Variable
Constant
X-1
X-2
X-3
X-4
X-5
Sum Squares
326.13
86.17
412.30
Coefficient
.363
.00275
76.65
164.3
.00331
46.2
Mean Sqr.
65.226
3.590
Std. Error
.196
.00104
93.70
235.4
.00126
12.1
F-Stat
18.17
T-Value
1.852
2.644
.818
.698
2.627
-3.818
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
"explaining" restaurant sales?
(d) What proportion of the variation in restaurant sales is "explained" by the regression equation?
Solutions:
(a)
Y = .363 + .00275X1 + 76.65X2 + 164.3X3 + .00331X4  46.2X5
1
(b)
a = .363
b1 = .00275
b2 = 76.65
b3 = 164.3
b4 = .00331
b5 = 46.2
(c)
Value of dependent variable (Y) when all independent variables (X's) are
equal to zero.
For a one dollar increase in per capita disposable income, expected restaurant
sales will increase by .00275( $1000) = $2.7
Expected annual restaurant sales are higher for a restaurant with a license to
sell beer/wine than for one without such a license.
Expected annual restaurant sales are higher for a restaurant located within
one-half mile of an interstate highway.
For a one person increase in population, expected restaurant sales will
increase by .00331( $1000) = $3.31.
For a one unit increase in the number of restaurants within a 2-mile radius,
expected annual restaurant sales decrease by 46.2( $1000)= $46,200.
H0:  i = 0
H1:  i  0
Reject H0 if t > t.025, 24 = 2.064 or t < 2.064.
The t-values of X1 and X4 are greater than +2.064 (and the t-value of X5 is less than -2.064). Therefore X1, X4,
and X5 are statistically significant at the .05 level in "explaining" restaurant sales.
(d)
According to the R-SQUARE statistic, 79 percent of the variation in restaurant sales is
"explained" by the regression equation.
2. The British Automobile Company is introducing a brand new model called the "London Special." Using the
latest forecasting techniques, BAC economists have developed the following demand function for the
"London Special":
QD = 1,200,000  40P
What is the point price elasticity of demand at prices of (a) $8,000 and (b) $10,000?
Solutions:
(a)
= .36
2
(b)
= .50
3. A firm has decided to invest in a piece of land. Management has estimated that the land can be sold in 5 years
for the following possible prices:
Price
10,000
15,000
20,000
25,000
(a)
(b)
(c)
Probability
.20
.30
.40
.10
Determine the expected selling price for the land.
Determine the standard deviation of the possible sales prices.
Determine the coefficient of variation.
Solutions:
1.
(a)
= 10,000 (.20) + 15,000 (.30) + 20,000 (.40) + 25,000 (.10)
= $17,000
(b)
= [(10,000  17,000)2 (.20) + (15,000  17,000)2 (.30) + (20,000  17,000)2 (.40) +
(25,000  17,000)2 (.10)].5
= [21,000,000].5
= $4583
(c)
=
= 0.270
3