4. Regression Analysis II a) Organic Foods Inc. owns a chain of 14 supermarkets
ID: 2922106 • Letter: 4
Question
4. Regression Analysis II
a) Organic Foods Inc. owns a chain of 14 supermarkets in Metro Vancouver. Using in-store promotions, Organic managers recently ran an experiment intended to identify the demand for its “private label” frozen pizzas. For the month of September the price, p, in each store was different, ranging from $5.00 per pizza to $11.50 in increments of 50¢. They also used census data to obtain the average annual household income, Y, in thousands in the neighbourhood around each store. They counted the number of pizzas, q, sold per 1000 customers in each store. The data set is as follows.
q
p
Y
46
5
70
41
5.5
82
36
6
65
43
6.5
110
41
7
104
30
7.5
58
38
8
91
33
8.5
68
33
9
87
22
9.5
60
31
10
112
25
10.5
96
24
11
74
24
11.5
85
Use the regression tool in Excel to estimate a linear demand function: q = a + bp + cY. No diagram is necessary but cut and paste your regression output below. Do not include the “ANOVA” table and do not include the confidence intervals. State whether the coefficients on price and income are statistically significantly different from zero at the 5% significance level and explain how you know that. What is the R2?
b) Based on your estimated demand curve, if p = 6 and Y = 100, what is the point elasticity of demand? What is the income elasticity of demand at that point? (Start by stating the demand function, then do your calculations.) According to this estimated demand curve, what price would maximize revenue? (No diagram is needed.)
q
p
Y
46
5
70
41
5.5
82
36
6
65
43
6.5
110
41
7
104
30
7.5
58
38
8
91
33
8.5
68
33
9
87
22
9.5
60
31
10
112
25
10.5
96
24
11
74
24
11.5
85
Explanation / Answer
a).
Use the regression tool in Excel to estimate a linear demand function: q = a + bp + cY. No diagram is necessary but cut and paste your regression output below. Do not include the “ANOVA” table and do not include the confidence intervals. State whether the coefficients on price and income are statistically significantly different from zero at the 5% significance level and explain how you know that. What is the R2?
Coefficients
Standard Error
t Stat
P-value
Intercept
48.3697091
3.940058351
12.2763941
9.202E-08
p
-3.45818986
0.327038359
-10.574264
4.2199E-07
Y
0.16286145
0.037975728
4.28856677
0.00128022
Test for coefficients on price , t=-10.5743, P=0.000 which is < 0.05 level. The coefficient is significantly different from zero.
Test for coefficients on income, t=4.2885, P=0.000 which is < 0.05 level. The coefficient is significantly different from zero.
Regression Statistics
Multiple R
0.957356021
R Square
0.916530552
Adjusted R Square
0.901354288
Standard Error
2.44717427
Observations
14
b) Based on your estimated demand curve, if p = 6 and Y = 100, what is the point elasticity of demand? What is the income elasticity of demand at that point? (Start by stating the demand function, then do your calculations.) According to this estimated demand curve, what price would maximize revenue? (No diagram is needed.)
estimated demand curve, q=48.3697-3.4582*p+0.1629*Y
when p = 6 and Y = 100,
q =48.3697-3.4582*6+0.1629*100 = 43.9105.
Income elasticity of demand at this point =43.9105.
Coefficients
Standard Error
t Stat
P-value
Intercept
48.3697091
3.940058351
12.2763941
9.202E-08
p
-3.45818986
0.327038359
-10.574264
4.2199E-07
Y
0.16286145
0.037975728
4.28856677
0.00128022
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