Below is data on weekly Quantity demanded of pizza in a small town in South Geor
ID: 1095579 • Letter: B
Question
Below is data on weekly Quantity demanded of pizza in a small town in South Georgia, prices and average household incomes. Use the data to perform a linear regression analysis of price and income on quantity demanded. (20 points) a) How well does the regression fit the data? b) What is the income elasticity of demand for pizza when the income (M) is $40 (thousand) and the price (P) is $30?
Quantity
Price
Income (thousand)
1
183
29.25
30.72
2
207
30.1
37.57
3
183
30.54
29.43
4
192
28.67
37.2
5
182
30.23
35.87
6
217
29.76
35.16
7
180
31.77
27.7
8
195
31.01
32.96
9
200
29.21
32.3
10
198
30.79
36.1
11
195
29.75
32.68
12
205
29.98
37.49
13
182
30.06
31.32
14
218
28.94
38.67
15
231
29.76
34.82
16
212
27.94
42.27
17
222
30.75
40.03
18
150
28.96
30.02
19
183
30.96
34.3
20
158
29.03
29.89
21
199
30.83
35.27
22
196
30.6
33.55
23
234
29.98
40.03
24
171
29.27
29.91
25
171
31.42
33.69
26
170
29.24
31.51
27
210
27.61
30.6
28
184
30.64
34.36
29
223
29.97
37.59
30
177
31.87
31.78
31
168
30.06
27.47
32
192
28.83
40.64
33
201
30.91
36.2
34
207
29.84
38.05
35
241
29.94
39.55
36
216
30.67
35.38
37
193
31.03
40.42
38
187
28.45
37.29
39
194
30.02
29.68
40
212
30.85
40.61
41
141
30.46
28.23
42
217
28.85
36.87
43
194
29.34
36.59
44
182
30.1
29.56
45
225
28.88
36.26
46
214
30.2
34.29
47
198
28.56
41.7
48
183
29.51
30.92
49
206
29.86
31.22
50
198
30.83
32.39
Quantity
Price
Income (thousand)
1
183
29.25
30.72
2
207
30.1
37.57
3
183
30.54
29.43
4
192
28.67
37.2
5
182
30.23
35.87
6
217
29.76
35.16
7
180
31.77
27.7
8
195
31.01
32.96
9
200
29.21
32.3
10
198
30.79
36.1
11
195
29.75
32.68
12
205
29.98
37.49
13
182
30.06
31.32
14
218
28.94
38.67
15
231
29.76
34.82
16
212
27.94
42.27
17
222
30.75
40.03
18
150
28.96
30.02
19
183
30.96
34.3
20
158
29.03
29.89
21
199
30.83
35.27
22
196
30.6
33.55
23
234
29.98
40.03
24
171
29.27
29.91
25
171
31.42
33.69
26
170
29.24
31.51
27
210
27.61
30.6
28
184
30.64
34.36
29
223
29.97
37.59
30
177
31.87
31.78
31
168
30.06
27.47
32
192
28.83
40.64
33
201
30.91
36.2
34
207
29.84
38.05
35
241
29.94
39.55
36
216
30.67
35.38
37
193
31.03
40.42
38
187
28.45
37.29
39
194
30.02
29.68
40
212
30.85
40.61
41
141
30.46
28.23
42
217
28.85
36.87
43
194
29.34
36.59
44
182
30.1
29.56
45
225
28.88
36.26
46
214
30.2
34.29
47
198
28.56
41.7
48
183
29.51
30.92
49
206
29.86
31.22
50
198
30.83
32.39
Explanation / Answer
Below is data on weekly Quantity demanded of pizza in a small town in South Georgia, prices and average household incomes.
Use the data to perform a regression analysis of price and income on quantity demanded. (20 points) a.) How well does the regression fit the data. b.) What is the income elasticity of demand for pizza?
Quantity
Price
Income
1
183
29.25
30.72
2
207
30.1
37.57
3
183
30.54
29.43
4
192
28.67
37.2
5
182
30.23
35.87
6
217
29.76
35.16
7
180
31.77
27.7
8
195
31.01
32.96
9
200
29.21
32.3
10
198
30.79
36.1
11
195
29.75
32.68
12
205
29.98
37.49
13
182
30.06
31.32
14
218
28.94
38.67
15
231
29.76
34.82
16
212
27.94
42.27
17
222
30.75
40.03
18
150
28.96
30.02
19
183
30.96
34.3
20
158
29.03
29.89
21
199
30.83
35.27
22
196
30.6
33.55
23
234
29.98
40.03
24
171
29.27
29.91
25
171
31.42
33.69
26
170
29.24
31.51
27
210
27.61
30.6
28
184
30.64
34.36
29
223
29.97
37.59
30
177
31.87
31.78
31
168
30.06
27.47
32
192
28.83
40.64
33
201
30.91
36.2
34
207
29.84
38.05
35
241
29.94
39.55
36
216
30.67
35.38
37
193
31.03
40.42
38
187
28.45
37.29
39
194
30.02
29.68
40
212
30.85
40.61
41
141
30.46
28.23
42
217
28.85
36.87
43
194
29.34
36.59
44
182
30.1
29.56
45
225
28.88
36.26
46
214
30.2
34.29
47
198
28.56
41.7
48
183
29.51
30.92
49
206
29.86
31.22
50
198
30.83
32.39
Answer:
We regress quantity demanded on price and income using ordinary least square.
The regression output has been given below: [refer excel sheet for details]
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.644179584
R Square
0.414967336
Adjusted R Square
0.390072329
Standard Error
16.42551057
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
2
8994.34232
4497.17116
16.66869734
3.37857E-06
Residual
47
12680.47768
269.7973974
Total
49
21674.82
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Intercept
81.6969373
81.48518399
1.002598672
0.321188612
-82.23010861
Price
-0.121581938
2.518148135
-0.048282282
0.961695866
-5.187442561
Income
3.410691125
0.600170294
5.682872276
8.10149E-07
2.203304229
a.) How well does the regression fit the data
Answer:
It is the value of R-square that represents how well regression fit the data. From the table above, we note that value of R-Square is 0.414967 which is very low. In other words, only 41.49% of the total variation in quantity demanded is explained within the model (or only 41.49% of the total variation in quantity demanded is explained by price and income together). Since the value of R-square is low, we say that regression does not fit the data well.
However, when we do the joint test (or test the significance of model), we find that the model is significant (or price and income together significantly affect the quantity demanded for pizza) as represented by significantly high value of F-statistics (16.67).
b.) What is the income elasticity of demand for pizza?
Answer:
To derive income elasticity of demand, we take all variables in log form. Then rerun the regression using log(quantity) as dependent variable and log(price) and log(income) as dependent variable. In the resulting regression output, the coefficient of log(income) would denote income elasticity of demand for pizza.
The regression output has been given below; [refer excel sheet for details]
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.657289805
R Square
0.432029887
Adjusted R Square
0.407860947
Standard Error
0.036887474
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
2
0.04864565
0.024322825
17.87541656
1.68519E-06
Residual
47
0.063952231
0.001360686
Total
49
0.112597881
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Intercept
1.318226864
0.619475112
2.127973891
0.038613043
0.072003684
log(Price)
0.003752581
0.387408005
0.009686379
0.992312508
-0.775611799
log(Income)
0.628878391
0.106536254
5.902951992
3.77361E-07
0.414555094
From the above table we note that coefficient of log(Income) is 0.628878391. So, income elasticity of demand for pizza is 0.628878391.
Quantity
Price
Income
1
183
29.25
30.72
2
207
30.1
37.57
3
183
30.54
29.43
4
192
28.67
37.2
5
182
30.23
35.87
6
217
29.76
35.16
7
180
31.77
27.7
8
195
31.01
32.96
9
200
29.21
32.3
10
198
30.79
36.1
11
195
29.75
32.68
12
205
29.98
37.49
13
182
30.06
31.32
14
218
28.94
38.67
15
231
29.76
34.82
16
212
27.94
42.27
17
222
30.75
40.03
18
150
28.96
30.02
19
183
30.96
34.3
20
158
29.03
29.89
21
199
30.83
35.27
22
196
30.6
33.55
23
234
29.98
40.03
24
171
29.27
29.91
25
171
31.42
33.69
26
170
29.24
31.51
27
210
27.61
30.6
28
184
30.64
34.36
29
223
29.97
37.59
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