Question

	Chicken Sandwiches (CS)
	Qcs
Store 1	Quantity of chicken sandwiches sold per day	Price CS	Price H	A = Advertising expenditures in thousands of dollars	I = After tax Income per week
1	1000	3.59	3	20	280
2	1100	3.39	2.89	16	280
3	1050	3.39	2.29	12	300
4	2000	2.99	2.69	20	450
5	2200	2.79	3	22	460
6	2100	2.49	3	22	450
7	1900	2.97	3	21	320
8	1100	3.49	2.59	16	280
9	870	3.79	2.39	16	260
10	1650	2.79	2.79	17	370
11	1420	2.99	2.69	24	330
12	1930	2.79	3	26	400
13	1228	3.19	2.59	22	320
14	1675	2.97	2.89	24	270
15	1300	3.09	2.79	14	280
16	1422	3.49	2.89	15	350
17	1877	2.99	3	22	360
18	1943	2.99	3.09	20	370
19	1622	3.19	3.49	21	350
20	1273	3.29	2.59	15	330
21	1064	3.59	2.49	13	330
22	1467	3.29	2.69	22	360
23	1598	3.19	2.9	18	360
24	1743	2.99	3	21	400
25	1289	3.2	2.79	25	360
26	1345	3	2.99	27	300
27	1987	2.79	3.09	29	380
28	1356	3.09	2.79	23	350
29	1098	3.19	2.49	20	330
30	2436	2.49	3.29	16	430
31	2875	2.29	2.69	28	460
32	2134	2.9	2.79	18	400
33	2579	2.69	3.49	28	410
34	2098	2.76	3.39	22	430
35	2468	2.59	3.49	25	460
36	987	3.29	2.89	12	320
37	1093	3.19	2.79	15	370
38	2543	2.69	3.09	28	320
39	3721	2.99	3.09	31	500
40	3214	2.99	3	18	250
41	2156	2.99	3.09	22	410
42	445	2.69	2.69	25	450
43	1324	3	2.69	16	300
44	1654	3.09	2.89	18	340
45	1789	2.99	2.99	19	360
46	1357	3.09	2.59	14	350
47	2146	2.99	3.09	26	390
48	2183	2.59	3.29	20	380
49	2265	2.39	3.19	21	400
50	2343	2.89	3.09	23	410
51	1904	2.99	3	20	370
52	1752	2.79	2.89	19	310
53	2354	3.09	3.19	26	400
54	2876	2.69	3.09	29	410
55	2169	2.89	3	21	320
56	3052	2.59	2.89	31	440
57	1654	3.29	2.69	17	320
averages	1810.140351	3.00	2.92	20.89	362.98

Problem Set

Week 2

100 Points

Question 1: Run a regression analysis using the data provided. If data analysis is not installed then follow these steps: (32 Points)

• Go to Data Analysis

• click on file, then options, then add-ins, then analysis tool pack scroll down to regression.

• Input y range - your dependent variable "quantity of chicken sandwiches"

• Input x range - your independent variables "Price CS, Price H, A, I)

• Select OK

• Write the equation interpret your results.

Instructions: Questions 2-18 are 4 points each.

Question 2: Are the goods substitutes or complements?

Question 3: Is there a positive or negative relationship between price of cs and Qcs? Is this relationshipsignificant?

Question 4: Is there a positive or negative relationship between price of H and Qcs? Is this relationship significant?

Question 5. Is there a positive or negative relationship between Advertising and Qcs? Is this relationship significant?

Question 6: Is there a positive or negative relationship between income and Qcs? Is this relationship significant?

Question 7: Which of the data points appear to be from a store located on a college campus? Explain.

Question 8: Which of the data points appear to be from a store located in a very competitive area? Explain.

Question 9: Which store appears to be in a high-income area?

Question 10: What is the average price of CS, price of Hamburgers, amount of advertising and weekly take home income?

Question 11: Plug in the average numbers into the regression equation.

Question 12: Estimate the change in chicken sandwiches if the price of the sandwich rises to $4.

Question 13: What would happen to Qcs if the advertising budget was increased by $2000? (or 2 since the numbers are in thousands)

Question 14: Solve for the price elasticity of demand. See page 82 and 83 of your textbook.

Question 15: Is the good elastic, inelastic or unit elastic?

Question 16: Solve for the income elasticity.

Question 17: Is the good a luxury, necessity or inferior product?

Question 18: Solve for the cross-price elasticity between hamburgers and chicken sandwiches

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.741702076
R Square	0.55012197
Adjusted R Square	0.515515967
Standard Error	446.9473625
Observations	57
ANOVA
	df	SS	MS	F	Significance F
Regression	4	12702239.75	3175559.936	15.89672116	1.46301E-08
Residual	52	10387621.13	199761.9448
Total	56	23089860.88
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	572.5975477	1549.674374	0.369495397	0.713258982	-2537.051583	3682.246679	-2537.051583	3682.246679
Price CS	-604.5746764	280.8597382	-2.152585772	0.036012589	-1168.160973	-40.98838016	-1168.160973	-40.98838016
Price H	645.1749975	275.3295182	2.343283066	0.022974221	92.68589944	1197.664096	92.68589944	1197.664096
A	32.65949404	15.61168861	2.091989845	0.041339495	1.332348959	63.98663912	1.332348959	63.98663912
Income	1.339313822	1.371717799	0.976377082	0.333398178	-1.413239316	4.091866961	-1.413239316	4.091866961

The regression equation can be written as:

Qcs= 572.59-604.57Pcs+645.17Ph+32.66A+1.34I

About 74% of the variation in the quantity demand is explained by the variables chosen above as indicated by the value of R square.

2. The substitute goods are those when the increase in the price of one good increases the supply of other good or there is a direct relationship between the price of one good and quantity of other good. while the relationship gets reverse in case of complement goods. here the coefficient of Price H is positive which means that for every one unit increase in the price of H would cause a 645 point increase in the quantity of CS. since this is a positive or direct relationship thus these goods are substitutes.

3. The coefficient of Pcs is negative (-604.57), thus there is a negative relationship between the price of CS and quantity demanded of CS. However, if we look at the p-value which is 0.036 and less than 0.05, it implies that the coefficient is significant at a 5% significance level.

4. The coefficient of Ph is positive (645.17), thus there is a positive relationship between the price of H and quantity demanded of CS. However, if we look at the p-value which is 0.023 and less than 0.05, it implies that the coefficient is significant at a 5% significance level.

5. The coefficient of A is positive (32.66), thus there is a positive relationship between the Advertising and the quantity demanded of CS. However, if we look at the p-value which is 0.041 and less than 0.05, it implies that the coefficient is significant at a 5% significance level.

6. The coefficient of I is also positive (1.34), thus there is a positive relationship between the income and the quantity demanded of CS. However, if we look at the p-value which is 0.33, it implies that the coefficient is significant at a 5% significance level.