Question

Below is a case on estimation and analysis of demand for home delivery pizza.

Read the case carefully and use the appropriate techniques given in the text book on demand estimation and analysis and make your decisions, judgments and evaluation based on the results.

Consider Al Barkat Pizza, one of the home delivery pizza firms serving the Muweileh, Sharjah. The manager and owner of Barkat Pizza, Mariam, knows that her customers are rather price-conscious. She knows that Pizza buyers in Muwilah pay close attention to the price she charges for a home-delivered pizza and the price her competitors charge.

Mariam decides to estimate the empirical demand function for her firm’s pizza. She collects data on the last 24 months of pizza sales from her own company records. She knows the price she charged for her pizza during that time period, and she also has kept a record of the prices charged at Al’s Pizza Oven. She is able to obtain average household income figures from the Small Business Development Center. The only other competitor in the neighborhood is the local branch of McDonald’s. Mariam is able to find the price of a Big Mac for the last 24 months from advertisements in old newspapers. The data she collected are presented in table 1.

Table 1: Data for Checkers Pizza

Observation	Quantity of Pizza (Q)	Pizza Price (P)	Household Income (M)	Price of Pizza at AIs (	Price of Big Mac (
1	2659	8.65	25500	10.55	1.25
2	2870	8.65	25600	10.45	1.35
3	2875	8.65	25700	10.35	1.55
4	2849	8.65	25970	10.30	1.05
5	2842	8.65	25970	10.30	0.95
6	2816	8.65	25750	10.25	0.95
7	3039	7.50	25750	10.25	0.85
8	3059	7.50	25950	10.15	1.15
9	3040	7.50	25950	10.00	1.25
10	3090	7.50	26120	10.00	1.75
11	2934	8.50	26120	10.25	1.75
12	2942	8.50	26120	10.25	1.85
13	2834	8.50	26200	9.75	1.50
14	2517	9.99	26350	9.75	1.10
15	2503	9.99	26450	9.65	1.05
16	2502	9.99	26350	9.60	1.25
17	2557	9.99	26850	10.00	0.55
18	2586	10.25	27350	10.25	0.55
19	2623	10.25	27350	10.20	1.15
20	2633	10.25	27950	10.00	1.15
21	2721	9.75	28159	10.10	0.55
22	2729	9.75	28264	10.10	0.55
23	2791	9.75	28444	10.10	1.20
24	2821	9.75	28500	10.25	1.20

Question

A. Using the data in Table 1, specify a linear functional form for the demand for home delivery pizza, and run a regression to estimate the demand for pizza.

Answer 1

Soln

Steps for Regression in Excel

• Import the data in Excel
• In Data Analysis tool from Data Tab.
• Click on regression and select the Y values and X values. Select Labels and click OK.

Regression Output

Regression Statistics
Multiple R	0.9775
R Square	0.9555
Adjusted R Square	0.9461
Standard Error	42.4112
Observations	24
ANOVA
	df	SS	MS	F	Significance F
Regression	4	7,33,155.80	1,83,288.95	101.90	0.00
Residual	19	34,175.53	1,798.71
Total	23	7,67,331.33
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1,183.80	506.30	2.34	0.03	124.11	2,243.50
Pizza Price (P)	-213.42	13.49	-15.83	0.00	-241.65	-185.19
Household Income	0.09	0.01	7.34	0.00	0.07	0.12
Price of Pizza at Ais	101.30	38.75	2.61	0.02	20.20	182.40
Price of Big Mac	71.84	27.10	2.65	0.02	15.12	128.57

Regression Equation

Quantity of Pizza (Q) = 1183.8 – 213.42 * Pizza Price + 0.09 Household Income + 101.3 Price of Pizza at Ais + 71.84 Price of Big Mac

From the ANOVA Table, we get the p-value less than 0.001. Hence the model is significant

R Square of the model is 0.9555 ie 95.55% of the variation in dependent variable can be explained by the independent variables.

P-value of all the independent variables is less than 0.05. Hence all the independent variables are significant at alpha = 0.05