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. Evaluate your regression results by examining signs of parameters, p-values (or t-ratios), and the R².

Answer 1

The image attached below is derived from excel by running a regression analysis on the given data, where y/dependant variable is the quantity of pizza demanded and the 4 independent variables are 1) Pizza Price (P) 2) Household Income (M) 3) Price of pizza at Als 4) Prize of Big Mac.

Model Hypothesis

H0: The factors Pizza Price (P),  Household Income (M), Price of pizza at Als and Prize of Big Mac don’t have a significant effect on quantity demanded, other factors held constant.

H1: The factors Pizza Price (P),  Household Income (M), Price of pizza at Als and Prize of Big Mac have a significant effect on quantity demanded, other factors held constant.

Quantity demanded = A + B1 (Pizza Price (P)) + B2 (Household Income (M)) + B3 (Price of pizza at Als) + B4(Prize of Big Mac)
The regression coefficients B1, B2, B3, B4 are known as partial regression or partial slope coefficients. The meaning of partial slope coefficients is as follows:-
B1 measures the change in the mean value of Y (Quantity demanded) per unit change in X1 (Pizza Price (P))
B2 measures the change in the mean value of Y (Quantity demanded) per unit change in X2 (Household Income (M))
B3 measures the change in the mean value of Y (Quantity demanded) per unit change in X3 (Price of pizza at Als)
B4 measures the change in the mean value of Y (Quantity demanded) per unit change in X4 (Prize of Big Mac)

Hence from the table in the picture, we get the following equation:

Quantity demanded = 1183.802486 + -213.4219011(Pizza Price (P)) + 0.091088289 (Household Income (M)) + 101.3028564(Price of pizza at Als) + 71.84479909(Prize of Big Mac)

For example- 1 unit increase in Pizza Price (P) will negatively affect quantity of pizza demanded by 213.42

1 unit increase in Household Income (M) will positively affect quantity demanded by 0.091.

T-Test

1) H0: B1 equals to 0
H1: B1 does not equal to 0
We observe that the significance(p-value) of the t-stat for B1 (2.13823E-12) is less than 0.05. Therefore we reject the null hypothesis.
This means that B1 is significant. Therefore Pizza Price (P) significantly affects the Quantity Demanded.

2) H0: B2 equals to 0
H1: B2 does not equal to 0
We observe that the significance of the t-stat for B2 (5.87592E-07) is less than 0.05. Therefore we reject the null hypothesis.
This means that B2 is significant. Therefore Household Income (M) significantly affects the Quantity Demanded.

3) H0: B3 equals to 0
H1: B3 does not equal to 0
We observe that the significance of the t-stat for B3 (0.017051999) is less than 0.05. Therefore we reject the null hypothesis.
This means that B3 is significant. Therefore Price of Pizza at AIs significantly affects the Quantity Demanded.

4) H0: B4 equals to 0
H1: B4 does not equal to 0
We observe that the significance of the t-stat for B4 (0.015762653) is less than 0.05. Therefore we reject the null hypothesis.
This means that B4 is significant. Therefore Price of Big Mac significantly affects the Quantity Demanded.

MODEL FIT

R SQUARE (coefficient of determination)

The R square value of multiple regression test has a value of 0.95

Hence we can conclude that 95% of the variation in the dependant variable(quantity demanded) is explained by the independent variables ( 1. Pizza Price (P) 2. Household Income (M) 3. Price of pizza at Als 4. Prize of Big Mac.)