Question

The Prime Corporation’s marketing manager calculates a regression, where the quantity demanded of the firm’s product is the dependent variable(Q_X^D) and the price of the product (designated as “P_X”), the price of a related product (designated as “P_Y”) and consumers’ disposable income (designated as “Income”) are independent variables.

SUMMARY	OUTPUT
Regression	Statistics
Multiple R	0.9806
R Square	0.9616
Adjusted R Square	0.9534
Standard Error	14.3947
Observations	18
ANOVA
	df	SS	MS	F	Significance F
Regression	3	72689.3823	24229.7941	116.9353102	3.7867E-10
Residual	14	2900.8955	207.2068
Total	17	75590.2778
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	786.8849	82.4564	9.5430	0.0000	610.0336	963.7363
PX	-1.2065	0.0950	-12.6959	0.0000	-1.4103	-1.0027
PY	0.2926	0.0390	7.4998	0.0000	0.2089	0.3763
Income	0.0050	0.0014	3.5410	0.0033	0.0020	0.0080

1. What is the estimated intercept of the regression? Interpret it.
2. What is the estimated regression coefficient of the product’s own price? Interpret it.
3. What is the multiple coefficient of determination? Interpret it.
4. What is the estimated quantity demanded for P_X=$750, P_Y=$900, and Income=$30,000.
5. What is the point price elasticity of demand for P_X=$750, P_Y=$900, and Income=$30,000.

Answer 1

Solution:

(a) The fitted regression model will be

Here, the estimated ntercept of regression model  is 786.8849 and it shows increasing trends of model.

(b) The estimated coefficient of the product are -1.2065, 0.2926 and 0.005.

(c) The multiple coefficient of determination is 0.9806, i.e., it shows the 98 % variation explained by the model.

(d) The estimated quantity demand for the product is

i.e., QXD= $295.354

(e) The point price elasticity of demand will be