Question

Suppose demand for a product is determined by its price, consumers’ income, and the price of a related good. Use Q for demand, P for price, M for income, and PR for price of related good. The demand function is estimated using regression analysis.

The results are reported below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.814752135
R Square	0.663821042
Adjusted R Square	0.159552605
Standard Error	530.2842631
Observations	66
	Coefficients	Standard Error	t Stat	P-value
Intercept	125.56	15.87
P	-5.39	2.19	???
M	0.069			0.046
PR	-10.98	2.73

What is the R₂ of this regression?

What is the degrees of freedom of this regression?

What is the effect of a one-dollar increase in price (P) on demand (Q)?

What is the effect of a one-dollar increase in income (M) on demand (Q)?

What is the effect of a one-dollar increase in price of related good (PR) on demand (Q)?

Calculate the t Stat (or t ratio marked with “???” in the table) for the coefficient on P?

Test whether the effect of P on Q is significant at the 5% significance level. Show your work.

Using the p-value 0.046 in the table, test if the effect of M on Q is significant at the 5% significance level.

Using the values P=100, M=35,000, and PR=40, predict the demand (Q)?

Using the value of predicted Q you just calculated for part 9), calculate the estimates of

                        The price elasticity of demand. Show your work.

                        The income elasticity of demand. Show your work.

                        The cross-price elasticity of demand. Show your work.

Answer 1

What is the R2 of this regression?

R sq=0.6638

What is the degrees of freedom of this regression

df=n-1=66-1=65

What is the effect of a one-dollar increase in price (P) on demand (Q)?

For a one-dollar increase in price (P),demand decreases by 5.39 units.

What is the effect of a one-dollar increase in income (M) on demand (Q)?

For a one-dollar increase in income ,demand increases by 0.069 units.

What is the effect of a one-dollar increase in price of related good (PR) on demand (Q)?

For a one-dollar increase in price of related good (PR),demand decreases by 10.98 units

Calculate the t Stat (or t ratio marked with “???” in the table) for the coefficient on P?

t=coefficient/std error

=-5.39/2.19

=-2.461187

Using the p-value 0.046 in the table, test if the effect of M on Q is significant at the 5% significance level.

p=0.046

alpha=0.05

p<0.05

Reject H0

Accept H1

the effect of M on Q is significant.

Using the values P=100, M=35,000, and PR=40, predict the demand (Q)?

the regression eq is

Q=125.56-5.39*P+0.069*M-10.98PR

given P=100

M=35000

PR=40

Q=125.56-5.39*100+0.069*35000-10.98*40

Q= 1562.36 units

predicted demand=1562.36 units