Suppose demand for a product is determined by its price, consumers’ income, and
ID: 2949515 • Letter: S
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.
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
Explanation / Answer
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