Assume your research staff used regression analysis to estimate the industry dem

Question

Assume your research staff used regression analysis to estimate the industry demand curve for Product X.

Qx = 10,000 - 100 Px + 0.5 Y - 1000 r

(3,000)  

(20)     

(0.3)     

(105)

Also, the following information is provided about the regression equation. Number of observations = 98 R2 = 0.95 F-statistic = 7.5

a. What is the number of degrees of freedom? b. What percentage of the variation in the dependent variable is explained by the equation? c. Which of the estimated coefficients are significant at the 5% level using a 2-tailed test; be sure to indicate the t-statistic for each of the coefficients. d. Perform an F test at the 5% level of the overall explanatory power of the model. e. If prices remain constant next year but income is expected to increase by 50 and interest rates rise by two percentage points (by 0.02), what is the expected change in the quantity demanded?

Qx = 10,000 - 100 Px + 0.5 Y - 1000 r

(3,000)  

(20)     

(0.3)     

(105)

Explanation / Answer

A) degress of freedom=n-p where n is the total number of observations and p is the number of independent variables+1

hence the degrees of freedom is 98-4=94

B) since R^2=0.95 hence it gives us the percentage of variation in the dependent variable explained by the independent variables data.

C) t statistic= A/se(A) where se(A) is the standard error of coeffiecnt A and A is the value of the coefficient.

the two hypothesis are

H0: coefficient=0

H1: coefficient is not equal to 0

t(Px)=-5 and the critical value of t statistic at 94 degrees of freedom and 5% significance is 1.986

since absolute value of t> critical t therefore coeffcient of Px is significant.

t(Y)=1.666 and is lesser than critical value of t and hence the coeffcient of Y is insignificant.

t(r)=-9.52 and the absolute value is greater than critical t hence the coefficient is significant.

D) we have to find the critical value of F at 5% significance.2.701

the hypothesis are

H0: all the coefficients are 0

H1: at least one coefficient is non 0

F theoretical=7.5

since F> critical F

therefore the regression is significant.

E) expected change in quantity demanded= -100*dPx+0.5*dY-1000*dr

where dPx is change in price, dY is change in income and dr is change in interest rate

dPx=0

therefore expected change= 0.5*50-1000*0.02=5 units

for any further discussion please comment

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