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)
Where Qx is the quantity demanded of Product X, Px is the price of X, Y is income, and r is the prime interest rate (given in decimals, e.g., 0.02 or 0.05) The standard error of each estimated coefficient is given in parentheses below it.
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?
a) Alright, so degrees of freedom is going to be the number of observations reduced by the number of parameters+1. In this case, you have 98 observations, and 3 parameters. So, there are 94 degrees of freedom.
b) This can be answered directly from the reported R^2 ...
The solution assists with answer questions regarding an estimate of the industry's demand curve for Product X.