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Analyzing the regression results

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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) (25) (0.12) (900)
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,
N = 100
R2 = 0.9
F = 15

a. How many degrees of freedom are there?
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
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 fall by two percentage points, what is the expected rate of change in the quantity demanded?

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Solution Summary

Solution analyzes the given regression results.

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a. How many degrees of freedom are there?
Sample size=n=100
Number of independent parameters=k=3
Degrees of freedom=n-k-1=100-3-1=96

b. What percentage of the variation in the dependent variable is explained by the equation?
R^2=0.90
We can say that 90% 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
Critical value of t can be found by the using tinv function in MS Excel with 5% significance level and 96 degrees of ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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