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Analyzing the regression results

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Wilpen Company, a price-setting firm, produces nearly 80 percent of all tennis balls purchased in the United States. Wilpen estimates the U.S demand for its tennis balls by using the following linear specifications:

Q= a + bP + cM = dP R

Where Q is the number of cans of tennis balls sold quarterly, P is the wholesale price Wilpen charges for a can of tennis balls, M is the consumer's average household income, and PR is the average price of tennis rackets. The regression results are as follows:

DEPENDENT VARIABLE:Q R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 20 0.8435 28.75 0.001
VARIABLE PARAMETER STANDARD
ESTIMATE ERROR T-RATIO P-VALUE
INTERCEPT 425120.0 220300.0 1.93 0.0716
P -37260.6 12587 -22.96 0.0093
M 1.49 0.3651 4.08 0.0009
PR -1456.0 460.75 -3.16 0.0060

A. Discuss the statistical significance of the parameter estimates a^, b^, c^, d^ using p-values. Are the signs of b^, c^, and d^ consistent with the theory of demand?
B. What is estimated number of cans of tennis balls demanded?
C. At the values of P, M and PR given, what are estimated values of price (E), Income (Em^) and cross price elasticities (EXR^) of demand?
D. What will happen in percentage terms, to the number of cans of tennis balls demanded if the price of tennis balls decreases 15 percent?
E. What will happen in percentage terms, to the number of cans of tennis balls demanded if average household income increases by 20 percent?
F. What will happen in percentage terms, to the number of cans of tennis balls demanded if average price of tennis rackets increases 25 percent?

For questions B thru F: Wilpen plans to charge a wholesale price of $1.65 per can. The average price of a tennis racket is $110, and consumer's average household income is $24,600.

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Solution analyzes the given regression results.

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a)
The p-value for ^b, ^c, and ^d are lower than 0.01, which means that the parameter estimates for b, c and d are statistically significant at 1% significance level.
However, the parameter estimate for the intercept term (a) is not statistically significant at 1% significance level as the p-value for intercept term is more than 0.01

The sign is negative for price, which means that price and quantity demanded have inverse relationship in the given case. It is in accordance with the demand theory.
The sign for income is positive. We know that sign of Income (M) should be positive for normal goods. It is again in accordance with the theory of demand.
Negative sign ...

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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