# The regression results

Wilpen Company, a price setting firm, produces nearly 80 ercent of all tennis balls purchased in the US. Wilpen estimates the US demand for its tennis balls by using the following linear specification:

Q= a + bP + cM + dP (R)

where Q is gthe number of cans of tennis balls sold quarterly, P is the wholesale price Wilpen charges for a can of tennis balls, M isthe consumers' average household income, and P(R) isthe 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 Estimate Standard 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 and d using the p values. Are the signs of b, c and d consistent with the theory of demand.

b). what ist he estimated number of cans of tennis balls demanded:

c) at the values of P, M, and P(R) given, what are the estimated values of the price (E) income (E M) and cross price elasticities (E XR) of demand.

d).What will happen in percnetage 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 t the number of cans of tennis balls demanded if the average household income increases by 20 percent.

f).what will happen, in perentage terms to the number of cans of tennis galls demanded if the average price of tennis rackets increases 25 percent.

https://brainmass.com/economics/regression/the-regression-results-272792

#### Solution Preview

a) Discuss the statistical significance of the parameter estimates a,b,c, and d using the p-values. Are the sign of b,c and d consistent with the theory of demand?

The p_value corresponding to b_hat (i.e., coefficient of P) is 0.0093, which means that it is significantly different from zero if we are satisfied with a 1% level of significance. The negative sign of b_hat conforms to expectation: if price rises, the quantity sold will drop.

The p_value corresponding to c_hat (i.e., coefficient of M) is 0.0009, which means that it is significantly different from zero if we are satisfied with a 1% level of significance. The positive sign of c_hat conforms to expectation: if consumers' household income ...

#### Solution Summary

The regression results are examined.

Interpreting the Given Regression Results.

A multiplicative demand function of the form: Qd = a*P^b1*Y^b2*Po^b3 is estimated using cross-sectional data and 224 observations. The regression results were as follows:

Constant (a) Price(P) Income(Y) Price of other good (Po)

Coefficient 0.02248 -0.2243 1.3458 0.1034

Standard Error 0.01885 0.0563 0.5012 0.8145

a. How should the coefficients be interpreted in this equation?

b. What is the quantity demanded if price is $10, income is $9000, and price of the other good is $15?

c. Is demand elastic or inelastic? How can you tell? What impact would a price increase have on total revenue and on total profit?

d. How are these two goods related? Should the firm be concerned about a change in the price of the other good?

e. Is this product a luxury, necessity, or inferior good?