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.
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 ...
The regression results are examined.