Category:Gujarati -> Chapter 08
Question:
08.11To explain what determines the price of air conditioners, T.T. Ratchford, obtained the following regression results based on a sample of 19 air conditioners:

where Y = the price, in dollars
        X2 = the BTU rating of air conditioner
        X3 = the energy efficiency ratio
        X4 = the number of settings
        se = standard errors

a. Interpret the regression results.
b. Do the results make economic sense?
c. At α = 5%, test the hypothesis that the BTU rating has no effect on the price of an air conditioner versus that it has a positive effect.
d. Would you accept the null hypothesis that the three explanatory variables explain a substantial variation in the prices of air conditioners? Show clearly all your calculations.

Answers:

08.11 a
Ceteris paribus, if the BTU rating of an air conditioner goes up by a unit, the average price of the air conditioner goes up by about 2.3 cents. Other partial slope coefficients should be interpreted similarly. The intercept value has no viable economic meaning in the present case.

08.11 b
Yes. A priori, each X variable is expected to have a positive impact on the price.

08.11 c
For 15 d.f. the 5% one-tailed critical t value is 1.753. The observed t value of 0.023 / 0.005 = 4.6 exceeds this critical t value. Hence, we reject the null hypothesis.

08.11 d
Null H0: R^2 = 0 and alternative H1: R^2 > 0.
Using the F test, we obtain

F = [0.84/3] / [0.16/15] = 26.25

This F value is significant beyond the 0.01 level of significance. So, reject the null hypothesis.

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