Econometrics: MULTIPLE REGRESSION: ESTIMATION AND HYPOTHESIS TESTING To explain

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Econometrics: MULTIPLE REGRESSION: ESTIMATION AND HYPOTHESIS TESTING

To explain what determines the price of air conditioners, B. T. Ratchford^24 obtained the following regression results based on a sample of 19 air conditioners: cap Y_i = -68.236 + 0.023X_2i + 19.729X_3i + 7.653X_4iR^2 = 0.84 se = (0.005) (8.992) (3.082) where Y = the price, in dollars X_2 = the BTU rating of air conditioner X_3 = the energy efficiency ratio X_4 = the number of settings se = standard errors Interpret the regression results. Do the results make economic sense At a = 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. 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.

Explanation / Answer

(a) if the BTU rating of an air conditioner goes up by a unit, other things remaining the same, the average price of the air conditioner goes up by about 2.3 cents.similaly, if the enegy efficiency ratio goes up by a unit, other things remaining the same, the average price of the air conditioner goes up by 1979.9 cents. in case of X4, if one more setting is added to the air conditioner, other things remaining the same, the price of air conditioner goes up by 765.3 cents. The intercept value has no viable economic meaning in the present case.

(b) Yes. obviously from the nature of given X variables , each X variable is expected to have a positive impact on the price.

(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 that BTU rating has no effect on the price of an air conditioner.

(d) H0 : R2 = 0 and H1 : R2 > 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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