To explain what determines the price of air conditioners, B. T. Ratchford obtained the following regression results based on a sample of 19 air conditioners:
Yi = - 68.236 + 0.023X2i + 19.729X3i + 7.653X4iR2 = 0.84
se = (0.005) (8.992) (3.082)
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 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.
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.