A study was conducted to determine whether certain features could be used to explain variably in the price of furnaces. For a sample of 19 furnaces, the following regression was estimated:
y = - 68.236 + 0.0023X1 + 19.729X2 + 7.653X3 R^2 = 0.84
(0.005) (8.992) (3.082)
where
y = price, in dollars,
x1 = rating of furnace, in BTU per hour
x2 = energy efficiency ratio
x3 = number of settings
The number in parentheses under the coefficients are estimated coefficient standard errors.
a. Find a 95% confidence interval for the expected increase in price resulting from an additional setting when the values of the rating and the energy efficiency ratio remain fixed.
b. Test the null hypotheses that, all else being equal, the energy efficiency ratio of furnaces does no affect their price against the alternative that the higher the energy efficiency ratio, the higher the price.