12.33 A study was conducted to determine whether certain features could be used to explain variability in the prices of furnaces. For a sample of 21 furnaces, the following regression was estimated:

yn = -64.64 + 0.0011x1 10.0052

+ 23.799x2 110.0562

- 5.403x3 13.8332 R2 = 0.87 where y = price in euros x1 = the rating of the furnace in BTU per hour x2 = the energy efficiency ratio x3 = the number of settings The numbers in parentheses under the coefficients are the 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 hypothesis that, all else being equal, the energy efficiency ratio of furnaces does not affect their price against the alternative that the higher the energy efficiency ratio, the higher the price.