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:

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.

Transcribed Image Text:

ŷ = -64.64 + 0.0011x₁ + 23.799x2 (0.005) (10.056) 5.403x3 R² = 0.87 (3.833)