If we fit the model y = 0 + 1 x 1 + 2

If we fit the model y = β₀ + β₁x₁+ β₂x₂+ β₃x²₂ + β₄x₁x₂ + ϵ to the real estate sales price data in Table 15.4, we find that the least squares point estimates of the model parameters and their associated p-values (given in parentheses) are b₀ = 27.438 (.001), b₁ = 5.0813 (.001),
b₂ = 7.2899 (.001), b₃ = -.5311 (.001), and b₄ = .11473 (.014).

a. A point prediction of and a 95 percent prediction interval for the sales price of a house having 2000 square feet (x1= 20) and a niceness rating of 8 (x2 = 8)re 171.751 ($171,751) and [168.836, 174.665]. Using the above model, show how the point prediction is calculated.

b. Below we give model predictions of sales prices of houses for six combinations of x₁ and x₂, along with plots of the predictions needed to interpret the interaction between x₁ and x₂ . Carefully interpret this interaction.

Data from Table 15.4

Transcribed Image Text:

X₂ 2 5 8 X₁ x 13 108.933 124.124 129.756 22 156.730 175.019 183.748 190 180 170 160 when x₂ =5 150 140 130 120 110 100 ŷ when x₂ = 8 12 14 16 ŷ when x₂ = 2 18 20 TX1 22 190 180 170 160 150 140 130 120 110 100 2 ŷ when x₁ = 22 3 T 4 y when x₁ = 13 T 7 T T 5 6 TX₂ 8