A 40-year-old masonry duplex structure has recently undergone a passive solar retrofit with features including insulated exterior walls, heat distribution systems, storm sashes, and air-lock entries. To gauge the effectiveness of the improvements, architectural engineers monitored the winter energy usage of the structure for 2 years prior to the retrofit and for 2 years after the retrofit. The engineers want to use the data to fit a regression model relating monthly energy usage y (therms per billing day) to weather intensity x₁ (ddh/bd) and x₂, where

a. Write the complete second-order model for E(y).

b. Graph the contour lines for the model of part a.

c. Hypothesize a first-order model that allows for a constant difference between the mean monthly usage prior to and after the retrofit at different levels of weather intensity.

d. Graph the contour lines for the model of part c.

Transcribed Image Text:

Si if prior to retrofit X2 lo if after retrofit