sold homes in the space, the following variables are used in a multiple regression model. \[ \begin{array}{l}y=\text { sales price (in thousands of dollars) } \\ x_{1}=\text { total floor area (in square feet) } \\ x_{2}=\text { number of bedrooms } \\ x_{3}=\text { distance to nearest high school (in miles) } \\ \text { The estimated model is as follows. } \\ \hat{y}=177+0.055 x_{1}+23 x_{2}-3 x_{3} \\ \text { Answer the questions below for the interpretation of the coefficient of } x_{1} \text { in this model. } \\ \begin{array}{l}\text { (a) Holding the other variables fixed, what is the average change in sales price for each } \\ \text { 100-square-foot increase in floor area? } \\ \text { dollars }\end{array} \\ \text { (b) Is this change an increase or a decrease? } \\ \text { O increase }\end{array} \]
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When interpreting the coefficient of \(x_1\) (total floor area) in the regression model, every 100-square-foot increase in floor area results in an average increase in sales price of \(0.055 \times 100 = 5.5\) thousand dollars. So, we're looking at an exciting upward shift of about $5,500 in price with each 100 square feet added. Now, regarding whether this change is an increase or decrease, it’s clear from the positive coefficient of 0.055 that it’s an increase! More floor area typically means more space and possibly higher value, so happy house hunting!
