Chapter 8.2, Problem 55PE

Many statistics courses cover a topic called multiple regression. This provides a means to predict the value of a dependent variable $y$ based on two or more independent variables $x_1,x_2,\mathrm{...},x_n.$ The model $y=a{x}_1+b{x}_2+c$ is a linear model that predicts $y$ based on two independent variables $x_1$ and $x_2.$ While statistical techniques may be used to find the values of $a,b,$ and $c$ based on a large number of data points, we can form a crude model given three data values $\left(x_1,x_2,y\right)$ . Use the information given in Exercises 55-56 to form a system of three equations and three variables to solve for $a,b,$ and $c.$

The selling price of a homey (in $\text{\$}1000$ ) is given based on the living area $x_1$ (in $100{\text{ ft}}^{\text{2}}$ ) and on the lot size $x_2$ (in acres).

a. Use the data to create a model of the form $y=a{x}_1+b{x}_2+c$ .

b. Use the model from part (a) to predict the selling price of a home that is $2000{\text{ ft}}^2$ on a 0.4-acre lot.