Chapter 8.2, Problem 56PE

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 gas mileage $y$ (in mpg) for city driving is given based on the weight of the vehicle $x_1$ (in lb) and on the number of cylinders.

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

b. Use the model from part (a) to predict the gas mileage of a vehicle that is $3800\text{ lb}$ and has $6$ cylinders.