Below is a simplified 1993 dataset of US cars. The columns list index, make, model, price (in $\$ 1000)$, miles per gallon, number of passengers, length and width in inches, and weight (in pounds). The data are displayed in $R$ as follows (abbreviated):

It is reasonable to assume that prices for different makes of car are independent. We model the logarithm of the price as a linear combination of the other quantitative properties of the cars and an error term. Write down this model mathematically. How would you instruct $R$ to fit this model and assign it to a variable "fit"?

$R$ provides the following (slightly abbreviated) summary:

Briefly explain the information that is being provided in each column of the table. What are your conclusions and how would you try to improve the model?