We expect a car's highway gas mileage to be related to its city gas mileage. Data for all $1198$vehicles in the government's $2008$Fuel Economy Guide give the regression line predicted highway $mpg=4.62+1.109$(city mpg).

(a) What’s the slope of this line? Interpret this value in context.

(b) What’s the intercept? Explain why the value of the intercept is not statistically meaningful.

(c) Find the predicted highway mileage for a car that gets $16$miles per gallon in the city. Do the same for a car with a city mileage of $28$mpg.

The regression line predicted highway $mpg=4.62+1.109$(city mpg).

A regression line's slope is the indirect relationship between the $x$- and $y$-variables.

$\text{Slope}=1.109$

In each of the two variables, $x$(city mpg) and $y$(highway mpg) represents the increase in the $y-$variable.

Note: mpg =miles per gallon

The regression line predicted highway $mpg=4.62+1.109$(city mpg).

Statistics have meaning only when a value is in line with reality.

In these circumstances, the car will get $0$miles per gallon in the city since the intercept is$4.62$highway mpg.

If the explanatory variable is $0$, the y-intercept is the value of the response variable.

The regression line predicted highway $mpg=4.62+1.109$(city mpg).

$$\begin{gathered} Highwaympg=4.62+1.109 \\ Highwaympg=4.62+1.109 \\ Highwaympg=4.62+17.74 \\ =22.36 \end{gathered}$$(city mpg)

Using the regression equation for the regression line, we can calculate the predicted highway mileage given the city mileage of the vehicle.

$$\begin{gathered} Highwaympg=4.62+1.109 \\ Highway\mathit{}mpg=4.62+1.109\left(28\right) \\ Highway\mathit{}mpg=4.62+31.05=35.67 \end{gathered}$$ (city mpg)