Chapter 3.2, Problem 50E

To determine

To use the equation of the least square regression line and the residual plot to estimate the actual fuel consumption of the car when driving $20$ kilometres per hour.

Answer to Problem 50E

The actual fuel consumption when driving $20$ kilometres per hour is approximately $13.2426$ liters per $100$ km driven.

Explanation of Solution

It is given that:

  $\widehat{y}=11.0358-0.01466x$

Let us first find out the predicted weight by the regression line which can be obtained by evaluating the equation of the regression line as:

  $\begin{array}{l}\widehat{y}=11.0358-0.01466x\\ =11.0358-0.01466(20)\\ =10.7426\end{array}$

Now, we note that the residual corresponding to $20$ kilometres per hour is approximately $2.5$ in the residual plot =. Thus, the residual will be:

Residual $=2.5$

As we know the residual is the actual decreased by the predicted value, so,

  $\begin{array}{l}\text{Residual}=y-\widehat{y}\\ \Rightarrow y=\text{Residual+}\widehat{y}\\ =2.5+10.7426\\ =13.2426\end{array}$

Thus, the units of the fuel consumption are in liters per $100$ km driven and thus the actual fuel consumption when driving $20$ kilometres per hour is approximately

  $13.2426$ liters per $100$ km driven.