Question

Actual consumption Refer to Exercise 48. Use the equation of the least-squares regression line and the residual plot to estimate the actual fuel consumption of the car when driving 20 kilometers per hour.

Short answer

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

Step-by-step solution

Given information

It is given that:

$\stackrel{⏜}{y}=11.0358-0.01466x$

The figure is

Concept

The formula used:$Residual=y-\stackrel{⏜}{y}$

Calculation

Let's start by determining the regression line's anticipated weight, which can be done by evaluating the regression line's equation, which is:

$$\begin{gathered} \stackrel{⏜}{y}=11.0358-0.01466x \\ =11.0358-0.01466\left(20\right) \\ =10.7426 \end{gathered}$$

In the residual plot, we can see that the residual corresponding to $20$kilometers per hour is around $2.5$

Thus, the residual will be:

$Residual=2.5$

The residual, as we know, is the actual value reduced by the anticipated value, so

$$\begin{gathered} Residual=y-\stackrel{⏜}{y} \\ \Rightarrow y=Residual+\stackrel{⏜}{y} \\ =2.5+10.7426 \\ =13.2426 \end{gathered}$$

As a result, the fuel consumption units are in litres per $100$ kilometres driven, and the actual fuel consumption at $20$ kilometres per hour is roughly $13.2426$ litres per $100$ kilometres driven.