How does the fuel consumption of a car change as its speed increases? Here are data for a British Ford Escort. Speed is measured in kilometers per hour, and fuel consumption is measured in liters of gasoline used per $100$kilometers ${\text{traveled.}}^5$

role="math" localid="1649315389612" $\begin{array}{ccccc}\begin{array}{c}\text{Speed}\\ (\mathbf{km}/\mathrm{h})\end{array}& \begin{array}{c}\text{Fuel used}\\ \text{(liters/100 km)}\end{array}& & \begin{array}{c}\text{Speed}\\ (\mathrm{km}/\mathrm{h})\end{array}& \begin{array}{c}\text{Fuel used}\\ \text{(liters/100 km)}\end{array}\\ 10& 21.00& & 90& 7.57\\ 20& 13.00& & 100& 8.27\\ 30& 10.00& & 110& 9.03\\ 40& 8.00& & 120& 9.87\\ 50& 7.00& & 130& 10.79\\ 60& 5.90& & 140& 11.77\\ 70& 6.30& & 150& 12.83\\ 80& 6.95& & & \\ & & & & \end{array}$

(a) Make a scatterplot on your calculator.

(b) Describe the form of the relationship. Why is it not linear? Explain why the form of the relationship makes sense.

(c) It does not make sense to describe the variables as either positively associated or negatively associated. Why?

(d) Is the relationship reasonably strong or quite weak? Explain your answer.

The relationship between two quantitative variables recorded on the same individuals is depicted by a scatterplot. The horizontal axis represents the values of one variable, while the vertical axis shows the data of the other variable. Each participant in the data is shown by a point on the graph.

The Speed is on the horizontal axis and the Fuel used is on the vertical axis.

The graph is:

Form: Because the scatterplot has curvature, it is curved.

Because the points are not all basically on the same line, the graph is not linear.

This makes sense because the best fuel efficiency is found at modest speeds.

The graph is:

It does not make sense to describe the variables as positively or negatively associated, because

At speeds below $60\mathrm{km}/\mathrm{h}$, Because the scatterplot slopes downwards, the factors are negatively related.

At speeds above $60\mathrm{km}/\mathrm{h}$, The scatterplot is sloped upwards, indicating that the variables are positively related.

However, two variables cannot be both positively and negatively related, thus describing them as either makes no sense.

The graph is:

Because the points all appear to be on the same curve and no points break from the general pattern, the link is very strong.