Question

Question: Testing tires for wear. Underinflated or overinflated tires can increase tire wear. A new tire was tested for wear at different pressures, with the results shown in the following table.

Pressure, x (pounds per inch square)	Mileage, y (thousands)
30	29
31	32
32	36
33	38
34	37
35	33
36	26

a. Plot the data on a scatterplot.

b. If you were given only the information for$\mathbf{x}\mathbf{=}\mathbf{30}\mathbf{,}\mathbf{31}\mathbf{,}\mathbf{32}\mathbf{,}\mathbf{33}$, what kind of model would you suggest? For$\mathbf{x}\mathbf{=}\mathbf{33}\mathbf{,}\mathbf{34}\mathbf{,}\mathbf{35}\mathbf{,}\mathbf{36}$? For all the data?

Short answer

Answer

a. The scatter plot of the data is:

b. For the values$x=30,31,32,33$, a linear model would be best to fit the data here. And for the values$x=33,34,35,36$, a quadratic model would be the best fit for this data.

Step-by-step solution

Given Information

Let x is pressure (pounds per inch square) and y is mileage (in thousands).

Scatter plot

To draw the scatter plot, the individual pairs of x and y are taken. An independent variable values (pressure values) are plotted on the x-axis and t dependent variable values, mileage values are plotted on the y- axis. If any relationship amongst the variable is observed, a line is drawn to connect all the individual pairs.

 Step 3: Model suggestion

Based on the information for $x=30,31,32,33$, it can be seen from graph that the scatter plot gives anincreasing linear relationship between x and y values. A linear model would be best to fit the data here.

However, for values$x=33,34,35,36$ the scatter plot gives a concave curve indicating quadratic relation between x and y. So, a quadratic model would be the best fit for this data.

For full data values, the scatter plot gives an arc indicating a quadratic relation between x and y. So, a quadratic model would be the best fit for the data.