Q152SE Question: Testing tires for wear... [FREE SOLUTION]

91影视

Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 12: Q152SE (page 809)

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 $x = 30, 31, 32, 33$ , what kind of model would you suggest? For $x = 33, 34, 35, 36$ ? For all the data?

Short Answer

Expert verified

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.