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Chapter 4: Q.4.162 (page 191)

Gas Gurzlers. The data for gas mileage and engine displacement for 121vehicles from Exercise 4.78 are provided on the WeissStats site.

a. decide whether the use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then also do parts (b) and (c).

b. obtain the linear correlation coefficient.

c. interpret the value of r in terms of the linear relationship between the mo variables in question.

Short Answer

Expert verified

The concave upward curving pattern may be seen in the data. As a result, there is no linear trend in the data. So, portions (b) through (c) will be omitted.

Step by step solution

01

Part (a) Step 1: Given Information

The data for gas mileage and engine displacement for 121 vehicles from Exercise 4.78 are provided on the WeissStats site.

02

Part (a) Step 2: Explanation

The MINITAB: can be used to create a scatterplot for the given data.

Step 1: Select Graph > Scatterplot from the drop-down menu.

Step 2: Click OK after selecting With Connect Line.

Step 3: Add an MPG column to the Yvariables section.

Step 4: Add a Disp column to the Xvariables section.

Step 5: Click the OK button.

The resulting scatterplot will be

Finding a regression line for the data is not acceptable since the observations are not dispersed around a line in the scatterplot above.

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Most popular questions from this chapter

A value of rclose to -1suggests a strong------ linear relationship between the variables.

4.76 PCBs and Pelicans, Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United States in 1979and by the Stockholm Convention on Persistent Organic Pollutants in 2001. One study, published in 1972 by R. Risebrough, is titled "Effects of Environmental Pollutants Upon Animals Other Than Man" (Proceedings of the 6th Berkeley Symposium on Mathematics and Statistics, Vl, University of California Press, Pp. 443-463). In that study, 60Anacapa pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and concentration of PCBs, in parts per million (ppm). The data are on the Weiss Stats site.

a. Obtain a scatterplot for the data.

b. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f).

In Exercise 4.11, we give linear equations. For each equation,

a. find the y-intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

Given equation is,

y=2

6. What kind of plot is useful for deciding whether finding a regression line for a set of data points is reasonable?

A measure of the amount of variation in the observed values of the response variable not explained by the regression is the----. The mathematical abbreviation for it is----.
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