Q. 4.78 - Elementary Statistics

Question

4.78 Gas Guzzlers. The magazine Consumer Reports publishes information on automobile gas mileage and variables that affect gas mileage. In one issue, data on gas mileage (in miles per gallon) and engine displacement (in liters) were published for $121$ vehicles. Those data are available 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).

Step-by-Step Solution

Answer

a. The scatter plot is as,

b. No, finding the regression line for the supplied data is not reasonable.

Part (a) Step 1: Given Information

Consumer Reports present information on automotive gas mileage and the factors that influence it. Data on gas mileage (in miles per gallon) and engine displacement (in liters) for 121 automobiles were published in one issue. These figures can be found on the Weiss Stats website.

The scatterplot for the given data must be determined.

Part (a) Step 2: Explanation

Using MINITAB, the scatterplot can be drawn as:

• Save the data in the $x$ and $y$ columns, correspondingly.
• Select Scatter plot from the graph menu.
• Specify the MPG column in the Y variables text box to create a scatter plot.
• In the X variables text box, type the column of Disp. 
• Click OK.

The scatterplot can be made as follows,

Part (b) Step 1: Given Information

To establish whether or not the regression line's evaluation is reasonable.

Part (b) Step 2: Explanation

No, finding the regression line for the supplied data is not plausible due to the concave upward curving pattern. Furthermore, when the variable miles per gallon (MPG) fell, so did the variable engine displacement. As a result, the data does not appear to follow a linear pattern.

As a result, portions (c) through (f) are omitted.