Q 62. Driving speed and fuel consumpti... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 3: Q 62. (page 194)

Driving speed and fuel consumption Exercise $9$ (page $159$ ) gives data on the fuel consumption y
of a car at various speeds x. Fuel consumption is measured in liters of gasoline per $100$ kilometers
driven and speed is measured in kilometers per hour. A statistical software package gives the least-squares regression line and the residual plot shown below. The regression line is $y 藛 = 11.058 鈭�$ $0.01466 x$ Would it be appropriate to use the regression line to predict $y$ from $x$ ? Justify your answer.

Short Answer

Expert verified

It would not be appropriate to use the regression line to predict $Y$ from $X$

Step by step solution

Given information

The regression line is $\overset{铃�}{y} = 11.058 鈭� 0.01466 x$

Concept

A regression line is a straight line that depicts the change in a response variable $y$ when an explanatory variable $x$ changes. By putting this $x$ into the equation of the line, you may use a regression line to predict the value of $y$ for any value of $x$

Explanation

The shown residual graphic effectively horizontalizes the regression line. It amplifies the points' deviations from the line; if the regression line reflects the main pattern of the data, the residuals should be devoid of pattern. A residual plot with a visible curved pattern is shown in the image. For these data, a straight line is not an effective model. As a result, using the regression line to predict $Y$ from $X$ would be inappropriate.