Question

The relationship of horsepower of motorcycles to miles per gallon is represented by the following scatter plot:

Scatter plot with horsepower on the x axis and observed MPG on the y axis. The points plotted are 62 and 32, 63 and 31, 66 and 30, 71 and 30, 75 and 29, 81 and 27, 91 and 24, 94 and 25, 97 and 21, 99 and 20, 104 and 21, 114 and 18, 115 and 19, 120 and 17.

Jorge created the following residual plot:

Residual plot with x axis labeled horsepower and y axis labeled residuals. The points plotted are 62 and 0.44, 63 and negative 0.3, 66 and negative 0.52, 71 and 0.78, 75 and 0.82, 81 and 0.38, 91 and negative 0.02, 94 and 1.76, 97 and negative 1.46, 99 and negative 1.94, 104 and 0.36, 114 and negative 0.04, 115 and 1.22, 120 and 0.52.

Does his residual plot make sense based on the scatter plot? Explain.

The random residual plot makes sense because the scatter plot appears to have a linear relationship.
The random residual plot makes sense because the scatter plot appears to have a negative relationship.
The random residual plot does not make sense because it should have a linear relationship like the scatter plot.
The random residual plot does not make sense because it should have a nonlinear curve, as the scatter plot is negative.

Answer 1

A residual plot should show a random scatter of residuals if the linear regression model is appropriate. Jorge's residual plot makes sense if it displays residuals randomly dispersed around the horizontal axis, supporting the negative linear relationship shown in the scatter plot.

Step-by-step explanation:

In statistics, a residual plot is used to show the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data. Based upon the provided scatter plot with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis showing a negative correlation, as horsepower increases, MPG tends to decrease. This indicates that a linear model could be a good fit for this data.

The residual plot should typically show no clear pattern if the linear model is a good fit. If Jorge's residual plot shows residuals randomly scattered around the horizontal axis (with no clear pattern), then his residual plot does make sense because it supports the idea that the relationship between horsepower and MPG suits a linear model. Without seeing the actual scatter plot and residual plot, we cannot say for certain if the residual plot 'makes sense.' However, if the scatter plot shows a clear negative linear relationship, then a residual plot with residuals randomly scattered around the horizontal axis would confirm that a linear model is appropriate.