The correct answer is (d) the residual plot clearly contradicts the linearity of the data.
The residual plot in this case shows a clear pattern, with the residuals increasing as the speed increases. This suggests that the linear model is not a good fit for the data.
Step 1: Calculate the residuals
The first step is to calculate the residuals for each data point. The residual is simply the difference between the observed value of the dependent variable (fuel consumption) and the predicted value of the dependent variable based on the least squares line.
To calculate the residuals, follow these steps:
Fit a least squares line to the data. This will give you the equation of the line and the values of the intercept and slope.
For each data point, calculate the predicted value of the dependent variable using the equation of the least squares line.
Subtract the predicted value from the observed value to get the residual.
Step 2: Create the residual plot
The second step is to create the residual plot. The residual plot is a scatter plot of the residuals on the y-axis and the independent variable (speed) on the x-axis.
To create the residual plot, follow these steps:
Plot the independent variable (speed) on the x-axis and the residuals on the y-axis.
Label the axes and add a title to the graph.
Step 3: Analyze the residual plot
The final step is to analyze the residual plot to see if it confirms the linearity of the data. A good residual plot should show no pattern in the residuals. If there is a pattern, then this suggests that the linear model is not a good fit for the data.
There are a few things to look for when analyzing a residual plot:
Randomness: The residuals should be scattered randomly around the x-axis. If there is a pattern, then this suggests that the linear model is not a good fit for the data.
Constant variance: The width of the scatter of residuals should be relatively constant across the range of the independent variable. If the width of the scatter increases or decreases as the independent variable increases, then this suggests that the linear model is not a good fit for the data.
No outliers: There should be no outliers, which are data points that are far away from the rest of the data. Outliers can distort the residual plot and make it difficult to interpret.
Question
a study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). a least squares line was fit to the data. here is the residual plot from this least squares fit. what does the pattern of the residuals tell you about the linear model? (a) the evidence is inconclusive. (b) the residual plot confirms the linearity of the fuel economy data. (c) the residual plot does not confirm the linearity of the data. (d) the residual plot clearly contradicts the linearity of the data. (e) none of the above