Final answer:
To confirm if a linear model is suitable for the relationship between a car's fuel consumption and speed, we evaluate the pattern in the residual plot, which should show randomly scattered residuals if the model is appropriate. Patterns or systematic structures in the residuals suggest a linear model might not be suitable.
Step-by-step explanation:
To determine if a linear model is appropriate for the relationship between the fuel consumption y of a car and various speeds x, we need to evaluate the residual plot. If the linear model is appropriate, the residuals should display no obvious patterns or systematic structures, meaning they should be randomly scattered around the horizontal line at zero, without any discernible form.
Patterns in a residual plot that would indicate a linear model is not appropriate include: clear curves or bends, increasing or decreasing spread of residuals as x increases, or clustering of residuals in a particular area. If the residuals are fanned out or show a curve, a linear model may not be the best choice, and a different type of model might provide a better fit. Additionally, if there are outliers or influential points, these can significantly impact the regression line, making it less representative of the data as a whole.
If our residual plot shows random scatter without any discernible pattern, we can conclude that the linear model is a good fit for the data, otherwise we need to consider a different model.