Question

What diagnostic plot can you use to determine whether the incorrect model has been used? What should the plot look like if the correct model has been used?

Short answer

Answer: A residuals versus fitted values plot, also called a residuals plot, can be used to determine whether an incorrect model has been used in a statistical analysis. If the correct model has been used, the plot should show random scatter, homoscedasticity, and an overall mean close to zero with no significant outliers.

Step-by-step solution

1. Identifying the Diagnostic Plot

A diagnostic plot commonly used to determine whether the correct model has been used is the residuals versus fitted values plot, also called a residuals plot. This plot shows the residuals, which are the differences between the observed values and the predicted values (fitted values), against the fitted values.

2. Analyzing Residuals Plot for the Correct Model

If the correct model has been used, the residuals plot should have the following characteristics: - There should be no clear pattern in the residuals; they should be scattered randomly. - The points should be homoscedastic, meaning the spread of the residuals should be consistent across the fitted values. - The overall mean of the residuals should be approximately zero. - There should be no significant outliers, meaning most of the points should be close to the horizontal line at zero.

3. Analyzing Residuals Plot for the Incorrect Model

If an incorrect model has been used, the residuals plot may exhibit the following characteristics: - There might be a clear pattern, and the residuals might not be distributed randomly. - The plot may show heteroscedasticity, meaning the spread of the residuals may not be consistent across the range of fitted values. - Large residuals or significant outliers might be present, indicating that the model is not accurately capturing the data. - Curvature in the plot may suggest that a nonlinear model would better describe the data. In conclusion, to determine whether the incorrect model has been used, one can use a residuals versus fitted values plot. If the correct model has been used, the plot should show random scatter, homoscedasticity, and an overall mean close to zero with no significant outliers. If these characteristics are not present, this may indicate that an incorrect model has been used.