A residual plot is a scatterplot that displays the difference between the observed response and the fitted response values. It is a graphical tool used to assess the goodness of fit of a regression model. The horizontal axis of the plot represents the independent variable, while the vertical axis represents the residuals, which are the differences between the observed values and the predicted values.

A residual plot can show the following:

• Linearity: A residual plot can help identify whether the relationship between the independent and dependent variables is linear. If the residuals are randomly scattered around the horizontal axis, then the relationship is likely linear. If there is a pattern in the residuals, such as a curve or a straight line, then the relationship may not be linear.

• Homoscedasticity: A residual plot can also help identify whether the variance of the residuals is constant across the range of the independent variable. If the residuals are randomly scattered around the horizontal axis with approximately equal variability, then the variance is likely constant. If the variability of the residuals changes across the range of the independent variable, then the variance is not constant, and the data is said to be heteroscedastic.

• Outliers: A residual plot can help identify outliers, which are data points that are far away from the other data points. Outliers can have a significant impact on the regression model, and it is important to identify and address them.

In summary, a residual plot shows the difference between the observed response and the fitted response values and is used to assess the goodness of fit of a regression model. It can help identify linearity, homoscedasticity, and outliers in the data.