A residual plot is a graph that shows the difference between the predicted value of a dependent variable and the actual observed value. It is a useful tool for evaluating the quality of a regression model and checking for any patterns that may indicate problems with the model. In this article, we will explore what a residual plot shows and how it can be used to improve regression analysis.
What is a Residual?
A residual is the difference between the predicted value of a dependent variable and the actual observed value. In other words, it is the error of the regression model. Residuals can be positive or negative, depending on whether the observed value is greater or less than the predicted value.
For example, if we have a regression model that predicts the sales of a product based on the price, and the predicted sales for a particular price are 100, but the actual sales are 90, then the residual for that data point is -10.
What is a Residual Plot?
A residual plot is a graph that shows the residuals for each data point in a regression model. It is a scatter plot that has the predicted values on the x-axis and the residuals on the y-axis. Each data point is represented by a dot on the graph.
The residual plot can be used to evaluate the quality of the regression model. If the model is good, then the residuals should be randomly scattered around the horizontal line at zero. However, if there is a pattern in the residuals, then it may indicate a problem with the model.
What Does a Good Residual Plot Look Like?
A good residual plot should have the following characteristics:
- The residuals should be randomly scattered around the horizontal line at zero.
- There should be no obvious patterns in the residuals.
- The residuals should have a roughly equal spread across the range of predicted values.
If a residual plot has these characteristics, then it is a good indication that the regression model is a good fit for the data.
What Does a Bad Residual Plot Look Like?
A bad residual plot may have one or more of the following characteristics:
- There is a clear pattern in the residuals, such as a curve or a line.
- The residuals have a non-random pattern, such as a U-shape or an inverted U-shape.
- The residuals have a wide spread at one end of the predicted values and a narrow spread at the other end.
If a residual plot has any of these characteristics, then it may indicate that the regression model is not a good fit for the data. The model may need to be revised or a different model may need to be used.
What Can a Residual Plot Tell Us?
A residual plot can tell us several things about the regression model:
- Whether the model is a good fit for the data.
- Whether there are any patterns in the residuals that may indicate problems with the model.
- Whether there are any outliers in the data that may be affecting the model.
- Whether there are any non-linear relationships between the variables that may need to be accounted for.
By interpreting the residual plot, we can improve the regression model and make more accurate predictions.
Conclusion
A residual plot is a useful tool for evaluating the quality of a regression model. It shows the difference between the predicted value of a dependent variable and the actual observed value. A good residual plot should have the residuals randomly scattered around the horizontal line at zero, with no obvious patterns. A bad residual plot may have a pattern in the residuals, a non-random pattern, or a wide spread at one end of the predicted values. By interpreting the residual plot, we can improve the regression model and make more accurate predictions.
