A residual in an algebraic equation is the difference between the actual value and the predicted value of a dependent variable. It is calculated by subtracting the predicted value from the actual value.
Residuals are used to determine the accuracy of a predictive model. If the residuals are small and randomly distributed around 0, it indicates that the model is a good fit for the data. However, if the residuals are large and show a pattern, it indicates that the model may not be the best fit for the data.
In a residual plot, the x-axis represents the predicted values and the y-axis represents the residuals. A scatter plot with no pattern or trend indicates a good fit for the data. A plot with a funnel shape or a curve indicates that the model may not be the best fit for the data. It is important to also check for any outliers in the plot.
A residual of 0 means that the predicted value and the actual value are the same. This indicates that the model perfectly fits the data, and there is no error in the predictions.
The sum of squared residuals (SSR) is calculated by squaring each residual and adding them together. It is a measure of the total error in the model. A lower SSR indicates a better fit for the data.