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How to Find a Problem With a Residual Plot

In statistics, the residuals are the differences between the values of the dependent variable predicted by the model and the values of the actual dependent variable. Ordinary regression assumes that the residuals are normally distributed. It also assumes that the variance of the residuals is constant across levels of the independent variables, and that the residuals are not related to the independent. One way of checking the last two assumptions is to look at a residual plot, which plots an independent variable on the x axis and the residuals on the y axis.

Instructions

- 1
  Check for change in spread of variance as the independent variable increases. Look at the residuals near the lower end of the x-axis, near the middle of the x-axis and near the upper end. The distance between the highest and lowest residuals should be approximately equal across the levels of the independent variable. If they are not, you have a problem known as heteroscedasticity.
- 2
  Look for an increase or decrease in the residuals as the independent variable increases. At all levels of the independent variable, the residuals ought to be centered around 0. There should be neither an increase nor decrease, nor should there be a U-shaped pattern (low in the middle, high at either end) or an inverted U-shaped pattern. The plot should look like a blob. If it does not, then you have a problem with the variables that are in the model.
- 3
  Look for outliers. No residual ought to be much higher than the others. If one point jumps out, or a few do, either much lower or much higher than the others, then those may be associated with outliers. This could be a data entry error, or it might be a highly unusual case.

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