Residual Plots

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Purpose

Residual Plots (also known as error plots) show the difference between the data points and the fitted value. To verify the fit of the mathematical model to the data, often in conjunction with ANOVA and Regression, to suggest alternative models and identify the presence of outliers.


Anatomy

Residual Plot DiagnosticsUse Plots To Check Model Validity

Terminology

A. Distribution of the residuals presented as a Normal Plot – It provides a visual check of the assumption that the residuals are normally distributed. They tend to form a straight line for a normal distribution.

B. Histogram of Residuals – Similar to the function of Normal Plot, it provides an alternate presentation to check if the shape of the residual distribution resembles a normal distribution.

C. Individual (I) Chart of residuals – It helps to check if the residuals are time dependent and provides information to identify outliers. When the residuals form a trend or fall outside the upper or lower control limits, the data point should be examined closely for special causes.

D. Residuals plotted against the fit of the mathematical model – It provides visual clues to verify if the variance of the residual is constant. The distance between the residual points and the centerline represents how closely the mathematical model fits the data point.

Patterns other than a horizontal band of randomly distributed residuals may indicate problems such as a data measuring instrument problem, or data coming from an asymmetrical distribution.

Major Considerations

Since residual analysis is an essential step to validate the mathematical model, it should be carried out routinely. For the residual analysis on Regression, the data must be entered in pairs.

Application Cookbook

1. While carrying out analyses such as Regression or ANOVA (ANOVA one way unstacked does not support residual plot), pick Graph, then select one or more of the Residual Plots. Residual Plots will be displayed individually with the analysis.

2. Alternatively, pick Storage, then select options for Residuals and Fits when performing analyses such as Regression, ANOVA, etc. The residuals and fits associated with the analysis will be stored in columns labeled REST1 and FITS1 or the equivalent.

3. Carry out residual analysis by checking if the residual is normally distributed, (i.e. straight line in the Normal plot, and the histogram in the shape of normal distribution).

4. Check if the residuals in the I-Chart form a trend which is often indicative of a problem in data collection. Examining points outside the control limits for special causes.

5. Check if the residuals are randomly distributed. Converging or diverging patterns as shown below tend to suggests measuring problem with an error proportional to the measured value, or data from an asymmetrical distribution.

From Residual Plots to Six Sigma Tools.

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