Minitab generates residual plots that you can use to examine the goodness
of model fit. You can choose the following residual plots:
· Histogram
of residuals.
An exploratory tool to show general characteristics of the data, including:
- Typical
values, spread or variation, and shape
-
Unusual
values in the data
Long tails in the plot may indicate skewness
in the data. If one or two bars are far from the others, those points
may be outliers. Because the appearance of the histogram
changes depending on the number of intervals used to group the data, use
the normal probability plot
and goodness-of-fit tests to assess the normality
of the residuals.
· Normal
probability plot of residuals. The points in this plot should generally
form a straight line if the residuals are normally distributed. If the
points on the plot depart from a straight line, the normality assumption
may be invalid. If your data have fewer than 50 observations, the plot
may display curvature in the tails even if the residuals are normally
distributed. As the number of observations decreases, the probability
plot may show substantial variation and nonlinearity even if the residuals
are normally distributed. Use the probability plot and goodness-of-fit
tests, such as the Anderson-Darling statistic,
to assess whether the residuals are normally distributed.
You can display the Anderson-Darling statistic
(AD)
on the plot, which can indicate whether the data are normal. If the p-value
is lower than the chosen a-level,
the data do not follow a normal distribution. To display the Anderson-Darling
statistic, choose Tools
> Options > Linear
Models > Residual Plots. For additional tests of normality, see
Stat
> Basic Statistics > Normality Test.
· Residuals
versus fits.
This plot should show a random pattern of residuals on both sides of 0.
If a point lies far from the majority of points, it may be an outlier.
Also, there should not be any recognizable patterns in the residual plot.
The following may indicate error that is not random:
- a
series of increasing or decreasing points
- a
predominance of positive residuals, or a predominance of negative residuals
- patterns,
such as increasing residuals with increasing fits
· Residuals
versus order. This is a plot of all residuals in the order that
the data was collected and can be used to find non-random error, especially
of time-related effects. A positive correlation is indicated by a clustering
of residuals with the same sign. A negative correlation is indicated by
rapid changes in the signs of consecutive residuals.
· Four
in one. Select this option to produce
a normal plot of residuals, a histogram of residuals, a plot of residuals
versus fits, and a plot of residuals versus order in one graph window.
· Residuals
versus other variables. This is a plot of all residuals versus
another variable. Plot the residuals against:
- Each
predictor
to look for curvature or differences in the magnitude of the residuals
- Important
variables left out of the model to see if they have critical additional
effects on the response.
If certain residual values are of concern, you can brush your graph
to identify them. See graph
brushing.
Residual Plot Choices