Residual plots are widely used in linear regression analyses. By
examining the pattern of residual plots, one can identify whether
there are additional variables that should be included in the
regression model. Residual plots also can help analysts find outliers
in the data set. More often, residual plots are used to diagnose
whether a model or a distribution can fit the data well.
Residual Plot
A residual plot is a graph that shows the residuals on the vertical axis and
the independent variable on the horizontal axis. If the points in a residual
plot are randomly dispersed around the horizontal axis, a linear regression
model is appropriate for the data; otherwise, a non-linear model is more
appropriate.
Below, the residual plots show three typical patterns. The first plot shows a
random pattern, indicating a good fit for a linear model. The other plot
patterns are non-random (U-shaped and inverted U), suggesting a better fit
for a non-linear model.
Random pattern
Non-random: U-shaped curve Non-random: Inverted U
http://stattrek.com/AP-Statistics-1/Residual.aspx
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What to plot
What are the predictor variables?
Which is the response variable?
Scatterplots
try each of the predictors v the response
what is the relationship - do they have a high 'little r'? is
it sensible to do a linear or non-linear regression ?
Regression
If they have a moderate to strong relationship do
regression analysis - what does the equation mean in
terms of your variables?
What is the value of big R2? outliers - are there any?
What happens when you remove them? residual plot what is the shape and scatter - was linear regression
appropriate? Intrapolation - does it give an 'accurate'
result? Extrapolation - does it give sensible predictions