Outliers

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Lesson 7b
Judging Whether a Regression Line Adequately
Describes the Data

• Outliers
• Residual plot
• Visual keys to selecting the correct model

Main Ideas
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• 1. Outliers
• An outlier is an observation that doesnt appear
  to fit the pattern of the other data.
• An outlier can have a significant effect on the
  regression line, especially if it occurs at the
  extreme of the data set.

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• 2. Outlier Will Change Equation of Line

With outlier y 3.65 .52x
Without outlier y 1.76 1.11x
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• 3. Residual Plot
• This is a plot of x versus the residuals (a
  residual is same as DEV which is how far above or
  below the line a point is).
• What to look for?
• Are residuals randomly scattered about 0?
• If not random, what trend do the residuals
  follow?
• Do the residuals show greater variability for
  some xs than others?

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• 4. Some Non-Random Patterns in Residuals.

Quadratic-like Trend
Increasing Variability
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• 5. Residuals Plots Can Help Select the Right
  Equation for the Data
• Generally, if some pattern in the residual is
  present it will lead us to consider some way to
  describe the data other than with a straight
  line.
• Curved pattern may mean a quadratic equation.
• If variability depends on x, then a
  transformation, such as a logarithmic
  transformation, may be appropriate.

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• 6. Before and After a Transformation.
• Comparing x vs y and x vs log10(y)

x vs y
x vs log10(y)
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• 7. Residual Plots for the Previous Graphs

Curved pattern for residuals
Residuals scattered about 0
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Why isnt a plot of x vs. y good enough? Why do
need residual plots?
Residual plots are particularly useful in
so-called multiple regression where we use more
than one predictor at once. What we are doing
now is illustrating an idea.
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