Transcript Lecture 9

Statistics 350
Lecture 9
Today
• Last Day: Old Faithful,
• Today: Start Chapter 3
• Homework #3:
• Chapter 2 Problems (page 89-99): 13, 16,55, 56
• Due: February 7
• Read Sections 3.1-3.3
Diagnostics for the Predictor Variable
• Good idea to attempt to identify extreme values of the predictor variable
• Can use a box-plot
• Could also do a sequence plot because
Residuals
• Recall,, a residual is defined by:
• Can be used to assess violations from the linear regression model:
• Note: we do not have the true errors
the fitted line.
. We only have observed errors from
Residuals
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Recall properties of residuals:
1.  Xiei=0
2.  ei=0 which implies
3. Variance of residuals
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1 and 2 together imply that:
Common Violations
1.
2.
3.
4.
5.
6.
Residual Diagnostics
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Plot of residuals versus explanatory variable:
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Help check for:
1.
2.
3.
Residual Diagnostics
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If there are no problems you expect to see:
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If regression function is non-linear, expect to see
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If variance is not constant, often see
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If have outliers in data:
Residual Diagnostics
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Plot of residuals versus fitted values:
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Helps check for:
1.
2.
3.
Residual Diagnostics
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For simple linear regression, use this plot in same what as the residuals versus
the predictors, Xi
Residual Diagnostics
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Plot of residuals versus time (or order in which they were collected):
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Help check for:
1.
2.
Residual Diagnostics
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If there are no problems, expect to see:
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If there are problems, often see:
Residual Diagnostics
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Plot of residuals omitted predictor variable:
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Help check for:
1.
Residual Diagnostics
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If there are no problems, expect to see:
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If there are problems, often see:
Residual Diagnostics
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Box-plot or histogram of residuals:
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Help check for:
1.
2.
Residual Diagnostics
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If there are no problems, expect to see:
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If there are problems, often see:
Residual Diagnostics
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Normal probability plots:
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Help check for:
1.
2.
Residual Diagnostics
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If there are no problems, expect to see:
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If there are problems, often see:
Residual Diagnostics
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Notes: