1. 1. An example for using graphics
Lecture 17
Outline:
1. An example for using graphics
2. What/how to deal with unusual observations?
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ST3131, Lecture 17

2. (a). What assumption can be verified by the graph?
Problem 4.6 Page The following graphs are used to verify some of the Assumptions of the ordinary least squares regression of Y on X1, X2, …, Xp. For each of these graphs,
(a). What assumption can be verified by the graph?
(b). Draw an example of the graph where the assumption doesn’t seem to be violated.
(c). Draw an example of the graph which indicates the violation of the assumption.
1. The scatter plot of Y versus each predictor Xj
2. The scatter plot matrix of the variables X1, X2, …,Xp
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ST3131, Lecture 17

3. 4. The residuals versus fitted values
3. The normal probability plot of the internally standardized residuals
4. The residuals versus fitted values
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ST3131, Lecture 17

4. 5. The Potential-Residual plot
6. Index plot of Cook’s distance/Wesch and Kuh measure/Hadi’s influence measure
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5. What /How to do with unusual observations? Basic Principles:
Outliers and influential observations should not be routinely deleted
or automatically down-weighted. (WHY?)
Reasons: (1) They may not be bad observations
(2) They may be most informative observations
Example: Computer Repair Data (Page 117) n=24, p=1
Y(Minutes) versus X (Units)
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6. Potential Residual Plot24
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7. General Principles for dealing with unusual observations:
a). Carefully examine each of unusual observations to determine
Why they are outliers or influential points.
b).Corrective Actions for unusual observations:
1. Correct error in the data (if unusual observations due to typo)
2. Delete or Down-weigh the unusual observations (if unusual observations belong to other population)
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ST3131, Lecture 17

8. 5. Collect more data.(the data are not enough)
3. Transform the data/Consider a different model (the linear model fails)
4. Redesign the experiment or the sample survey (the design is inappropriate)
5. Collect more data.(the data are not enough)
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ST3131, Lecture 17

9. After-class Questions:
How will you deal with the unusual observations in your project data?
Are there any other ways that can be used to deal with unusual observations?
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ST3131, Lecture 17