Stat 324

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Stat 324

• Review II

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Grading Notes
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What Weve Been Doing Multiple Regression

• Partial coefficients after considering
  combined effect of other variables already in
  model
• Matrix scatterplots, correlation matrix
• Added variable plots, multicollinearity
• Testing multiple coefficients simultaneously
• Overall F test, partial F test (full vs. reduced
  models)
• Is the simpler model good enough? (parsimony)
• Unusual observations
• Extreme in x-space
• Influential to model
• Special terms polynomial, indicator variables,
  interaction terms
• Supercedes two-sample procedures, ANOVA
• Variable selection techniques and validation

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Modelling

• Example Salary vs. education
• What if
• Huge increase for college education?
• Decrease in pay for graduate education?
• Transformation?
• Indicator variables?
• EV Colleges?

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Mallows Cp
Picking a single model from among all those
with small Cp is usually a matter of selecting
the most convenient one whose coefficients
all differ significantly from zero

• If want just one model, choose smallest Cp
• Read list in order, stop first time Cp gets near
  p
• Take several models where Cp is small, near p and
  consider them further

This one probably good enough
This one better
Is age statistically significant?
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FEV vs. smoking

• On average, smokers have higher FEV
• 3.28-2.57.71
• On average, smokers are older

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FEV vs. smoking

• After adjusting for age

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Terminology

• Interaction term
• Does the effect of age depend on smoking status?
• Quadratic term
• Does the effect of age different for younger
  people than older people?
• Multicollinearity
• Is the effect of age indistinguishable from the
  effect of education?

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Interesting case study
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Minitab Options

• Durbin-Watson statistic
• Looks at correlation between consecutive terms
  (time dependence)
• Weighted Regression
• In response to unequal variances
• For example, EV observations are the mean value
  of some measurement and have different group
  sizes
• Pay more attention to the more precise
  observations

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Other notes

• Insignificant terms
• Doesnt really hurt to leave them in the model as
  long as you clarify that they are not significant
• vs. Parsimony, R2adj
• Could keep in by request of subject matter expert
  or for sake of completeness (e.g., lower order
  terms of polynomial, set of indicator variables,
  indicators in presence of interactions)

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Study advice

• Learn from the HW assignments
• Read text
• Ch. 6 and 7 are pretty readable
• Ch. 8!
• Think globally and how everything ties together
• Implications of model
• What was the ending moral of some of the
  questions?
• What were some of the repeated messages?