Psych 611 Lecture 10

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Psych 611Lecture 10

• Multiple RegressionChapters 20

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Starters

• Lit review grade from your advisor must be
  emailed to me by Dec 14
• Last round of presentations on Dec 14, Exam 4
  right afterwards and through the weekend
• You cannot log out and log back in
• Different version of testing system

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Starters

• Exam 3 adjusted questions

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Starters

• Dummy coding lab
• Complements lecture material
• Prep for general linear model, 612
• Method 2 confusion from lab on Monday before
  Thanksgiving
• This method used multiple regression to
  illustrate the idea of partialling out the effect
  of a variable

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Partial Correlation

• ANCOVA involves at least three variables the IV,
  DV, and covariate
• The effect of the IV on the DV is tested after
  removing the covariates effect on the DV
• Similarly, you may want to test a correlation
  after removing the relationship a third variable
  might have with the variables of interest

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Partial Correlation

• The relationship of weight and hours of TV above
  and beyond education level
• Word frequency and reaction time above and
  beyond word length
• Job satisfaction and salaryabove and beyond age

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Partial Correlation
r123
http//www.gseis.ucla.edu/courses/ed230bc1/notes1/
con1.html
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4. Homoscedasticity
Betas give how Y changes with changes in each
X,while holding all other X values constant
http//www-stat.wharton.upenn.edu/stine/mich/Lect
ure4.pdf
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http//www.sjsu.edu/faculty/gerstman/EpiInfo/cont-
mult.htm
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Predict Y given set of Xs

• Anova summary table significance test
• R2 (multiple correlation squared) variation in
  Y accounted for by the set of predictors
• Adjusted R2 sample variation around R2 can only
  lead to inflation of the value. The adjustment
  takes into account the size of the sample and
  number of predictors to adjust the value to be a
  better estimate of the population value.

http//www.csun.edu/ata20315/psy524/docs/Psy5242
0Lecture20520MR.ppt
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Is each X contributing to the prediction of Y?

• Test if each regression coefficient is
  significantly different than zero given the
  variables standard error.
• T-test for each regression coefficient

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Can you predict future scores?

• Can the regression equation be generalized to
  other data?
• Can be done by randomly separating a data set
  into two halves, i.e., cross-validation
• Estimate regression equation with one half
• Apply it to the other half and see if it predicts

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Bivariate Regression Starter
http//www.csun.edu/gk45683/Lecture201220-20Re
gression20Significance20and20Multiple.pdf
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http//www.palgrave.com/pdfs/0333734718.pdf
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Interaction Terms

• As mentioned, for simple additive model
• Betas give how Y changes with changes in each X,
  while holding all other X values constant
• But what about relationships where the effect of
  X1 on Y changes depending on the value of X2?
• Add a multiplicative interaction term

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Model Selection

• When you have many predictors (Xs), how do you
  choose among them?
• Some may be too correlated with each, raising
  problem of multicollinearity
• Some may not be significant when other variables
  are included
• Choices based on theory or principles are
  preferred
• Hierarchical regression
• But when these are not available

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Model Selection

• Forward Selection
• Add Xs one at a time, from most to least
  correlated with Y, until non-significant
• Backward Elimination
• Remove Xs one at a time, from least to greatest
  contribution to R2, until significant
  contribution
• Stepwise Regression
• Same as forward, except recheck all vars at each
  step, and remove any that become non-significant

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Multiple Regression Bias

• Including many Xs increases the likelihood that
  variance will be accounted for by chance
• Adjusted R2, cross-validation
• Excluding Xs will tend to inflate regression
  coefficients for the included Xs

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For Lab on Monday

• Fabricate data for a multiple regression analysis
  with three predictors and dependent variable
• Variables must be NEW
• Research questions must be NEW
• Test assumptions, multicollinearity
• Create data that pass standard assumptions