Psychology 202a
Advanced Psychological
Statistics
November 3, 2015
The plan for today
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An example of probabilistic reasoning
The t test as regression (continued)
Restriction of range
Introducing multiple regression
The t test as regression
• Recall that regression is a model for the
conditional mean.
• Sometimes, the variable on which we
condition can be artificially constructed for
a special purpose.
• Long digression in SAS.
The unity of assumptions
• Initially, the assumptions underlying
regression and the t test appear different.
• However, when they are all satisfied, they
become the same.
Restriction of range
• When the range is restricted, the estimate
of the correlation is biased toward zero.
• Regression estimates are unbiased, but
are estimated with less precision.
• Illustration in R.
Introducing multiple linear
regression
• Multiple regression has more than one predictor
on the right hand side of the equation.
• Example:
Neuroticism   0  1 Agreeabili ty
  2 Depression  
When is multiple regression like
simple regression?
• Illustration with artificial data
• (digression in SAS)
• The simple regression slope is identical to
the multiple regression slope only when
the predictors are perfectly uncorrelated.
• That won’t happen except by design.