Observation X1 X2 X3 ' ' ' XK Y

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Sample size n
Observation X1 X2 X3 . . . XK
Y 1 2 3 4 . . . n
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Postulated Model
Estimated Model
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Coefficients of Two Regressions
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Testing bj
Objective Is Bj different from zero? If not, we
want it out of the model.
We know that
Therefore
where k is the number of independent variables.
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Multicolinearity An Example
X1 X2 Y 1.1 1.0 4.0 2.3 2.7
8.1 3.0 3.1 11.8 4.7 4.3 16.8 5.2 5.1 19.7

Possible Models
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Possible Problems with Regression Line

• Multicolinearity (M/C)
• A linear relationship between two independent
  variables
• Why is it a problem?
• One of the independent variables becomes
  redundant
• When should one suspect M/C?
• When you expect a linear relationship between two
  independent variables
• When the correlation between two independent
  variables is higher than 0.7
• When the signs of (significant) variables are
  distorted

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Correlation Matrix
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Dealing with Multicolinearity
Remove the one with highest p-value (or smallest
absolute t-test--its the same thing).
neither is significant
Two independent variables are highly
correlated (positively or negatively).
Remove the one with highest p-value.
one is significant
leave both, unless you believe there is a very
strong linear relationship between them or if the
signs are distorted.
both are significant