Lecture notes 12 multicollinearity

Question 1

What is perfectly multicollinearity and what is the implication of it?

Answer 1

• When variables that are being regressed are a function of each other X1 = -2X2

This means the coefficients cannot be determined uniquely

Question 2

What is an example of perfect multicollinearity?

Answer 2

X1 + X2 = 1

Eg the same dummy is used twice but with 1 and 0 being shifted.

Question 3

How can you show multicollinearity

Answer 3

Sub into the regression the relationship between the categorical variables and then when you collect coefficients it shows there are not unique solutions to the equations.

Question 4

What is imperfect multicollinearity?

What is the issue of this?

Answer 4

The regressor variables are highly correlated

Eg Age and Work experience (highly correlated)

Difficult to see which variable causing the issue.

Question 5

What happens to the variance when you have highly correlated regressors?

Answer 5

Xbar - x is in the denominator and as denominator gets to 0 the whole fraction getd larger so variance gets really large

Question 6

What can be done to mitigate multicollinearity?

Answer 6

-Try and drop variable

-Perform a transformation to the variables