8.) Multicollinearity

Question 1

Strictly speaking, perfect multicollinearity is the..

Answer 1

violation of Classical Assumption VI - that no independent variable is a perfect linear function of one or more other independent variables.

Question 2

Recall that the coefficient betak can be thought of as…

Answer 2

the impact on the dependent variable of a one-unit increase in the independent variable Xk holding constant the other independent variables in the equations.

Question 3

Perfect multicollinearity violates …

Answer 3

Classical Assumption VI, which specifies that no explanatory variable is a perfect linear function of any other variable.

Question 4

A perfect linear function has all data points..

Answer 4

on the same straight line.

Question 5

Perfect multicollinearity ruins our ability to…

Answer 5

estimate the coefficients because the two variables cannot be distinguished.

Question 6

Dominant Variable

Answer 6

is by definition related so highly correlated with the independent variable that it completely masks the effects of all other independent variables in the equation.

Question 7

Dominant variables should be recognized as..

Answer 7

being virtually identical to the dependent variable.

Question 8

imperfect Multicolinearity can be defined as…

Answer 8

a linear functional relationship between two or more independent variable that is so strong that it can significantly affect the estimation of the coefficients of the variable

Question 9

What are the consequences of multicolinearity?

Answer 9

1. ) Estimates will remain unbiased.
2. ) The variances and standard errors of the estimates will increase.
3. ) The computed t-scores will fall.
4. ) Estimates will become very sensitive to changes in specification.
5. ) The overall fit of the equation and the estimation of the coefficients of multicollinear variables will be largely unaffected.

Question 10

The main purpose in discussing multicollinearity is to learn to determine…

Answer 10

how much multicolinearity exists in an equation, not whether any multicolinearity exists.

Question 11

The severity of multicollinearity in a given equation can change from sample to sample …

Answer 11

depending on the characteristics of the sample

Question 12

The trick is to find variables that are…

Answer 12

theoretically relevant (for meaningful interpretation) and that are also statistically nonmulticolinear (for meaningful inference)

Question 13

Are there accepted tests to find multicolinearity?

Answer 13

No, there are none.

Question 14

The use of simple correlation coefficients as an indication of the extent of multicolinearity involves..

Answer 14

a major limitation if there are more than two explanatory variables.

Question 15

r is high if..

Answer 15

it causes unacceptably large variances in the coefficient estimates in which we’re interested.

Question 16

The variance inflation factor (VIF)

Answer 16

is a method of detecting the severity of multicollinearity by looking at the extent to which a given explanatory variable can be explained by all the other explanatory variables in the equation.

Question 17

There is a VIF for…

Answer 17

every explanatory variable in an equation.

Question 18

What are the steps for variance inflation factor (VIF)

Answer 18

1. ) Run an OLS regression that has Xi as a function of all the other explanatory variables in the equation
2. ) Calculate the variance inflation factor for beta hat i.