week 2 part 3

Question 1

When can the desirable properties of OLS estimators be negatively affected?

Answer 1

When one or more model assumptions are violated.

Question 2

What is commonly used to investigate the assumptions?

Answer 2

The residuals

Question 3

What are the 6 assumptions?

Answer 3

1. Assumption of linearity
2. Assumption of no perfect multicollinearity
3. Assumption of constant variability
4. Assumption of no autocorrelation
5. Assumption of no endogeneity
6. Assumption that the error term is normally distributed.

Question 4

What does the Assumption of linearity claim?

Answer 4

That the regression model is linear, and the parameters are correctly specified.

Question 5

What do we do if there is no linearity?

Answer 5

Adapt the model to the non-linearity by making simple transformations of the dependent variable and/or the explanatory variables.

Question 5

What can we use to identify non-linear patterns?

Answer 5

We can use residual plots. Linearity is confirmed if the residuals are randomly distributed over the observations of an explanatory variable. A clear trend in the residuals indicates a non-linear pattern.

Question 6

What does the Assumption of no perfect multicollinearity claim?

Answer 6

That there is no exact linear relationship between the explanatory variables.

Question 7

When does Perfect multicollinearity occur?

Answer 7

When two or more explanatory variables have an exact linear relationship. Perfect multicollinearity is easy to detect because the model cannot be estimated.

Question 8

What is the problem with Multicollinearity?

Answer 8

Its presence results in uncertain estimates of the regression coefficients. Thus, multicollinearity makes it difficult to separate the various influences of the explanatory variables on the dependent variable. If the multicollinearity is severe, we can see that some important explanatory variables become insignificant, and some coefficient estimates may even have incorrect signs.

Question 9

How do we detect multicollinearity?

Answer 9

With informal methods.
- A high R2 and adjusted R2 combined with individually insignificant explanatory variables, indicate multicollinearity.
- Another guideline is that if the correlation coefficient between two explanatory variables is more than 0.8 or less than -0.8, it suggests serious multicollinearity.
- Unexpected signs in the estimated regression coefficients also indicate this.

Question 10

What should we do if we found strong multicollinearity?

Answer 10

• Remove one of the collinear variables (those that essentially measure the same thing). Or,
• Obtain more data.
• In some cases, the best option is to do nothing at all if there is justification for keeping all variables.