# 2nd Midterm Class Notes Flashcards

Interaction Terms

If the effect of Xi on Y depends on the value of X2, you should include the interaction of X1 and X2 as an explanatory variable.

Some notes on interaction terms

- ) You should never drop Xk as an explanatory variable, even if it is insignificant, if your model includes interaction terms involving Xk.
- ) Be careful interpreting Bk when you model includes interaction terms involving Xk.

In regards to non-linear terms…

- ) You should never drop Xk as an explanatory variable, even if it is insignificant, if you model includes higher-order terms involving Xk.
- ) Be careful in interpreting Bk when your model includes higher-order terms involving Xk.

- A one-unit increase in X2 would not increase Y by B2. Rather, a one-unit increase in X2 would increase Y by B2 + 2B3 + 2B3X2 (This marginal effect can be found by taking the derivative of Y with respect to X2)

If a categorical variable includes C categories, you can…

include C-1 dummy variables in your model

Measurement Error of Xk

- ) What is the nature of the problem?

a. ) Observed/measured Xk = True Xk + e - ) What are the consequences of the problem?

a. ) Bk will be biased towards zero because the poorer the measurement of Xk, the less information we have to find a relation between Y and Xk, the flatter our regression line. - ) How is the problem diagnosed?

a. ) Typically via a theoretical understanding of the process by which Xk is measured and thinking about whether that measurement is precise. Often, Xk is included as a proxy measure for something that is harder to measure. - ) What remedies for the problem are available?

a. ) Get better measurement of Xk.

- Find an instrumental variable for Xk

- Be aware of bias.

What is the nature of the problem with imperfect multicollinearity?

Xk is highly predicted by other variables in the model (i.e. Rk2 is high)

How is the problem of multicolinearity diagnosed?

- As a simple check for potential multicollinearity problems, first test the correlation of your x variables
- Or as a second test, if both of the two correlated variables lack significance in the regression, test the joint significance using an f-test. If the F-test shows that one of the two variables is significant, you probably have a .multicollinearity problem.
- The most sophisticated and best way to test for this is to compute the “Variance Inflation Factor” VIF

What are the remedies for multicollinearity?

- Only include one of the two correlated variables in your model.
- Get more observations because multicollinearity is less of a problem in large samples

Non-Linear Models are a failure of ?

classical assumption 1

What is the nature of the non-linear model problem?

Relationship btw Xk and Y is non-linear.

What are the consequences of the non-linear model problem?

One could improve fit of Y-hat to Y by including non-linear terms (e.g., square of Xk, ln(Xk), etc.) or by transforming the dependent variable (e.g., ln(Y)). Failure to do so could produce heteroskedastic errors

How is the non-linear model problem diagnosed?

- ) Theory
- ) Scatterplots of Xk versus Y. Look for relationships that are non-linear
- ) Scatterplots of the error terms versus Y. Look for relationships that are non-linear.

What remedies are there for non-linear models?

Include non-linear terms or transform the dependent variable.

When explanatory variables are correlated with the error term this is a failure of…

classical assumption 3

What is the nature of the problem with explanatory variables that are correlated with the error term?

XK is correlated with e.