Week 3A Flashcards
Define when an omitted variable bias exists in a OLS estimate
When Both:
- E(X2|X1) does not = 0
( X2 is related to X1)
and
- B2 does not = 0
(X2 has an effect on Y)
What is an omitted variable bias
Violation of Assumption 4 (ZCM)
regression was too simple and another variable was captured in the error term
What are the five Guass-Markov Assumptions for MLR?
- Linear in parameters
- Random Sampling
- No perfect collinearity
- Zero Conditional Mean
- Homoscedasticity
What is perfect collinearity means?
There is an exact linear relationship among the independent variables
What is an endogenous variable
When a regressor is correlated to a variable in the error term.
The biased regressor is endogenous
Violates ZCM
What is an exogenous variable
An unbiased regressor that is not correlated to any variables in the error term
Does not violate ZCM
Explain multicollinearity
When two or more independent variables are highly correlated, making it difficult to isolate the individual effect of each variable on the dependent variable.
Increased the Var(B^j)
Explain Homoscedasticity
When the variance of the residuals is constant across all levels of the independent variables
What is the Var(bj^) formula and how do its components interact
σ^2(Error Variance):
This is the variance of the error term for the entire model — it reflects how much the actual outcomes vary from the model’s predictions.
Higher 𝜎^2 increases the variance of Bj^, making the estimate less precise.
Ideally, we want this to be low.
SSTj = total Variation in Predictor Xj
Measures how much Xj varies in the data.
Low variation in Xj makes it harder to estimate its effect, increasing the variance of Bj^
We want this to be high.
R^2j from regressing Xj on other predictors
- tells us how much Xj can be explained by other independant variables
- want to be low
Explain the Frisch-Waugh theorem
States that if you have a MLR, and you regress the other regressors against the regressor of interest, the residuals of this regression is equal to b^j in the original MLR. It represents how Bj^ uniquely explains Y
This is called partialling out
