2. Multiple Variable Linear Regression Model Flashcards
How often is the two variable model used?
Rarely because important factors are often left out which makes the zero conditional mean invalid
What happens if one out of 50 variables is correlated with u
The OLS estimators will be biased since the zero conditional mean won’t hold
What are the normal equations?
They are the first order conditions we get when we do the minimisation of the SSR. There are k+1 equations
What happens to our estimators if there is a strong correlation between x1 and x2?
We get less information since we are unsure which variable it is that affects y
Partialing out
We partial out the part of the variation in y that could be explained by either x1 or x2 or both.
Gauss Markov assumptions
- Linear in parameters
- Random sampling
- No perfect collinearity
- Zero conditional mean
- Homoskedasticity
What do we do if two variables are perfectly collinear?
Exclude one of them
What happens to our estimate if MLR4 isn’t valid?
The estimation is possible but it will be biased. This is hard to solve
What is Rj^2?
A measure of the correlation between xj and all the other explanatory variables
What things affect the variation of our estimate of Bj?
- increased var(u) increases it
- increased sample size decreases it
- increased variation in explanatory variables of x decreases it
- increased Rj^2 increases it
Multicollinearity
When Rj^2 increases so does the variance of our variables, this is the only downside from using MLR over SLR
How does the problem of multicollinearity affect our model?
- it doesn’t cause bias
* it seriously inflates our variation of our estimates of variables when the correlation is very high
How can we help the problem of multicollinearity?
- Increasing the sample size
* it is tempting to remove a variable but this will cause bias
When are OLS estimators BLUE?
When the Gauss markov assumptions hold
Null hypothesis
Ho- it is the original hypothesis which we are challenging
