5/6/7- Multiple Linear Regression Flashcards
What is homoskedasticity?
The assumption that the error has the same variance for any value of x
var(u|x) = σ^2
What is the meaning of β1 in multiple linear regression?
The effect on Y of a change in X1, holding X2 constant
What are the 3 main properties of the fitted values and residuals?
- The sample average of the variables is zero
- The sample correlation and covariance between each independent variable and the residuals is zero
- The average of all the variables are on the fitted regression line
How is the original β1 related to the new β2 when a new variable x2 is added to the regression?
β1 = β1 + δ1β2
What are the 4 assumptions for unbiasedness of OLS estimator in MLR?
- Linear in parameters
- Random sampling
- No perfect collinearity
- Zero conditional mean
What does it mean that there is no perfect collinearity?
No independent variable is constant and there are no exact linear relationships among the independent variables
What is the assumption of zero conditional mean?
E(u|x1,x1…xk)=0
u cannot be correlated with any of the x variables
When is a variable irrelevant?
When its beta is zero
What is omitted variable bias (OVB)?
The bias in the OLS estimator that occurs as a result of an omitted factor, or variable
What are the 2 necessary conditions of the omitted variable for omitted variable bias to occur?
The omitted variable must be a determinant of Y and be correlated with regressor X
How do you calculate the magnitude of the OVB?
β2δ1
Where δ1 is the coefficient of x1 when you regress x2 on x1
How can you determine the size of the bias?
We can put bounds on the true effect like so:
-Positive bias if E(β1) - β1 > 0
-Negative bias if E(β1) - β1 < 0
so the upper bound is: β1 at most as large as E(β1)
lower bound: β1 is at least as large as E(β1)
What is the fifth assumption you add to the unbiased MLR conditions to make the Gauss-Markov theorem?
Homoskedasticity
What is the formula for an unbiased estimate of σ^2?
SSR/n-k-1
What does it imply for OLS estimators when they are under the assumptions of the Gauss-Markov theorem?
It implies that they are the best linear unbiased estimator
