Formulate the simple OLS regression model.
Find the OLS estimators.
Show the 3 implications for the simple model.
Name the 6 assumtions for multiple OLS regression
Linearity-Assumption AL
Rank-Assumption AR
Exogeneity-Assumption AX
Homoscedasticity-Assumption AH
Uncorrelatedness-Assumption AC
Normality-Assumption AN
Find the estimator for a multiple OLS regression.
Name the normal equation and the 5 implied algebraic properties of the OLS estimator.
X’y - X’Xβ = X’(y - Xβ) = X’ε = 0
Sum of OLS residuals is zero
Sample covariance between residuals and predictors is zero
Fitted values and residuals are orthogonal
Mean of fitted values is equal to the sample mean
Means of predictors evaluate to the sample mean
Name the necessary and the sufficient condition for (X’X) being invertible.
Necessary:
positive sample variance for each predictor x_k
no perfect linear relation between two predictors x_k, x_l
Sufficient:
the predictors X_1, …, X_k are not linearly dependent
What is the coefficient of determination?
How is it computed?
How can it be interpreted?
R² is a measure of goodness of fit.
Sum of squares of residuals:
SSR = ε’ε
Total sum of squares:
SST = Ns_y²
R² = 1 - SSR / SST
R² close to 1 … very good model fit (100% explained by the model)
R² close to 0 … bad model fit
Proof that SST ≥ SSR.
How can one interpret β_k?
Show the Unbiasedness of the OLS estimator.
Find the (conditional and unconditional) Covariance matrix of the OLS estimator.
What is the covariance matrix of the OLS estimator in a simple regression?
Explain the concept of Multicollinearity. How can one see that a regressor is highly redundant?
How can one find the standard error of the OLS estimator using an unbiased estimator of the error variance?
What is the sampling distribution of the OLS estimator?
What is the sampling distribution of the SSR?
What does the Gauss-Markov Theorem state?
How to test a single coefficient when σ² is known?
How to test a single coefficient when σ² is unknown?
How to test more than one coefficient
What do you know about predicting an out-of-sample value? (prediction error variance, prediction interval)
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