3. Econometrics

Ols Regression — Quiz

Test your understanding of ols regression with 5 practice questions.

Practice Questions

Question 1

Which property does the residual vector $\hat u$ from an OLS regression with an intercept always satisfy?

Question 2

Suppose a researcher estimates a restricted model with $SSE_r=300$, an unrestricted model with $SSE_{ur}=200$, has $n=100$ observations, and the restricted model has $p_r=2$ parameters while the unrestricted has $p_{ur}=3$. What is the F‐statistic for testing the restriction?

Question 3

Given $\sum_i (x_i-\bar x)^2=64$ and an unbiased estimate of the error variance $\hat\sigma^2=9$, what is the standard error of the slope estimate $\hat\beta_1$?

Question 4

In the regression model $y=\beta_0+\beta_1 x+\beta_2 D+u$ where $D$ is a dummy variable equal to 1 for females and 0 for males, how should $\beta_2$ be interpreted?

Question 5

Which statement about the hat matrix $H=X(X'X)^{-1}X'$ in OLS regression is correct?