Week 2 Flashcards
(15 cards)
What does the acronym BLUE stand for in the context of Ordinary Least Squares (OLS) estimation?
Best Linear Unbiased Estimator
What are the main assumptions under which the OLS estimator is BLUE?
the Gauss Markov Assumptions. They include assumptions like conditional zero mean and constant variance
What is meant by an estimator being “Unbiased”?
Unbiasedness means that the expected value of the estimator is equal to the true population parameter
What is meant by an estimator being “Best
Best” refers to Minimum Variance. Among all linear unbiased estimators, the OLS estimator has the smallest variance.
Why are the properties of Unbiasedness and Best important for the Least Squares estimator?
Given the classical assumptions, these desirable properties indicate that Least Squares is the best linear estimator available for calculating the slope and intercept of the regression line.
How is a Confidence Interval calculated for a regression coefficient estimate (e.g., β)?
A confidence interval is typically calculated as the estimated coefficient plus or minus the critical value (from a t-distribution) multiplied by the standard error of the coefficient. For a 95% interval, this would be estimate ± critical value * standard error.
How do you determine if a variable is statistically significant at a given significance level (e.g., 5%) using its confidence interval?
A variable (or its associated coefficient) is statistically significant if its confidence interval does not include zero.
What is the standard approach to hypothesis testing for an individual regression coefficient?
You formulate a Null Hypothesis (H0) and an Alternative Hypothesis (H1). You then calculate a Test Statistic (like a t-statistic). This is compared to a Critical Value (from a t-distribution, based on degrees of freedom and significance level).
How is the Test Statistic for a regression coefficient typically calculated?
The Test Statistic (specifically the t-statistic for an individual coefficient) is calculated as the estimated coefficient divided by its standard error
How do you make a Decision in a hypothesis test for a regression coefficient based on the Test Statistic and Critical Value?
If the absolute value of the Test Statistic is greater than the Critical Value, you reject the Null Hypothesis (H0). If it is less than or equal to the Critical Value, you fail to reject H0.
How can you use the p-value to make a decision in a hypothesis test?
If the p-value associated with the Test Statistic is less than the chosen significance level (e.g., 0.05 for a 5% level), you reject the Null Hypothesis (H0).
What is the Coefficient of Determination (R²) and how is it interpreted?
R² is calculated as ESS/TSS. It represents the proportion of the total variation in the dependent variable that is explained by the regression model. A value closer to 1 indicates a better fit of the model to the data.
What does ESS and TSS stand for in the context of calculating R²?
ESS stands for Explained Sum of Squares. TSS stands for Total Sum of Squares.
Why might you take the natural logarithm (Ln) of a variable in an economic model?
Taking the natural log can help normalize skewed distributions and also allows for coefficients to be interpreted as percentage changes (when the independent variable is not logged) or elasticities (when both are logged).
How can you test a linear restriction involving regression coefficients (e.g., testing if two coefficients are equal)?
You can reformulate the hypothesis (e.g., H0: β₂=β₃). This can be translated into a testable format by substituting the restriction into the original regression equation to create a “restricted” model. You then test the significance of the term representing the restriction in the reformulated model.
