class: center, middle, inverse, title-slide # Midterm Review ## EC 320: Introduction to Econometrics ### Winter 2022 --- class: inverse, middle # Prologue --- # Housekeeping Problem Set 3 - Due tonight by 23:59 on Canvas Midterm 2 on Wednesday - .hi[No lab this week] --- class: inverse, middle # Midterm II: The Weeds --- # Midterm Topics .green[Anything from the lectures, labs, or problem sets] .hi-green[is fair game!] 1. Simple Linear Regression: Estimation I & II 2. Classical Assumptions 3. Simple Linear Regression: Inference 4. Multiple Linear Regression: Estimation 5. Multiple Linear Regression: Inference 6. Regressions in .mono[R] --- # Midterm Topics ## 1. Simple Linear Regression: Estimation OLS mechanics - How does OLS pick parameter estimates? - What properties are a direct consequence of OLS? - Residuals *v.s.* errors Coefficient interpretation --- # Midterm Topics ## 1. Simple Linear Regression: Estimation (cont.) Goodness of fit - `\(R^2\)` interpretation - Understand `\(R^2\)` derivation - Use and misuse of `\(R^2\)` OLS by hand - Estimate coefficients and calculate `\(R^2\)`. --- # Midterm Topics ## 2. Classical Assumptions Six assumptions 1. Linearity 2. Sample variation/no perfect collinearity <!-- 3. Random sampling --> 3. Exogeneity 4. Homoskedasticity 5. Non-autocorrelation 6. Normality What do they buy? When are they satisfied? When are they violated? --- # Midterm Topics ## 2. Classical Assumptions (cont.) **So what?** - Coefficient interpretation - Hypothesis test validity --- # Midterm Topics ## 3. Simple Linear Regression: Inference Making inferences about population parameters - Population *v.s.* sample Hypothesis testing (*e.g.,* *t* tests) - Null hypotheses *v.s.* alternative hypotheses - Left-tailed, right-tailed, and two-tailed - Type I *v.s.* Type II error Confidence intervals --- # Midterm Topics ## 4. Multiple Linear Regression: Estimation OLS mechanics and properties Goodness of fit - `\(R^2\)` interpretation - Know the behavior of `\(R^2\)` as the number of explanatory variables increases. Make predictions for certain values of the explanatory values (*e.g.,* hedonic modeling) --- # Midterm Topics ## 4. Multiple Linear Regression: Estimation (cont.) Coefficient interpretation Omitted-variable bias - Know when omitting a variable causes bias. - Sign the bias. - Back out correlations between explanatory variables. --- # Midterm Topics ## 5. Multiple Linear Regression: Inference Confidence intervals and *t* tests - Other than degrees of freedom, same as before. Multicollinearity - Standard errors depend on the overlapping variation between the explanatory variable. - More overlap `\(\implies\)` bigger standard errors `\(\implies\)` less likely to reject null hypothesis. Irrelevant variables -- **No *F* tests on the midterm!** Stay tuned for the final. --- # Midterm Topics ## 6. Regressions in .mono[R] Write the code that generates regression output - I provide the console or R Markdown output and the name of the data file. - You provide the code that loads the necessary packages, imports the data, runs regressions, and generates a table. - Write the code as if it's in a .mono[.R] script. --- # Midterm Structure ## Fill in the Blank - 10 blanks - 3 points per blank (30 points total) ## True or False - 5 questions - 6 points per question (30 points total) ## Free Response - 5 multi-part questions with varying numbers of points (50 points total) - Explanations required for full credit --- # Midterm Protocol ## Materials - Writing utensil - 3-inch-by-5-inch note card - Basic or scientific calculator (no graphing or programming capabilities) - .hi[Nothing else] ## Procedure - 80 minutes from *"you may begin"* to *"pencils down"* - First 30 minutes: .hi[quiet period] (no questions, no getting up) - Last 50 minutes: ask lots of questions --- class: inverse, middle # Practice --- # Regression Table ## Example Suppose we have the following fitted model for wage equation (standard errors in parenthesis, n=500): $$ `\begin{aligned} \hat{\text{Earnings}} = -11.65 + &1.77 \text{ S} + 0.65 \text{ EXP} \\ &(0.211) \ \ \ (0.206) \end{aligned}` $$ `\(t_{0.975}(497)=1.96\)` and `\(t_{0.95}(497)=1.65\)` .smallest[ 1. Interpret the regression results 2. Perform two-tailed 5-percent test of the null hypothesis that schooling has no effect on hourly earnings. 3. Perform one-tailed 5-percent test of the null hypothesis that experience has no effect on earnings against the alternative hypothesis that experience has a positive effect on earnings. 4. Confidence interval ]