Lectures 19: Exam 2 review

1. Lectures 19:Exam 2 review March 26, 2014

2. Question • I think my performance on Exam 2 will be: • Better than Exam 1 • About the same as Exam 1 • Worse than Exam 1 • I have no idea.

3. Administrative • Quiz 4 results (out of 25): not so good… • Min 0 • Max 22.00 • Average 11.04 • Median 11.00 • sd 7.15 • Example Exam 2 question: on blackboard • Expect the files on the website to be gone Sunday night – Monday.

4. Exam 2 content • No Experiment/Causal Inference questions – there were slides on the last lecture that we never got to (and I’m not sure we will…)

5. Quiz 3 Review

6. Additional Questions • Dummy variables and can we recap on interactions. • Online reading + lecture 15 • See Quiz 3: more examples if time allows. • Can we also have a general idea of omitting explanatory variables. • Use Partial (aka incremental) F test to test for significant increase in explained variation • Homework 7: unconstrained (different than exam but more like real life)

7. Multiple categories

8. Interactions

9. Is the calibration plots the plot of residuals v.s. fit that shows first in the regression output? if so, can you explain me how to interpret it? • It’s not necessarily the first plot. It’s the plot of actual Y values by the predicted, or fitted, Y values. It’s a richer visual display of the R^2. • In Simple Regression we just looked at the scatterplot. In multiple regression we have to look at individual scatterplots which don’t account for relationships between the X variables. • So the calibration plot collapses all of the X values to the fitted Y value.

10. Calculating t-statistics Call: lm(formula = growth ~ rev_coups + tradeshare + yearsschool, data = growth) Residuals: Min 1Q Median 3Q Max -3.5887 -0.9873 -0.0719 0.8364 5.7051 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.0001517 0.6929193 ______ 0.9998 rev_coups -0.9637983 1.0245684 ______ 0.3506 tradeshare 2.1642518 0.7501064 ______ 0.0054 ** yearsschool 0.2213497 0.0883593 ______ 0.0149 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.686 on 61 degrees of freedom Multiple R-squared: 0.2468, Adjusted R-squared: 0.2098 F-statistic: 6.664 on 3 and 61 DF, p-value: 0.0005768 What is the t-statistic for the estimate of tradeshare? • t = estimate / std err = 2.164 / 0.75 = 2.885

11. MRM conditions • When checking for MRM conditions, when we look at the scatterplot, all of the plots have to be linear? If not we transform the variable which is not linear? Are we going to have such questions in the exam? • A linear relationship is needed for a linear regression model to be appropriate • Do you transform or not? • On the exam I’ll tell you what I want you to do (maybe not explicitly but you should be able to tell) • In the wild: less so… it also depends. Transformations sometimes help, sometimes they don’t. You should be motivated by theory more than empirical digging…

12. F-ratios • There's a question about making conclusion about the f test. Can you explain to me how do we make conclusions about the f test? • Basic F test is a test of the null hypothesis H0: β1 = β2 = 0 • Given or can calculate the corresponding p-value • p less than 0.05 implies that the F is statistically significant at the 95% level and we can reject the null hypothesis. • Therefore we know that the statement that [ β1= β2 = 0 ] is not true. Although it could be false for different reasons (β1 ≠ 0) or (β2≠ 0) or (β1≠ 0 and β2≠ 0)