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Final Review

Final Review. April 23, 2014. Exam details . In room 1185 AND 1032 You’ll receive an email from me if you’re in 1032, otherwise 1185. Spread out Don’t sit next to someone unless there are no other free computers. Starts at 9 am . No extensions .

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Final Review

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  1. Final Review April 23, 2014

  2. Exam details • In room 1185 AND 1032 • You’ll receive an email from me if you’re in 1032, otherwise 1185. • Spread out • Don’t sit next to someone unless there are no other free computers. • Starts at 9am. No extensions. • You should have more than enough time. • No electronic devices • (other than calculators, which I would NOT recommend). • Haven’t written it yet • Probably ~ 4 questions • Possible bonus question: IF response rate of student evaluations is >80% by Sunday at noon.

  3. 70-208: Regression & Forecasting • You learned a LOT of material this semester • Think about where you started and where you are now. • Long – exhausting – journey, but hopefully useful. • The exam… What’s going to be on it? • Everything… • But the course builds on itself. You can’t understand multiple regression if you don’t understand simple regression. • The final exam should be the easiest exam all semester: you’ve seen it all before! • Best way to study: previous exams.

  4. Simple regression • Review the homework and exam problems • Know the conditions and assumptions behind the S/MRM. • If I ask you to fit a model, fit a model but know that they are violated. • Is the association between y and x linear? • Maybe one could exist but you don’t obviously see it (much more common in multiple regression) • Have omitted/lurking variables been ruled out? • In the exam, I’ll try to give you the necessary info. • Are the errors evidently independent? • How do you verify this? • Are the variances of the residuals similar? • How do you verify this? • Are the residuals nearly normal? • How do you verify this? • Transformations • Don’t forget to convert back to the appropriate units! • Transformations are theoretically driven: • how do you estimate elasticity?

  5. Multiple regression • Marginal Slopes vs Partial slopes • Categorical variables • Constructing dummies; how many to include; reference groups • Interactions • Reduced form equations. • Interpretations!! • Adding/removing variables from a model • VIFs • Diagnostics • Model Validation • + all the stuff from simple regression

  6. Time series & Forecasting • Seasonality • Both moving average and regression techniques. • Smoothing models • AR(p) models • ADL models. • I’ll tell you what and how many lags to take. • Holdouts • Model validation for time series. • Forecasting 1 period ahead with confidence intervals • Forecasting multiple periods ahead (with an AR or ADL)

  7. Exam 3 • Excel Files posted. • Two versions: • BRK.A: odd numbers • XOM: even numbers. Common Mistakes: • Autoregression • AR(1) means one lag of the response variable • If response is difference in price, explanatory variable is the lag(difference in price) • Quite a few people estimated returns. I never asked for returns; just differences. • Review how to calculate the partial-F

  8. Interpreting Interactions We’re estimating: • The estimated salary for a woman with 7 years experience? • = β0 + β1 * (7) + β2 * (0)+ β3* (7 * 0) • = β0 + β1 * (7) • The estimated salary for a man with 6 years experience? • = (β0 + β2)+ (β1 + β3 )* (6) • The slope of the dummy variable is the difference between the intercepts (as before). The slope of the interaction is the difference between the estimated slopes

  9. Interactions: Common Mistakes Some common errors: • Omitting variables that are part of the interaction • If you want just the intercept to vary, include just the Dummy • If you want both the intercept and slope to vary by group, include both constituent terms and the interaction term • If you want (oddly) to slope to vary but force the intercept to be the same, include only one constituent term (and exclude the dummy) and the interaction • Failing to note the conditional nature of the coefficients. • Partial slopes of the constituent terms are conditional on the other constituent term being 0

  10. Leverage Leverage: • Statistic we can calculate for each observation • A measure of influence of the observation on the model. • Ranges from 0 to 1 (low to high influence). • Observations with leverage values larger than 3k / npotentially problematic • k = number of parameters (# explanatory variables +1) of the model • nis sample size • Why is it a function of k and n? • Leverage is just the potential for being problematic. Once you’ve identified potentially troubling observations, try re-estimating the model without that data point. • Even if your results change, it doesn’t mean you should drop the data point(s). It might be completely legitimate. But it helps you understand your data.

  11. Cook’s Distance • To look at potential outliers with high leverage, we can calculate the Cook’s Distance for an observation i • Cook’s Di < 0.5, usually fine. • 0.5 < Di < 1, might be problematic; • Di > 1, probably problematic. where: ei = residual for observation i k = number of parameters (# explanatory variables +1) of the model MSE = Mean Square Error = SSE / (n-k-1) = se2 hi = leverage of observation i • So I could provide the leverage values for each obs and have you calculate D, or identify leveraging observations, etc.

  12. Course Evaluations • Remember: 80% by Sunday @ noon, then a bonus question on the Final • Section W • Section X

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