Title Quantative Methods.pdf ✅

Last Revised: 07/25/2023 1 2024 Level 2 - Quantitative Methods This document should be used in conjunction with the corresponding learning modules in the 2024 Level 2 CFA® Program curriculum. Some of the graphs, charts, tables, examples, and figures are copyright 2023, CFA Institute. Reproduced and republished with permission from CFA Institute. All rights reserved. Required disclaimer: CFA Institute does not endorse, promote, or warrant accuracy or quality of the products or services offered by MarkMeldrum.com. CFA Institute, CFA®, and Chartered Financial Analyst® are trademarks owned by CFA Institute. © 2533695 Ontario Limited d/b/a MarkMeldrum.com. All rights reserved. Learning Modules Page Basics of Multiple Regression and Underlying Assumptions 2 Evaluating Regression Model Fit and Interpreting Model Results 6 Model Misspecification 11 Extensions of Multiple Regression 16 Time-Series Analysis 23 Machine Learning 32 Big Data Projects 43 Review 50 M.M134813896.
Last Revised: 07/25/2023 2 Basics of Multiple Regression and Underlying Assumptions a. describe the types of investment problems addressed by multiple linear regression and the regression process b. formulate a multiple linear regression model, describe the relation between the dependent variable and several independent variables, and interpret estimated regression coefficients c. explain the assumptions underlying a multiple linear regression model and interpret residual plots indicating potential violations of these assumptions M.M134813896.
Last Revised: 07/25/2023 3 Basics of Multiple Regression Main tasks Multiple regression used to: identify relationships between variables test existing theories forecast value of a DV - model: �� = �� + ����� + ����� + ⋯ + ����� + �� � = 1➞ n deterministic part � IVs or slope coefficients - partial slope coefficients % � ➞ estimated * Describe the types of investment problems addressed by multiple linear regression and the regression process partial slope coefficient: measures ∆DV for a 1 unit ∆IV holding all other IVs constant e.g./ RET = .0023 - 5.0585 BY - 2.1901 CS return bond yield credit spread when both IVs = 0, RET = .0023 BY ↑ 1, RET ↓ 5.0585 CS ↓ 1, RET ↑ 2.1901 Assumptions/ 1/ Linearity - relationship between the DV and IVs are linear 2/ Homoskedasticity - the variance of the regression residuals is the same for all observations i.e. ���(��) = ���.��/ * Formulate a multiple linear regression model, describe the relation between the dependent variable and several independent variables, and interpret estimated regression coefficients Page 2/ specify the model interpret the output Page 1/ intercept Stochastic part n > � M.M134813896.
Last Revised: 07/25/2023 4 Assumptions/ 3/ Independence of errors - the observations are independent of one another ∴ regression residuals are uncorrelated across observations 4/ Normality - regression residuals are normally distributed 5/ Independence of IVs 1/ IVs are not random (i.e. - they have a specific value) 2/ no exact linear relationship between 2 or more IVs Scatterplot matrix (pairs plot) - uses simple linear regression: DV vs. each IV + each IV vs. the other IVs what to see linear relationships * Explain the assumptions underlying a multiple linear regression model and interpret residual plots indicating potential violations of these assumptions pos. linear neg. linear almost no ‘apparent’ linear relationship * Explain the assumptions underlying a multiple linear regression model and interpret residual plots indicating potential violations of these assumptions Page 3/ Page 4/ don’t want to see linear relationships Scatterplot Matrix slight pos. relationship DV IVs since we can, and will, interpret output ➞ this is not a very useful step - any violations will be identified statistically, not visually ➞ ���� is sig. in the output however M.M134813896.