CFA Level 2: Quantitative Methods - Basics of Multiple Regression

Introduction

• This module is crucial for understanding future modules on multiple regression.
• Despite the term 'basics,' the content is foundational for future content.
• Emphasizes the new presentation style by CFA Institute, making topics more interconnected.

Key Learning Outcome Statements (LOS)

1. Simple Linear Regression Review
   • Dependent vs. independent variables.
2. Extension to Multiple Linear Regression
   • Adds more independent variables.
   • Interpretation of 'partial slope coefficients' (relationship while holding other variables constant).
3. Interpretation of Residual Plots
   • Most important for the module, as five questions in the end-of-module vignette focus on this.

Multiple Regression Model

• Equation: Dependent variable (Y), intercept term (b), slope coefficients (β) for multiple X variables.
• Error Term: Represents unexplained variance, important for graphing and analysis.

Objectives of Multiple Regression

1. Test Existing Theories - e.g., relationship between currency values and inflation.
2. Identify Relationships - e.g., hidden or latent relationships between variables.
3. Forecasting - Using the model to predict future values.

Statistical Measures & Significance

• Standard Error: Measures degree of error in estimates.
• Test Statistics and P-values: Determine statistical significance.
  • General rule: t-statistic > 2 for significance.
  • p-value < 0.05 for 95% confidence.

Assumptions of Multiple Regression (Unchanged from Simple Regression)

1. Linearity: Relationship between variables must be linear.
2. Independence: Independent variables should not be random.
3. No Perfect Multicollinearity: Independent variables should not have perfect linear relationships.
4. Zero Mean Error: Expected value of error term must be zero.
5. Homogeneity of Variance (Homoscedasticity): Consistent variance of error terms across observations.
6. No Autocorrelation: Error terms should not be correlated.
7. Normal Distribution of Error Terms: Essential for hypothesis testing and prediction.

Violation of Assumptions

1. Non-Linearity: Identified through residual plots.
2. Autocorrelation: Tested using Durbin-Watson statistic (between 0-4).
   • 2 = no autocorrelation, <2 = positive autocorrelation, >2 = negative autocorrelation.
3. Multicollinearity: Variance Inflation Factor (VIF) as an indicator.
   • VIF < 4: not concerning, >10: significant issue.
4. Heteroskedasticity: Visualized as funnel shapes in residual plots, indicating non-constant variance.

Graphical Representation

• Residual Plots: Visual tool for checking linearity, homoscedasticity, and appropriate variance.
• Normal QQ Plot: Checks for normal distribution of error terms.
  • Ideal: Points lie on a straight diagonal line.
  • Deviations indicate skewness or kurtosis.

Summary

• Revisits foundational concepts from level one on simple linear regression and extends into multiple regression.
• Importance of understanding assumptions and interpreting residual plots for exam preparation.

Action Item: Review the module's vignette questions that focus on interpreting the residual plots to solidify understanding.

Good luck and happy studying! 📘