Handle qualitative independent variables with a quantitative proxy or use a dummy variable. When using a dummy independent variables (such as assigning a number to the degree of consumer confidence), define a collectively exhaustive set of “j” categories, then j-1 (“j minus one”) will give you the number of dummy variables for inclusion in your […]

# CFA Exam Level 2

## Regression Analysis and Assumption Violations

Heteroskedasticity There are two types, Conditional and Unconditional. The type focused on in evaluating model validity is Conditional Heteroskedasticity. Conditional = the error terms change in a systematic manner that is correlated with the values of the independent variables. Look up a graph depicting this problem. The Breusch-Pagan test will test for Conditional Heteroskedasticity. When […]

## Multiple Regression and Coefficient of Determination (R-Squared)

For a multiple regression model, this value represents the percentage of total variation in Y that is explained by the regression equation. The value is between 0 and 1. R-squared has a mathematical relationship with TSS, SSE, and RSS. R2 = RSS/TSS = (TSS-SSE)/TSS = 1- (SSE/TSS) The coefficient of determination alone does not indicate […]

## Multiple Regression Analysis

Much of the concepts in simple regression are applicable, but watch out when determining your degrees of freedom for different analyses, as the values will be slightly different for models similar in observation count, but different in slope coefficient count. Six Assumptions of Multiple Regression (very similar to simple regression) Y and X must have […]

## Analysis of Variance or ANOVA

This is a tool to review a regression analysis and decompose the contribution of the variation in the independent X variable and the variation in the error (or residual) term in predicting the variation in the dependent Y variable. Regression Sum of Squares (RSS) measures the amount of variation in Y that is explained by […]

## Coefficient of Determination (R-Squared)

Typically noted as R2yx or R-squared in the stats report. This value measures the percentage of variation in Y that is explained by the model and will be between 0 and 1 (and not to be confused with the Correlation Coefficient which will be between -1 and 1). Example: a coefficient of determination/R-squared = .80 […]

## Confidence Intervals (CI) for Dependent Variable Prediction

In all likelihood, your model will not perfectly predict Y. The SEE can be extended to determine the confidence interval for a predicted Y value. A common CI to test for a predicted value is 95%. Your regression parameters, the y-intercept (b0) and slope coefficient (b1) will need to be tested for significance before you […]

## Standard Error of the Estimate or SEE

Also called Standard Error of the Regression Conceptually SEE helps to measure how imperfect your model is at predicting the value for a dependent variable, Y. Mathematically SEE can be seen a measure of deviation(s) around your model’s regression line, a line one deviation above and below the predicted equation line The following video explains […]

## Quants: Single Variable Linear Regression Analysis

This is the “least squares” method. Situational Example: “If a country’s broad stock index (X) appreciates 5%, by how much will the value of that index’s largest air transportation stock change?” You will apply this type of modeling in the equity section, when looking at the CAPM approach to asset valuation. Simple Regression can be […]

## Quants: Correlation Analysis

Correlation Correlation is math-speak for relationships. Is there a relationship between the change in the value of one variable and the change in value of another? Correlation and simple regression can help you: Verify a relationship between dependent variable Y and independent variable X. Identify the mathematical form of the relationship (ex. linear, exponential) Determine […]