The title of this section really just says “applied statistics for financial analysis.” Some of the basic principles in the quant section will appear in other exam sections, and this series will attempt to highlight such items. There will likely be one item set (six questions), but two is a possibility. Try not to let […]

# Quantitative Methods

## 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 […]

## 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 […]

## 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 […]

## 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 […]

## 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 […]

## 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 […]

## 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 […]

## 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 […]

## Fcalc – the Global Test for Regression Significance

A statistically significant Fcalc (i.e. one that passes the Fcritical threshold, based on your degrees of freedom) can indicate that your model as a whole is meaningful. This test is really applicable for multiple regressions, where there is more than one slope coefficient (b1, b2, b3 … bi), as a t-test will not work for […]