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Lesson 7 of 17

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 the variation in X.

Mean Sum of Squares of the Regression (MSSR) = RSS/degrees of freedom

Sum of the Squares of the Errors (SSE) measures the amount of variation in Y that is explained by the variation in the error term.

  • Mean Sum of Squares of the Errors (MSSE) = SSE/(n - x variables - 1)

    √MSSE = SEE

  • Be careful not to confuse SSE with the Standard Error of the Estimate (SEE) – SEE is one standard deviation above and below the model line, while SSE is measure of the error term’s contribution to the explanation of the dependent variable.

Total Sum of Squares (TSS) indicates the total amount in variation in Y and equals RSS + SSE.

Note that mathematical relationships exist among R2yx, RSS, SSE, and TSS, enabling the analyst to derive one value, if given values for the others.  Knowing these relationships can save you time on the exam and greatly simplify a problem that appears complex.

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Multiple Regression Analysis

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Quantitative Methods

17 lessons

Lessons

1
CFA L2: Quantitative Methods - Introduction
2
Quants: Correlation Analysis
3
Quants: Single Variable Linear Regression Analysis
4
Standard Error of the Estimate or SEE
5
Confidence Intervals (CI) for Dependent Variable Prediction
6
Coefficient of Determination (R-Squared)
7
Analysis of Variance or ANOVA
8
Multiple Regression Analysis
9
Multiple Regression and Coefficient of Determination (R-Squared)
10
Fcalc – the Global Test for Regression Significance
11
Regression Analysis and Assumption Violations
12
Qualitative and Dummy Variables in Regression Modeling
13
Time Series Analysis: Simple and Log-linear Trend Models
14
Auto-Regressive (AR) Time Series Models
15
Auto-Regressive Models - Random Walks and Unit Roots
16
ARMA Models and ARCH Testing
17
How to Select the Most Appropriate Time Series Model?
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