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Regression Analysis and Assumption Violations

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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 this problem is present, the model’s t-scores will be artificially high, indicating a false significance of relationships.

Serial Correlation

This is interaction of your model’s error terms.

When serial (or auto) correlation is present your SEE may be incorrect.
The Durbin-Watson test statistic can be used to determine the presence of Serial Correlation in multiple regression models, as well as simple and log linear time series models, but not on auto-regressive time series models.

Multi-collinearity

Two or more of your independent variables are highly correlated.

A tiny bit of multi-collinearity is tolerable and can be common in regression models involving several independent variables.
A common symptom of this problem is the presence of a high coefficient of determination (R2), despite having low t-scores for your independent variables (i.e. they are insignificant).

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Previous Lesson

Fcalc – the Global Test for Regression Significance

Qualitative and Dummy Variables in Regression Modeling

Quantitative Methods

17 lessons

CFA L2: Quantitative Methods - Introduction

Quants: Correlation Analysis

Quants: Single Variable Linear Regression Analysis

Standard Error of the Estimate or SEE

Confidence Intervals (CI) for Dependent Variable Prediction

Coefficient of Determination (R-Squared)

Analysis of Variance or ANOVA

Multiple Regression Analysis

Multiple Regression and Coefficient of Determination (R-Squared)

Fcalc – the Global Test for Regression Significance

Regression Analysis and Assumption Violations

Qualitative and Dummy Variables in Regression Modeling

Time Series Analysis: Simple and Log-linear Trend Models

Auto-Regressive (AR) Time Series Models

Auto-Regressive Models - Random Walks and Unit Roots

ARMA Models and ARCH Testing

How to Select the Most Appropriate Time Series Model?

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Risk Management

Statistical Methods