Chartered Financial Analyst (CFA) Practice Exam Level 2

What is the implication of heteroskedasticity in regression analysis?

1. Constant variance around the regression line

2. Variance of the error term varies with explanatory variables

3. Independence of errors across observations

4. Normal distribution of residuals

The correct answer is: Variance of the error term varies with explanatory variables

Heteroskedasticity refers to the condition in which the variance of the error terms in a regression model varies across different levels of an independent variable. This characteristic can lead to inefficient estimates and statistics that are not valid for hypothesis testing because standard errors might be biased. In regression analysis, the assumption of homoskedasticity (constant variance of error terms) is crucial for the reliability of statistical tests. When heteroskedasticity is present, it implies that, as the value of an explanatory variable changes, the spread of the residuals (the differences between observed and predicted values) also changes. This violation of the constant variance assumption means that some predictions may be more variable than others, thus affecting the accuracy and reliability of the model's predictive power. Understanding heteroskedasticity is essential because it impacts the interpretation of regression results, particularly the coefficients and the validity of statistical tests, which assume that residuals are equally dispersed regardless of the value of independent variables. Addressing heteroskedasticity often involves using weighted least squares or transforming the data to achieve homoskedasticity.