**Residual Variance** (also called *unexplained variance* or *error variance*) is the variance of any error (residual).

The *exact* definition depends on **what type of analysis you’re performing**. For example, in regression analysis, random fluctuations cause variation around the “true” regression line (Rethemeyer, n.d.). The total variance of a regression line is made up of two parts: explained variance and *unexplained* variance. The unexplained variance is simply what’s left over when you subtract the variance due to regression from the total variance of the dependent variable (Neal & Cardon, 2013).

In

**multilevel modeling**, residual variance is a reflection of the within-groups effect (Garson, 2019). Large residual variance coefficients indicate large differences within-groups (Xie, 2009). In ANOVA, Within-group variation is synonymous with residual variance.

## Symbol for Residual Variance

The symbols σ or σ^{2} are often used to denote unexplained variance. Make sure you know the author’s intent before trying to interpret residual variance: σ may also mean standard deviation, sample standard deviation or standard error of coefficient estimates (Rethemeyer, n.d.).

## Coefficient of Nondetermination

Residual variance, 1 – r^{2} is sometimes called the **coefficient of nondetermination**. The coefficient of determination, R^{2}, shows how differences in one variable can be explained by a difference in a second variable. Therefore, 100% of a dependent variable’s variance can be explained by r^{2} plus the “unknown”: the unexplained variance (Meyers et al., 2006).

## References

Garson, D. (2019). Multilevel Modeling: Applications in STATA®, IBM® SPSS®, SAS®, R, & HLM™. 1st Edition. SAGE.

Meyers, L. et al. (2006). Applied Multivariate Research: Design & Interpretation.

Neale, M. & Cardon, L. (2003). Methodology for Genetic Studies of Twins and Families (Nato Science Series D). Springer.

Rethemeyer, K. Commonly Used Terms, Symbols, and Expressions. Retrieved April 27, 2019 from: https://www.albany.edu/faculty/kretheme/PAD705/SupportMat/CourseTerms.pdf

Xie, Y. (2009). Sociological Methodology Volume 39: 1st Edition. Wiley-Blackwell.

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