Error variance refers to the variability in a set of data that cannot be explained by the model being used. It represents the portion of the total variance that is attributable to factors other than the independent variables included in the model. In simpler terms, error variance reflects how much of the data’s variability is random and unaccounted for by the predictors.
To calculate error variance, you first need to understand the concept of total variance. Total variance is the overall spread of the data points around the mean. From this, you subtract the explained variance, which is the part of the variance that can be accounted for by the model or by the predictors. The formula can be written as:
Error Variance = Total Variance – Explained Variance
In practical terms, you can compute the error variance using the following steps:
- Collect your dataset and run the regression or analysis to find the predicted values.
- Calculate the residuals, which are the differences between the observed values and the predicted values.
- Square these residuals to eliminate any negative values.
- Sum up all the squared residuals.
- Finally, divide this sum by the number of observations minus the number of predictors (degrees of freedom) to get the error variance.
The resultant value gives you insight into how much of the variability in your data is due to random error rather than the model you’ve created.