Explained Sum of Squares Calculator Guide
Explained sum of squares shows how much variation a regression model explains. It compares fitted values with the average observed value. A larger value means the model captures more movement in the response data. It is commonly used in regression ANOVA tables.
Why This Measure Matters
Regression separates total variation into parts. One part is explained by the model. Another part remains unexplained as residual error. The explained sum of squares helps you see whether fitted values move away from the mean in a useful way. When it is high compared with total variation, the model has stronger explanatory power.
This calculator is designed for manual analysis, coursework, audit checks, and model review. You can paste observed values and fitted values. You can also enter optional weights. Weighted analysis is useful when observations have different importance, frequency, or reliability. The tool then calculates the weighted mean, explained variation, residual variation, total variation, fit ratios, and common regression statistics.
Interpreting the Output
The explained ratio equals explained sum of squares divided by total sum of squares. It shows the share of total variation represented by fitted values. The residual based R squared uses one minus residual sum of squares divided by total sum of squares. In ordinary least squares models with an intercept, both ratios are usually close. A large gap can signal rounded predictions, missing intercept behavior, weights, or nonstandard fitted values.
The calculator also reports mean square regression, mean square error, F statistic, adjusted R squared, and the balance gap. These values help compare model strength while considering sample size and predictor count. The F statistic is only shown when degrees of freedom are valid.
Good Data Practice
Use aligned rows. The first observed value must match the first fitted value. The same rule applies to weights. Remove labels, currency marks, and extra notes before pasting data. Decimals and negative values are allowed. Weights should be positive.
This result is a statistical summary, not proof of causation. A high explained sum of squares can still come from overfitting, clustered data, or leakage. Always review residual patterns, assumptions, and subject knowledge before using results for decisions. Pair these numbers with plots, diagnostics, and clear reporting notes for better interpretation overall.