Coefficient of Determination Calculator
Reports the fraction of response variation accounted for by a fitted prediction relative to a mean-only baseline. The worked condition keeps the method and source values visible for an independent check.
Describe the observed data
Coefficient of determination
The model’s reference quantity before reporting
Recalculate one intermediate quantity from R² = 1 − SSE/SST and work back from the displayed answer. The source values should be sufficient for another analyst to reproduce coefficient of determination without guessing a convention.
Use a boundary case when possible: equal paired values, a probability near zero, a zero slope, or a rate of zero. The expected limiting behavior is often more informative than another decimal place. The chosen coefficient of determination convention remains attached to the source record. Before reusing coefficient of determination, write down the observed scale, the model boundary, and the convention behind the displayed value. A short record of that kind makes it possible to distinguish a changed dataset from a changed definition, and it gives the next analyst a clear route back to the original calculation.
Evidence beside the calculation under the stated model
The number answers one statistical question. It does not establish causation, model fit, representativeness, or a useful decision threshold by itself. The page-specific quantity is coefficient of determination.
Practical meaning depends on the measurement scale and consequences. State the comparison or benchmark before presenting coefficient of determination as evidence. Before reusing coefficient of determination, write down the observed scale, the model boundary, and the convention behind the displayed value. A short record of that kind makes it possible to distinguish a changed dataset from a changed definition, and it gives the next analyst a clear route back to the original calculation.
How to carry the result forward when the sample changes
R² can increase when predictors are added and does not establish causal adequacy or good out-of-sample performance. Outliers, dependence, sparse observations, extrapolation, or a mismatched parameterization can change the appropriate reference method. The page-specific quantity is coefficient of determination.
Choose an alternative because the design or data require it, not because its result is more favorable. Preserve the selected convention in the report. The chosen coefficient of determination convention remains attached to the source record.
Reading the inputs during an independent review
Save the entered values, units, formula version, exclusions, and unrounded output with coefficient of determination. A copied number without its data-generating condition is not reproducible.
Round after downstream calculations are complete. Extra digits cannot repair a biased sample, unstable fit, or unsupported distributional assumption. The chosen coefficient of determination convention remains attached to the source record.
For a related question, compare regression residual and adjusted r squared.
Interpreting the result at the chosen parameter values
Construct a second plausible scenario that changes one uncertain input while keeping the rest coherent. Compare the statistic and the practical interpretation across both cases. The page-specific quantity is coefficient of determination.
If a small defensible change reverses the conclusion, report the sensitivity rather than hiding it behind one preferred scenario. The chosen coefficient of determination convention remains attached to the source record.
A second look at the condition before comparing groups
Reports the fraction of response variation accounted for by a fitted prediction relative to a mean-only baseline. The displayed relationship is R² = 1 − SSE/SST, and each symbol is tied to a labeled field. The page-specific quantity is coefficient of determination.
SSE 72 against SST 240 gives R²=0.70. This example is a numerical check of the method, not proof that the model describes every dataset. The chosen coefficient of determination convention remains attached to the source record.
Before reporting this result
For a second scenario, how many digits should be reported?
Retain guard digits during checking, then round to the resolution supported by the source measurement. The reported quantity here is coefficient of determination.
Before comparing methods, does this result prove a causal relationship?
No. Statistical association or model arithmetic does not replace design, measurement, or substantive reasoning. The reported quantity here is coefficient of determination.
When the result is copied, what belongs in the saved record?
Preserve the source data or summaries, formula convention, units, exclusions, and method version. The reported quantity here is coefficient of determination.
Before interpreting the sign, what should be checked before reusing this result?
Keep the inputs, units, model name, exclusions, and unrounded output together. The reported quantity here is coefficient of determination.
Before reporting, why might another program return a different number?
Parameterization, tie rules, tail conventions, rounding, or distributional approximations can differ. The reported quantity here is coefficient of determination.
Under the stated model, when should the calculation be repeated?
Repeat it when an input, sample boundary, group definition, or model assumption changes. The reported quantity here is coefficient of determination.