Coefficient of Determination Calculator
Reports the fraction of response variation accounted for by a fitted prediction relative to a mean-only baseline. The form displays R² = 1 − SSE/SST beside coefficient of determination, using a worked condition that can be recalculated with the labeled inputs.
Describe the observed data
Coefficient of determination
Scope of the coefficient of determination method
The coefficient of determination page reports the fraction of response variation accounted for by a fitted prediction relative to a mean-only baseline.
Coefficient of determination is limited to the statistical quantity named by the result panel. The coefficient of determination calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Before entering the coefficient of determination data
- Total sum of squares: For coefficient of determination, the worked value for total sum of squares is 240 squared Y units. Treat the total sum of squares entry (240 squared Y units) explicitly as a count, proportion, rate, estimate, or model parameter before comparing coefficient of determination conditions. The form enforces minimum 1e-06.
- Residual sum of squares: For coefficient of determination, the worked value for residual sum of squares is 72 squared Y units. Treat the residual sum of squares entry (72 squared Y units) explicitly as a count, proportion, rate, estimate, or model parameter before comparing coefficient of determination conditions. The form enforces minimum 0.
The entries used for coefficient of determination must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid coefficient of determination arithmetic for a nonexistent study.
Following the coefficient of determination relationship
For coefficient of determination, match every symbol in the relationship to a labeled field before substituting numbers. Coefficient of determination is reported in ratio.
While checking coefficient of determination, inspect every denominator in R² = 1 − SSE/SST. For coefficient of determination, a zero or near-zero denominator can make coefficient of determination undefined or unstable.
Checking the displayed example
The default coefficient of determination condition is Total sum of squares = 240 squared Y units, Residual sum of squares = 72 squared Y units.
SSE 72 against SST 240 gives R²=0.70.
The live calculator reports R squared 0.7 · Explained variation 70 %. Repeating one intermediate step from R² = 1 − SSE/SST provides a fixed coefficient of determination reference check for later code changes.
Conditions attached to coefficient of determination
R² can increase when predictors are added and does not establish causal adequacy or good out-of-sample performance.
For coefficient of determination, a fitted coefficient or association is conditional on the model and observed range; it does not by itself show that changing one variable will cause another to change.
A nearby method may answer the next question: regression residual and adjusted r squared.
Reading coefficient of determination in context
When interpreting coefficient of determination, inspect residual behavior, influential observations, nonlinearity, dependence, and extrapolation before carrying a regression result to a new setting.
As a second check for coefficient of determination, reversing the numerator and denominator answers a different question, so retain the direction printed in R² = 1 − SSE/SST.
Input and rounding traps
Before accepting coefficient of determination, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For coefficient of determination, do not move a number between fields merely because the units look compatible; each label gives the number a different statistical role.
Another coefficient of determination failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on coefficient of determination, then round only the reported value.
Documenting the coefficient of determination result
Report coefficient of determination using R² = 1 − SSE/SST, followed by the entered values, units, exclusions, and analysis date. Name the coefficient of determination population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including R squared 0.7 · Explained variation 70 %. A later coefficient of determination review can then distinguish a changed input from a different convention or software implementation.
Questions about coefficient of determination
Does coefficient of determination establish a causal or population conclusion?
No. The displayed coefficient of determination value is conditional on the entered data and named method. The coefficient of determination design, measurement process, and assumptions determine what can be concluded beyond those values.
How should coefficient of determination be rounded?
Keep the unrounded coefficient of determination for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in coefficient of determination do not correct sampling or model error.
Which input deserves the closest boundary check?
For coefficient of determination, start with residual sum of squares and then total sum of squares. Confirm the coefficient of determination units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.
Why could another program report a different coefficient of determination?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change coefficient of determination. Compare the printed coefficient of determination formula and its input definitions before treating either output as wrong.