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Variance Ratio & Nested Regression F Statistic

Compute a two-variance ratio or the residual-sum-of-squares F statistic for restricted and unrestricted nested regression models.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Restricted and unrestricted residual sums of squares of 150 and 100, with two restrictions, 25 observations and five unrestricted coefficients, give F = 5.

Nested-model F = [(RSSrestricted − RSSfull)/J] / [RSSfull/(N − K)]; basic F = variance₁/variance₂

Worked example

Enter these known values and leave the other values blank.

Restricted-model residual sum of squares: 150
Unrestricted-model residual sum of squares: 100
Number of independent restrictions J: 2
Number of shared observations N: 25
Unrestricted fitted coefficient count K, including intercept: 5

F-statistic (F): 5

Assumptions and limitations

The models must be nested, use the same response and observations, and have the same error-scale definition. Restricted residual sum of squares cannot be below the unrestricted value.
N, K and J are positive whole counts, N must exceed K, and J cannot exceed K. Include an estimated intercept in the unrestricted coefficient count.
Equal residual sums of squares produce F = 0. A positive unrestricted residual sum of squares is required by this retained finite-denominator model.
The usual nested-model F inference assumes appropriate independent, homoscedastic errors. This calculator returns the statistic only, without a p-value, significance decision or robust covariance adjustment.

Common questions

Which sum of squares does SSR mean here?

Both inputs are residual sums of squares, also often called RSS or SSE. They are not the explained or regression sum of squares.

References

Bookify requires whole regression design counts and positive residual degrees of freedom, and accepts zero F when the nested models have equal residual sums of squares.

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