Multiple Regression Calculator

This calculator evaluates a regression model's fit from four summary numbers — Regression Sum of Squares (SSR), Error Sum of Squares (SSE), Number of Predictors (k), and Sample Size (n) — rather than raw data, computing R-Squared = SSR / (SSR + SSE) (line 12) and an F-statistic built from Mean Square Regression (SSR / k) and Mean Square Error (SSE / degrees of freedom, lines 22-23). SSR and SSE move R-Squared in opposite, closely matched directions at the calculator's defaults, with neither one clearly dominating the other. Number of Predictors genuinely appears in several formulas here — Mean Square Regression divides by it directly, and the AIC approximation adds 2×(k+1) to its result — but because the field only accepts whole numbers, a ±10% nudge from its default of 3 rounds right back down to 3, so this calculator's own automated sensitivity check reads it as having zero effect everywhere it's actually used.

SSR, by contrast, is genuinely and verifiably absent from Mean Square Error, the AIC approximation, and RMSE — those three formulas only read SSE, Number of Predictors, and Sample Size. P-Value sits pinned at exactly 0 across every input at the calculator's defaults, not because none of the four inputs matter to it, but because the underlying F-statistic (46.0 at the defaults) is large enough that the chi-square approximation's z-score exceeds 6, which the calculator's normal-CDF helper hard-clamps to exactly 1 (giving P-Value = 1 − 1 = 0) — a saturation of the approximation, not a true zero derivative. This calculator does not use the standard F-distribution to compute an exact p-value; it approximates one with a Wilson-Hilferty-style cube-root transform against the normal distribution, which loses accuracy for small or unusual degrees-of-freedom combinations.