Your δx and δy values set how much each point counts in the fit. This choice changes parameter uncertainties, not the fitted parameters. It also changes uncertainty bands and Evaluate uncertainties; weights, residuals and χ² are unchanged.

A percentage (Rule, for example 5%) makes δy proportional to y, which weights points like “1/y²” in other software. A constant δy weights all points equally.

Absolute treats your values as true 1σ measurement errors, such as calibrated instrument specifications. Parameter uncertainties follow from them directly, so scatter beyond those errors does not enlarge them. A χ²_red well above 1 then suggests missing error sources or an unsuitable model.

Nominal (the default, and curve.fit’s original behavior) trusts only their relative sizes, as when the overall error scale is unknown, and estimates the overall scale from the residual scatter, multiplying parameter uncertainties by . This assumes the model is correct. When χ²_red ≈ 1, both agree.

SciPy (curve_fit, ODR), lmfit, Origin and Mathematica scale like Nominal by default; IGOR Pro and Astropy treat supplied uncertainties as Absolute. Absolute needs Table or Rule uncertainties. More in Help.

Guess is where the fit starts; leave it blank and curve.fit chooses one. Fix holds a parameter at its guess. Limit opens lower and upper limits; its box is checked while limits are set, and fixing a parameter ignores them.

Fitted is each best-fit value and δ its uncertainty. 1σ shows the standard uncertainty. 95% multiplies it by Student’s t for the fit’s ν degrees of freedom under Nominal, or by 1.96 under Absolute; the note below the table gives the factor.

The plot’s band, PDF, Browser Report, Excel and CSV follow the 1σ | 95% choice. It never refits or changes the saved fit, and Evaluate always reports 1σ.

AT LIMIT marks a parameter that finished on a limit; it is held there and its uncertainty is unavailable (n/a). n/a alone means the data cannot determine that parameter separately. More in Help.

Evaluate the fitted model at values you choose. x → y computes y and δy from x and δx. y → x finds every x in the fitted range that gives y, with its δx.

δx and δy are 1σ standard uncertainties, and a blank one counts as 0. Results combine the fit’s parameter uncertainties with the δ you enter; they do not include new measurement scatter.

☰ evaluates up to 100 values in the chosen direction: type or paste a column, with uncertainties in a second column, then download the results as CSV. More in Help.