Note 1 to entry: The probability that the true value of the physical or chemical quantity will be within ± the “final expanded uncertainty” from the determined and bias-corrected value is “exactly” or “approximately” 95 %; in most cases, “approximately” is more suitable expression.

Note 1 to entry: Another data point is additionally produced by measuring “a new reference solution”.

Note 1 to entry: The n data points are typically obtained by measuring n different reference solutions. After the fitting, the fitted regression line is used as a measurement formula for determining the physical or chemical quantity of a sample.

Note 1 to entry: In this case, the fitted regression line will be different each time, i.e. the slope and intercept of the fitted regression line will vary.

Note 1 to entry: The predicted y value given by the regression line formula y = a + bx indicates the physical or chemical quantity that will be determined in response to the light or current signal intensity “x” measured by instrument. The square root of the estimate for the variance of the predicted y value is treated as the calibration uncertainty in this document.

Note 1 to entry: This uncertainty is typically estimated based on multiple measurements of the sample and should not be inferred from the mean squared error.

Note 1 to entry: OLS (ordinary least squares) regression handles the uniform variances. However, in WLS regression, the variances are assumed to be non-uniform and the weighting factors are used to handle the non-uniform variances.

Note 2 to entry: Let σ_x1²,…, σ_xn² be the variances of the variables x₁,…, x_n respectively. Then, in OLS regression, σ_x1² = ∙∙∙ = σ_xn² (= σ_x²), whereas, in WLS regression, typically σ_x1² ≠∙∙∙≠ σ_xn². However, even in the case of WLS regression, the equality w₁σ_x1² = ∙∙∙ = w_nσ_xn² (= σ_x²) can be established by utilizing the weighting factors w_i’s (i = 1,…, n).