Calibration is a critical issue in various industries, with many methods and models used to address it. Most models focus on simple linear calibration, commonly applied in chemical applications, such as calibrating pH meters, NIR instruments, and establishing calibration graphs in chromatography. Early work by Shukla (1972) highlighted the statistical dimensions of calibration, while Schwartz (1978) noted that non-linear models often lead to linear approximations. Kitsos and Muller (1995) emphasized that even with linear approximations, a nonlinear function must be estimated. When measurement variance arises from multiple sources, different techniques are used. Osborn (1991) reviewed statistical calibration, while Kitsos and Muller (1995) discussed robust approaches. Hochberg and Marom (1983) suggested statistical quality control methods, though not applicable in all cases. For multivariate calibration, references include Brown (1993), Brereton (2000), and Oman and Wax (1984). Cross-validation (Clark 1980) is also used in calibration development. The paper introduces a statistical problem and discusses optimal design approaches. A simple regression model is considered, where the goal is to estimate u₁ = u₀ given n = C. Two estimators, the classical predictor and inverse predictor, are compared based on sample size and error variance. The classical predictor is a maximum likelihood estimator under normality assumptions, while the inverse predictor is inconsistent. Confidence intervals for the inverse predictor can be problematic, as they may cover the entire real line. The optimal design approach is adopted to address these issues, with D-optimality for estimating (θ₀, θ₁) and c-optimality for estimating u₀. Bayesian and structural inference approaches are also discussed, with Bayesian methods showing that the inverse predictor coincides with the Bayesian estimator when k = 1. The paper concludes that calibration is often based on linear approximations of nonlinear models.Calibration is a critical issue in various industries, with many methods and models used to address it. Most models focus on simple linear calibration, commonly applied in chemical applications, such as calibrating pH meters, NIR instruments, and establishing calibration graphs in chromatography. Early work by Shukla (1972) highlighted the statistical dimensions of calibration, while Schwartz (1978) noted that non-linear models often lead to linear approximations. Kitsos and Muller (1995) emphasized that even with linear approximations, a nonlinear function must be estimated. When measurement variance arises from multiple sources, different techniques are used. Osborn (1991) reviewed statistical calibration, while Kitsos and Muller (1995) discussed robust approaches. Hochberg and Marom (1983) suggested statistical quality control methods, though not applicable in all cases. For multivariate calibration, references include Brown (1993), Brereton (2000), and Oman and Wax (1984). Cross-validation (Clark 1980) is also used in calibration development. The paper introduces a statistical problem and discusses optimal design approaches. A simple regression model is considered, where the goal is to estimate u₁ = u₀ given n = C. Two estimators, the classical predictor and inverse predictor, are compared based on sample size and error variance. The classical predictor is a maximum likelihood estimator under normality assumptions, while the inverse predictor is inconsistent. Confidence intervals for the inverse predictor can be problematic, as they may cover the entire real line. The optimal design approach is adopted to address these issues, with D-optimality for estimating (θ₀, θ₁) and c-optimality for estimating u₀. Bayesian and structural inference approaches are also discussed, with Bayesian methods showing that the inverse predictor coincides with the Bayesian estimator when k = 1. The paper concludes that calibration is often based on linear approximations of nonlinear models.