ABSTRACT
The chapter discusses the effects of measurement errors of regressor variables on estimating parameters of linear and nonlinear regression equations. Three cases are considered: the measurement error is uncorrelated with the true value (the classical case), or it is uncorrelated with the measured value (the Berkson case), or it is correlated both with true value and the measured value. It is shown how the bias of estimated simple linear regression is dependent on the measurement errors. It is also discussed how measurement errors affect the distribution of the measured values. If measurement error is uncorrelated with the true value, the measured distribution is too wide. If the measurement error is uncorrelated with the measured value, the distribution is too narrow. The distribution of measurements is too narrow when a variable is ‘measured’ using an ordinary regression equation or k-nn regression. In the k-nn regression the goals of obtaining realistic distribution of measured values is in conflict with the goal of obtaining small mean square error.
