title: [Locally adjusted linear regression and its possibilities for application].
abstract: A new numerical method is presented for a model free representation of the mean course in a series of measured data of an unknown functional connection. The usefulness of the method is demonstrated by some examples of different time series (chemical reaction kinetics, growth, damped oscillations of a physiological system, pharmacokinetics). The advantages of the new method compared with nonlinear regression or segmented linear regression are noted. For any argument within the interval of measurements, the local adjusted linear regression value may be calculated. In this way one get a continuous curve with a continuous 1st derivative, too. This local adjustment will be obtained by using a weight function which is from Gaussianlike type in our procedure. The calculated continuous approximation curve represents the mean course in the measured values and may serve for a further quantitative evaluation of the measured functional connection, for interpolative and smoothing purposes, or even for model construction and model proving procedures. The nonparametric estimation of a continuous (1 dimensional) distribution density function from realizations of a continuous random variable is another field of application of this method.
mesh_terms: D000818:Animals; D005260:Female; D005333:Fetus / Q000502:physiology; D006128:Growth; D006801:Humans; D008423:Maternal Age; D008433:Mathematics; D011247:Pregnancy; D012044:Regression Analysis
vernacular_title: Die lokal angepasste lineare Regression und ihre Anwendungsmöglichkeiten.