Parametric models play an important role in broad areas of science and technology. This paper presents a novel framework for parametric model fitting. The actual fitting step is just one component of the algorithm which also collects model inliers, detects model outliers and determines the a~priori unknown total number of meaningful models in the data. We achieve this with a quasi simultaneous application of a general Least Squares fitting which processes the input data together with its associated precision. An extracted model consists of the optimal parameter estimates and a set of data points which are classified as model inliers. The rigorous error propagation allows us to complement each model parameter with an appropriate precision. The precision of the input data and the geometric arrangement are both used to estimate these values. In addition to the input data and its precision, only one parameter has to be specified: The confidence level on which the various statistical tests for data and model classification are carried out. We demonstrate our algorithm by fitting straight lines in 2D and planes in 3D with applications to problems of Computer Vision and Pattern Recognition. Synthetic data is used to show the robustness and accuracy of the algorithm. Image data and range data are used to prove the applicability and relevance of the scheme for real-world problems, e.g., in the domain of image feature extraction.