This material is compiled for the course Empirical Modelling. Sections marked with a star (∗) are not central in the courses. The main source of inspiration when writing this text has been Chapter 4 in the book ”System Identification” by Söderström and Stoica (Prentice Hall, 1989) which also may be consulted for a more thorough treatment of the material presented here. The book is available for...

Probablistic Model: We start with the assumption that prior to starting a sequence of experiments we have a family of random variables with means that vary linearly with respect to some deterministic independent variable. That is, there exist an intercept β0 and a slope β1 such that for each value of the independent variable x, we have a random variable Y with mean β0 + β1x. We are then given p...

Article history: Received 26 September 2014 Accepted 6 February 2015 Available online 28 February 2015

Dual frame surveys, in which independent samples are selected from two frames to decrease survey costs or to improve coverage, can present challenges for regression coefficient estimation because of complex designs and unknown degree of overlap. In this research, we developed four regression coefficient estimators in dual frame surveys. Simulation results show that all the proposed methods work...

fuzzy linear regression models are used to obtain an appropriate linear relation between a dependent variable and several independent variables in a fuzzy environment. several methods for evaluating fuzzy coefficients in linear regression models have been proposed. the first attempts at estimating the parameters of a fuzzy regression model used mathematical programming methods. in this the...

In this paper, we consider the coefficient-based regularized least-squares regression problem with the lq-regularizer (1 ≤ q ≤ 2) and data dependent hypothesis spaces. Algorithms in data dependent hypothesis spaces perform well with the property of flexibility. We conduct a unified error analysis by a stepping stone technique. An empirical covering number technique is also employed in our study...

Linear regression analysis and calculation of the correlation coefficient are usually used to compare the results of two methods of measurement of the same substance. The limitations of these procedures are illustrated with numerical examples, in which X (the independent variable contains random errors of measurement. Formulas are given for estimating a linear functional relationship in this ca...

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, s...

many other biomedical journals dealing with cancer research, often publishes papers whose principal aim it is to test the association between quantative measurements of biological variables. When these are expressed on continuous scales, the statistics most frequently adopted to test their association are the Bravais-Pearson (parametric) and the Spearman (non-parametric) correlation coefficient...