Regression methods, assumptions multiple

Multiple linear regression is strictly a parametric supervised learning technique. A parametric technique is one which assumes that the variables conform to some distribution (often the Gaussian distribution) the properties of the distribution are assumed in the underlying statistical method. A non-parametric technique does not rely upon the assumption of any particular distribution. A supervised learning method is one which uses information about the dependent variable to derive the model. An unsupervised learning method does not. Thus cluster analysis, principal components analysis and factor analysis are all examples of unsupervised learning techniques. 

Assumptions of a multiple regression analysis are identical to those for linear regression except for the p independent variables in this case. To reach regression coefficient estimates b by the method of least squares, we again have to minimize... 

Because the British group applied extensively their statistical method to determine causation of large interindividual pharmacokinetic variations without describing its strengths and weaknesses, others have attempted to assess critically the application of multiple regression analysis for this particular purpose (31,32) While this statistical method has great potential, it requires considerable modification beyond its initial applications in this area (27-29), if that potential is to be realized (H,32). Thus far, its applications in pharmacokinetics (27-29) have been disappointing because those who have employed it neither formulated nor addressed, much less demonstrated fulfillment of, several fundamental assumptions inherent in its use ( 1, 32). 

As an aside, the error rate in Eq. (1.32) assumes that the hypothesis tests are independent. Although this assumption has never been proven in the regression literature, model development using stepwise methods undoubtedly produces multiple hypothesis tests which are correlated, probably in relation to the degree of correlation between predictor variables used in a model. In the case where two statistical tests are correl-... 

The statistical methods most often employed for developing ADMET in silico structure-property relationships are linear multivariate methods, such as multiple linear regression (MLR) orpartial least squares (PLS). Although aimed at the same end point, namely, to derive a statistically sound and predictive structure-property relationship, the underlying assumptions regarding the information contained in the independent variables, that is, the chemical... 

Data Envelopment Analysis (DEA) is a nonparametric, deterministic performance analysis tool. DEA is a "data oriented" approach for evaluating the performance of a set of peer units called Decision Making Units (DMUs) which convert multiple inputs into multiple outputs (Cooper et al., 2000). DEA is among the highly preferred methods of performance or efficiency analysis basically due to a number of advantages over parametric methods. Unlike most other approaches like regression analysis that need a priori assumptions, DEA requires very few assumptions. It does not attempt to explain the nature of the relations between the multiple inputs and multiple outputs that belong to the analysis units. 

Regression analysis, both simple regression (meaning only one independent variable) and multiple regression (more than one independent variable), has been developed over many years, and many of its characteristics are known. In particular, the least-squares method is valid only when the following four fundamental assumptions hold ... 

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