![]() The results were tested, both individually and simultaneously, whether the intercept was different from zero and the slope was different form unity. compared left ventricular myocardial weights of dogs by nuclear magnetic resonance imaging with actual measurements for different methods using simple linear regression analysis. It is of practical importance to conduct a joint test of intercept and slope coefficients in order to verify the compatibility with established or theoretical formulations. However, the quality of estimation and prediction in associating the response variable with the predictor variables is determined by the closely intertwined intercept and slope coefficients. In linear regression, the focus is often concerned with the existence and magnitude of the slope coefficients. The present article focuses on the validation process of linear regression analysis for comparison with postulated or acclaimed models. and Montgomery, Peck, and Vining and the references therein. Further details and related issues can be found in the importance texts of Kutner et al. Essentially, the fundamental utilities between model selection and model validation should be properly recognized and distinguished because a refined model that fits the data does not necessarily guarantee prediction accuracy. (, Section 9.6), Montgomery, Peck, and Vining (, Section 11.2), and Snee that there are three approaches to assessing the validity of regression models: (1) comparison of model predictions and coefficients with physical theory, prior experience, theoretical models, and other simulation results (2) collection of new data to check model predictions and (3) data splitting in which reservation of a portion of the available data is used to obtain an independent measure of the model prediction accuracy. In particular, it is emphasized in Kutner et al. Alternatively, model validation refers to the plausibility and generalizability of the regression function in terms of the stability and suitability of the regression coefficients. In the process of model selection, residual analysis and diagnostic checking are employed to identify influential observations, leverage, outliers, multicollinearity, and other lack of fit problems. Among the methodological issues and statistical implications of regression analysis, model adequacy and validity represent two vital aspects for justifying the usefulness of the underlying regression model. , and Montgomery, Peck, and Vining, among others. General guidelines and fundamental principles on regression analysis have been well documented in the standard texts of Cohen et al. ![]() The extensive utility incurs continuous investigations to give various interpretations, extensions, and computing algorithms for the development and formulation of empirical models. Regression analysis is the most commonly applied statistical method of all scientific fields.
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