![]() ![]() However, the particular method involves a convenient substitution of fixed mean parameter for random predictor variables. The presented formula has a computationally appealing expression and maintains reasonable accuracy in their simulation study. Accordingly, they require unique power procedures as discussed in Shieh and Tang, among others.įor the purposes of planning research designs and validating model formulation, a sample size procedure was presented in Colosimo et al. It is noteworthy that analysis of covariance (ANCOVA) models involving both categorical and continuous predictors incur different hypothesis testing procedures. On the other hand, Kelley, Krishnamoorthy and Xia, and Shieh discussed sample size determinations for constructing precise confidence intervals of strength of association. In the context of multiple regression and correlation, the distinct notions of fixed and random regression settings were emphasized and explicated in power and sample size calculations by Gatsonis and Sampson, Mendoza and Stafford, Sampson, and Shieh. The importance and implications of statistical power analysis in research studies are well addressed in Cohen, Kramer and Blasey, Murphy, Myros, and Wolach, and Ryan, among others. Thus, it is of considerable interest for related research to validate or compare the magnitudes of intercept and slope coefficients in their formulation. Note that the birth weights differ among ethic groups, cohort characteristics, and time periods. Also, Rose and McCallum proposed a simple regression formula for estimating the logarithm of feta weight with the sum of the ultrasound measurements of biparietal diameter, mean abdominal diameter, and femur length. 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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