Multiple regression, backward

Mapping displays 23 Matrix, confusion, 127 determinant, 212 dispersion, 82 identity, 206 inverse, 210 quadratic form, 212 singular, 211 square, 204 symmetric, 204 Matrix multiplication, 207 Mean centring, 17 Mean value, 2 Membership function, 117 Minkowski metrics, 99 Moving average, 36 Multiple correlation, 183 Multiple regression, backward elimination, 182... 

The plasma concentrations of clozapine and its metabolite norclozapine (N-desmethylclozapine) have been measured in samples from 3775 patients (2648 men, 1127 women) (308). Step-wise backward multiple regression analysis (37% of the total sample) of log plasma clozapine concentration against log clozapine dose (mg/day), age (years), sex (male = 0, female = 1), cigarette smoking (non-smokers = 0, smokers = 1), body weight (kg), and plasma clozapine/norclozapine ratio (MR) showed that these co-variates explained 48% of the observed variation... 

Table 4.1. models (using backwards elimination stepwise multiple regression) for the study lakes based on suites of parameters. The global indices based on annual and seasonal data, with and without lags (1 and 2-year) and deposition provided the best models. Local and regional-scale climate parameters (e.g., precipitation, temperature, etc.) did not provide significant models... 

The same backward multiple-regression analysis was used as in the initial study except that initial PbB level was used as the independent variable,... 

Alternatively, instead of using the EBE of the parameter of interest as the dependent variable, an estimate of the random effect (t ) can be used as the dependent variable, similar to how partial residuals are used in stepwise linear regression. Early population pharmacokinetic methodology advocated multiple linear regression using either forward, backwards, or stepwise models. A modification of this is to use multiple simple linear models, one for each covariate. For categorical covariates, analysis of variance is used instead. If the p-value for the omnibus F-test or p-value for the T-test is less than some cut-off value, usually 0.05, the covariate is moved forward for further examination. Many reports in the literature use this approach. 

Forward or backward elimination (as used in multiple linear regression)... 

Linear models were generated using multiple linear regression analysis techniques. Several methods were utilized to develop models for evaluation, including stepwise addition, backward elimination, and leaps and bounds regression techniques. The models were evaluated with respect to the multiple correlation coefficient (r), the standard error (s), and predictive ability of the model. 

Backward elimination is a variable selection algorithm for multiple linear regression it starts with all variables in the model and eliminates all nonsignificant variables see forward selection as well. 

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