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Regression with Several Predictors

There are many occasions when there are more than one cause behind a property, so that two or more predictors would be required to explain the phenomenon adequately. [Pg.174]

The simplest function with several predictors is a multi-linear function of the form [Pg.174]

The property can be dominated by only one predictor, while the other predictors provide minor corrections there are also times when several predictors have comparable influences. [Pg.174]

This is shown in figure 5.8. When we consider A f or /r as the single predictor, the regression results are [Pg.174]

if only one predictor is to be used, the number of chlorine atoms Nci is the best single predictor and the dipole moment is the worst single predictor. If we are not satisfied with a standard error (y — y ) of 33.4 °C, then we can escalate to [Pg.174]


Linear regression methods are convenient because they usually allow an interpretation, and methods like PLS or PCR avoid the problem of overfitting, especially if many parameters have to be estimated with only a few objects. However, the relation between a response variable and one or several predictor variables can in some situations be better described by nonlinear functions, like by the functional relation... [Pg.182]

Several studies assessed the evolution of CT over time (18,131,142). Pulmonary functional parameters improved only when GGO regressed on HRCT (18,131,142). Reticular or HC patterns reflect fibrosis and do not regress with treatment (18,131,142). Severe HC on CT is a strong predictor of mortality (>80% mortality within two years) (11,122,143). CT patterns typical of IPF/ UIP were associated with a higher mortality compared to atypical CT scans (114,144), suggesting that CT features typical of UIP likely reflect advanced disease. [Pg.345]

In recent years there has been much activity to devise methods for multivariate calibration that take non-linearities into account. Artificial neural networks (Chapter 44) are well suited for modelling non-linear behaviour and they have been applied with success in the field of multivariate calibration [47,48]. A drawback of neural net models is that interpretation and visualization of the model is difficult. Several non-linear variants of PCR and PLS regression have been proposed. Conceptually, the simplest approach towards introducing non-linearity in the regression model is to augment the set of predictor variables (jt, X2, ) with their respective squared terms (xf,. ..) and, optionally, their possible cross-product... [Pg.378]

In this paper the PLS method was introduced as a new tool in calculating statistical receptor models. It was compared with the two most popular methods currently applied to aerosol data Chemical Mass Balance Model and Target Transformation Factor Analysis. The characteristics of the PLS solution were discussed and its advantages over the other methods were pointed out. PLS is especially useful, when both the predictor and response variables are measured with noise and there is high correlation in both blocks. It has been proved in several other chemical applications, that its performance is equal to or better than multiple, stepwise, principal component and ridge regression. Our goal was to create a basis for its environmental chemical application. [Pg.295]

Classic univariate regression uses a single predictor, which is usually insufficient to model a property in complex samples. Multivariate regression takes into account several predictive variables simultaneously for increased accuracy. The purpose of a multivariate regression model is to extract relevant information from the available data. Observed data usually contains some noise and may also include irrelevant information. Noise can be considered as random data variation due to experimental error. It may also represent observed variation due to factors not initially included in the model. Further, the measured data may carry irrelevant information that has little or nothing to do with the attribute modeled. For instance, NIR absorbance... [Pg.399]

The data were analysed in several stages. Descriptive statistics and bivariate correlations were calculated for independent, dependent and control variables. Control variables with significant bivariate correlations with outcome as measured by the NBAS scales were used in forward stepwise multiple regression analyses to determine the best joint predictors of the NBAS. After the best multiple regression model was constructed from the non-lead variables, lead measurements recorded at the three time points were added to the model to determine the relationship between each of the lead measurements and the adjusted NBAS scores. The overall plan of analysis follows Bellinger et al (1984 this volume). Analyses were performed with SAS programs. [Pg.390]


See other pages where Regression with Several Predictors is mentioned: [Pg.153]    [Pg.174]    [Pg.153]    [Pg.174]    [Pg.66]    [Pg.472]    [Pg.142]    [Pg.333]    [Pg.191]    [Pg.775]    [Pg.67]    [Pg.384]    [Pg.1094]    [Pg.45]    [Pg.47]    [Pg.3]    [Pg.325]    [Pg.328]    [Pg.400]    [Pg.17]    [Pg.145]    [Pg.315]    [Pg.263]    [Pg.335]    [Pg.163]    [Pg.274]    [Pg.62]    [Pg.40]    [Pg.218]   


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