Univariate linear regression model

Aside from univariate linear regression models, inverse MLR models are probably the simplest types of models to construct for a process analytical application. Simplicity is of very high value in PAC, where ease of automation and long-term reliability are critical. Another advantage of MLR models is that they are rather easy to communicate to the customers of the process analytical technology, since each individual X-variable used in the equation refers to a single wavelength (in the case of NIR) that can often be related to a specific chemical or physical property of the process sample. 

It is well known that the accuracy of CE determinations using univariate calibration models, such as linear regression, relies on the selectivity of the electrophoretic data. Peaks of analytes must be baseline resolved and the occurrence of comigrations and minor impurities should be avoided. Note that peak contaminations lead to wrong integrations, and, consequently, the concentrations estimated from these data may be unreliable. 

Ayyalasomayajula et employed LIBS for the analysis of slurry samples. Three calibration models were developed using univariate calibration, multiple linear regression (MLR) and PLS. The LIBS analytical results obtained from the PLS model best fit the results obtained from inductively coupled plasma optical emission spectroscopy (ICP-OES) analysis. 

Traditionally, the determination of a difference in costs between groups has been made using the Student s r-test or analysis of variance (ANOVA) (univariate analysis) and ordinary least-squares regression (multivariable analysis). The recent proposal of the generalized linear model promises to improve the predictive power of multivariable analyses. 

The model for a multivariate regression spline is based on linear combinations of univariate spUne functions of the general form [10]... 

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