Multiple Linear Regression Analysis MLRA

One task of data analysis is to establish a model which quantitatively describes the relationships between data variables and can then be used for prediction. 

Linear regression models a linear relationship between two variables or vectors, x and y Thus, in two dimensions this relationship can be described by a straight line given by tJic equation y = ax + b, where a is the slope of tJie line and b is the intercept of the line on the y-axis. 

While simple linear regression uses only one independent variable for modeling, multiple linear regression uses more variables. 

Given n input variables, x , the variable y ( q. (2) is modeled analogously to the case with one input variable. 

should be uncorrclatcd. If they arc correlated, however, one way of finding a solution is stepwise MLR where only those x arc chosen for the model which arc not correlated with already used 

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Step S Building a Multiple Linear Regression Analysis (MLRA) Model... 

Also, one can utilize a group of descriptors. In the case of utilization of a group of descriptors the approach is well-known as multiple linear regression analysis (MLRA) ... 

Multiple linear regression analysis is a widely used method, in this case assuming that a linear relationship exists between solubility and the 18 input variables. The multilinear regression analy.si.s was performed by the SPSS program [30]. The training set was used to build a model, and the test set was used for the prediction of solubility. The MLRA model provided, for the training set, a correlation coefficient r = 0.92 and a standard deviation of, s = 0,78, and for the test set, r = 0.94 and s = 0.68. 

In many chemical studies, the measured properties of the system can be regarded as the linear sum of the fundamental effects or factors in that system. The most common example is multivariate calibration. In environmental studies, this approach, frequently called receptor modeling, was first applied in air quality studies. The aim of PCA with multiple linear regression analysis (PCA-MLRA), as of all bilinear models, is to solve the factor analysis problem stated below ... 

CNN = computational neural network MLRA = multiple linear regression analysis QSPR = quantitative structure-property relationships. 

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