Single response regression method

Each single combination of the factors has been replicated twiee to evaluate the significance of the factor modification on every dependent variable. Furthermore, the factorial analysis of variance (ANOVA) and the response surfaee method (RSM) have been applied, and the first-order regression models linking the dependent variable to the two control factors have been found and analyzed with an ANOVA. 

Previously, we have considered only the analysis of single-response data. Here, we discuss multiresponse regression, focusing primarily upon the extension of the least-squares method to the case of multiple, perhaps correlated, responses in each experiment. 

Differences in calibration graph results were found in amount and amount interval estimations in the use of three common data sets of the chemical pesticide fenvalerate by the individual methods of three researchers. Differences in the methods included constant variance treatments by weighting or transforming response values. Linear single and multiple curve functions and cubic spline functions were used to fit the data. Amount differences were found between three hand plotted methods and between the hand plotted and three different statistical regression line methods. Significant differences in the calculated amount interval estimates were found with the cubic spline function due to its limited scope of inference. Smaller differences were produced by the use of local versus global variance estimators and a simple Bonferroni adjustment. 

Linear least squares regression is the most common method of fitting a response that is a function of a single independent variable. Many nonlinear functions may be transformed to simple linear functions, extending the capabilities of the simplest regression algorithm. 

Least squares regression is known as a univariate method. Univariate methods assume that there is a direct relationship between two sets of values that can be described by a single equation. In univariate methods, there is generally one independent variable (in this case, spectral response) and one dependent variable (concentration). By knowing either one of these values, a solution can be calculated for the other. 

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