Multiple linear regression equations

Scheme 7.1, relevant to an amphiprotonic solvent). Using Eq. (7.2), the multiple linear regression equation for the fluorescence maximum (expressed in 103 cm-1) is... 

Multiple linear regression equations were also developed for foam capacity and stability based on pH and the data on composition of soluble and insoluble fractions in the suspensions sumarized in Figures 2 and 4 (Tables V and VI). 

The least-squares solution of a multiple linear regression equation can be calculated in one step, so the number of iterations performed is not an important issue to consider when selecting descriptors. Therefore, simulated annealing is an appropriate choice for performing the optimization. 

To obtain a more convenient form, the mass of data was reduced to multiple linear regression equations to give the following relationships ... 

Bioassav Data Sets and Multiple Linear Regression Equations The expert system predicts the acute toxicity of a chemical to four representative aquatic organisms and reports toxicity as either EC50--is the effective concentration at which either 50% of the animals (Daphnia pul ex or D. magna) were immobilized or 50% of the luminescence (the Microtox test) was diminished--or LC50, the lethal concentration for 50% of the fish (fathead minnows) in the study. 

Table II. Expert System Multiple Linear Regression Equations...

However, it is not sufficient to identify a set of non-correlated, well-distributed parameters and then simply press the button and derive a multiple linear regression equation. To derive a QSAR equation properly requires a lot of care. Some of the descriptors may have little or no relevance to the property being modelled. Moreover, one generally wants to achieve a balance between an equation that captures the essence of the problem and yet is predictive. Fortunately, there are a number of procedures that can help with some of these problems. 

Table 8), when correlated with t and a, lead to the multiple linear regression equation,... 

Heats of Transfer of the Et4N l Ion Pair. The AG c terms from methanol into nonprotic solvents for the tetraethylammonium iodide ion pair (30), reported by Abraham (44b), were discussed earlier in connection with the tt and d parameters. When results in the 18 protic and nonprotic aliphatic solvents (1,2,7,11,16,18,25,28,29,32,50,101,102,103,104,105,111,112) are considered together, the effects of type-A hydrogen bonding by HBD solvents to iodide become evident. The multiple linear regression equation becomes. 

Allowing also a partial dependence on x, the multiple linear regression equation becomes,... 

During 35 recording days 1100 observations of concurrently measured parameters (Tc-Ta, PS, ET and Rad) were obtained. These data were pooled for all three treatments, and multiple linear regression equations were calculated ... 

Creation of a simple linear regression equation is obvious there are just two variables involved and all that is required is the estimation of the slope and intercept parameters, usually by OLS. The construction of multiple linear regression equations, on the other hand, is by no means as clear since the selection of independent variables for the equation involves choice. How can this choice be made One obvious strategy is to use all of the independent variables and this in fact is the basis of one technique for... 

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