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A new approach for predicting a wide range of physical and thermodynamic properties is proposed. It involves calculation of the molecular descriptors of a target

Data transformation for obtaining the most accurate and statistically valid correlation is discussed. It is shown that the degree of a polynomial used in regression is limited by collinearity among the monomials. The significance of collinearity can best be measured by the truncation to natural error ratio. The truncation error is the error in representing the highest power term by a lower degree polynomial, and the natural error is due to the limited precision of the experimental data. Several transformations for reducing collinearity are introduced. The use of orthogonal polynomials provides an estimation of the truncation to natural error ratio on the basis of range and precision of the independent variable data. Consequently, the highest degree of polynomial adequate for a particular set of data can be predicted. It is shown that the transformation which yields values of the independent variable in the range of [-1,1] is the most effective in reducing collinearity and allows fitting the highest degree polynomial to data. In an example presented, the use of this transformation enables an increase in the degree of the statistically valid polynomial, thus yielding a much more accurate and well-behaved correlation.

Regression of the experimental data of one independent variable, y us. a linear combination of functions of an independent variable of the form y

SUMMARYThe numerical solution of n non-linear algebraic equations with n unknowns, when any or all of the variables are subjected to constraints, is discussed. Distinction is made between physical and absolute constraints. It is shown, using a set of test problems, that solution of constrained equations does require a special approach. It is found that the step length restricted Newton's method performs best for problems with absolute constraints. Physical constraints can be best handled using a continuation method or penalty functions.