Least Squares Regression
Zekeri̇ya Altaç · 2024
This chapter starts out by presenting the least-squares regression of univariate discrete data to polynomials. Determining the best fit model or curve, as well as the concepts of goodness of fit, overfitting, correlation coefficient (r-squared and adjusted r-squared), root-mean-square error, standard deviation, sum of the squares of the mean deviation, sum of the squares of residuals, residual plots, and predicted-observed data (PO) plots, are presented. Transforming variables to improve the linear model is discussed in detail. The linearization procedure for common nonlinear (power, exponential growth or decay, saturated growth or saturated decay) models is introduced. The theory and applications of multivariate linear and non-linear regressions are examined. The least-squares fit under the integral sign, and the solution of overdetermined and underdetermined systems of equations via the least-squares minimization technique is introduced. All numerical algorithms are presented as self-contained pseudo-modules that can be converted and used in any program. The examples and end-of-chapter exercise problems have been selected from various science and engineering disciplines.