regress argument See EPISTEMIC REGRESS ARGU -. MENT , INFINITE REGRESS ARGUMEN. regression analysis, a part of statistical theory concerned with the analysis of data with the aim of inferring a linear functional relationship between assumed independent (‘regressor’) variables and a dependent (‘response’) variable. A typical example involves the dependence of crop yield on the application of fertilizer. For the most part, higher amounts of fertilizer are associated with higher yields. But typically, if crop yield is plotted vertically on a graph with the horizontal axis representing amount of fertilizer applied, the resulting points will not fall in a straight line. This can be due either to random (‘stochastic’) fluctuations (involving measurement errors, irreproducible conditions, or physical indeterminism) or to failure to take into account other relevant independent variables (such as amount of rainfall). In any case, from any resulting ‘scatter diagram,’ it is possible mathematically to infer a ‘best-fitting’ line. One method is, roughly, to find the line that minimizes the average absolute distance between a line and the data points collected. More commonly, the average of the squares of these distances is minimized (this is the ‘least squares’ method). If more than one independent variable is suspected, the theory of multiple regression, which takes into account multiple regressors, can be applied: this can help to minimize an ‘error term’ involved in regression. Computers must be used for the complex computations typically encountered. Care must be taken in connection with the possibility that a lawlike, causal dependence is not really linear (even approximately) over all ranges of the regressor variables (e.g., in certain ranges of amounts of application, more fertilizer is good for a plant, but too much is bad). See also CURVE- FITTING PROBLE. E.Ee.