Evaluation of Correlation Coefficients Obtained with a Stepwise Regression Analysis

The least-squares linear regression analysis is a valuable method of analyzing experimental data where there is no established theoretical relation between the variables being studied. The extent to which the variation of one variable can be predicted by another quantity that can be more readily measured is expressed by the correlation coefficient. The standard error of estimate indicates the precision of the prediction. In general, no single number will adequately indicate the quality of a relationship. This fact places a responsibility on the investigator to exercise sound judgment in evaluating the regression equation. Two methods of evaluation that are generally effective in identifying problems in the relationship are (1) to plot the results in a two-dimensional graph, and (2) to repeat the experiment. A nonlinear relationship was well as nonrandomness in the errors can be identified when the data are plotted. Repeated experiments can aid in the identification of variables that may influence the relationship, as well as inaccuracies, and can explain one's inability to extrapolate beyond the immediate data set.