Methods of Correlation and Regression Analysis, Linear and Curvilinear

By Mordecai Ezekiel; Karl A. Fox | Go to book overview

CHAPTER 16
Short-cut graphic method of determining net regression lines and curves

In problems where the correlation is fairly high, the number of variables is not too large, and the number of observations is not over 50 to 100 cases, net regression lines and curves may be determined by a combination of inspection and graphic approximation which takes only a fraction of the time required by the methods previously presented in detail. This graphic method is very speedy, and in the hands of a careful worker can yield results almost as accurate as those obtained by the longer methods previously set forth. The short-cut method was invented by Louis H. Bean.1

The general basis of the short-cut method is to select, by inspection, several individual observations for which the values of one or more independent variables are constant, and then note the changes in the dependent variable for given changes in the remaining independent variable. This process is repeated for additional groups of observations for which the other independent variable or variables are constant (or practically so) but at a different level than for the first group. The relation between the dependent variable and the remaining independent variable, as indicated by a series of such groups, approaches the net regression line or curve, since the cases have been selected so as largely to eliminate the variation associated with other independent variables. A first approximation line or curve is then drawn in by eye, and the residuals from this curve, measured graphically, are used to determine the regression for the next variable, cases again being selected so as to eliminate the influence of other independent variables. The final fit of the several lines or curves is tested by the same successive approximation process employed in

____________________
1
L. H. Bean, "A simplified method of graphic curvilinear correlation", Journal of the American Statistical Association, Vol. XXIV, pp. 386-397, December, 1929.

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