Methods of Correlation and Regression Analysis, Linear and Curvilinear

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

SECTION VI
Miscellaneous Special Regression Methods

CHAPTER 21
Measuring the relation between one variable and two or more others operating jointly

In working out the change in one variable with changes in other variables up to this point we have assumed that the relation of the dependent factor to each independent factor did not change, no matter what combination of other independent factors was present. In the case of the yield of corn, for example, as worked out in Chapter 14, we assumed that the effect of a given change in rainfall upon the yield was the same, no matter what was the temperature for the season. The significance of this assumption may be shown by combining the estimate for rainfall with the estimate for temperature, and plotting the combined influence of the two variables. In Table 14.19 we already have this combined influence worked out, so all we have to do is to plot it. Figure 21.1 shows the resulting figure. In this figure inches of rainfall are read along the right-hand edge of the bottom of the cube, degrees of temperature along the left-hand edge, and the yield along the vertical edge. The yield for any combination of temperature and rainfall is shown by the distance the upper surface of the solid figure is above the point of intersection of the corresponding values in the base plane.1

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1

The way this figure is made may be thought of as follows: Suppose we drew a series of charts of the estimated differences in yield with differences in rainfall, with one chart for an average temperature of 70°, one for 72°, one for 74°, etc. Then if we cut these charts off at the yield line, and arrange them one back of the other, at even distances, we have a figure looking much like Figure 21.1. The lines sloping

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