Methods of Correlation and Regression Analysis, Linear and Curvilinear

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

CHAPTER II
Determining multiple regressions: (2) by fitting a linear regression equation

In equation (E) in Chapter 10 it was shown that an equation could be arrived at to express the average relation between income, acres, and cows, as follows:

Income = 439.74 + 1.33 × number of acres + 27.88 × number of cows

If we designate the three series of variable quantities, income, acres, and cows, by the symbol X with different subscripts, using X1 to represent dollars of income, X2 to represent number of acres, and X3 to represent the number of cows, we can rewrite the equation in the form

X1 = 439.74 + 1.33X2 + 27.88X3

If now we use the symbol a to represent the constant quantity 439.74; b2 to represent 1.33, the amount which X1 increases for each increase of one unit in X2 (one acre); and b3 to represent 27.88, the amount which X1 increases for each increase of one unit in X3 (one cow); the equation appears as

X1 = a + b2X2 + b3X3 (11.1)

Comparing this equation with the regression equation for the straight- line relation between two variables

Y= a + bX

we see that the two equations are just alike, except for the difference in the symbols used to represent the different variables and for our having added the expression for an additional variable. In equation (11.1), X1,

-170-

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