Encyclopedia of Sociology

CORRELATION AND REGRESSION ANALYSIS

Education

(years of school completed)

*

=the mean income for each education level

012 345 67 891011 12 13 14 15 16

Annual Income in Thousands of Dollars

Figure 1. Hypothetical Regression of Income on Education

Equation 1 is commonly written in a slightly
different form:

Y = ayx + byxX (^2 )

where Ŷ = the regression prediction for Y for a
given value of X, and ayx and byx are as defined
above, with Ŷ substituted for
|X.

Equations 1 and 2 are theoretically equivalent.

Equation 1 highlights the fact that the points on

the regression line are assumed to represent con-

ditional means (i.e., the mean Y for a given X).

Equation 2 highlights the fact that points on the

regression line are not ordinarily found by com-

puting a series of conditional means, but are found

by alternative computational procedures.