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.