The measure of standard error can also be applied to the parameter estimates resulting from linear regressions.

For example, consider the following linear regression equation that describes the relationship between education and wage:

WAGE

i

=

0

+

1

EDUC

i

+

i

WAGE

i

=

0

+

1

EDUC

i

+

i

whereWAGE

i

WAGE

i

is the hourly wage of personi

i

(i.e., any specific person) andEDUC

i

EDUC

i

is the number of years of education for that same person. The residual

i

i

encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero.

Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates:

WAGE

i

=11.5+6.4EDUC

i

WAGE

i

=

11.5

+

6.4

EDUC

i

If the standard error of the estimate of

1

1

is 1.19, then the true value of

1

1

lies between and . As the number of observations in a data set grows, you would expect this range to in size.