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:

WAGEi=0+1EDUCi+iWAGEi=0+1EDUCi+i

where WAGEiWAGEiis the hourly wage of person ii(i.e., any specific person) and EDUCiEDUCiis the number of years of education for that same person. The residual iiencompasses 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:

WAGEi=10.1+3.3EDUCiWAGEi=10.1+3.3EDUCi

If the standard error of the estimate of 11is 1.38, then the true value of 11lies between and . As the number of observations in a data set grows, you would expect this range to in size.