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​ = β0​ + β1​ EDUCi​ + εi
where WAGEi​ is the hourly wage of person i (i.e., any specific person) and EDUCi​ is the number of years of education for that same person. The residual εi 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: WAGEi​ =−11.1+4.3EDUCi​
If the standard error of the estimate of β1​ is 1 , then the true value of β1 lies between ___ and ___. As the number of observations in a data set grows, you would expect this range to ___ in size.