Standard error of slope
When b1 is used as an estimate of β1, the estimation error has a normal distribution,
error in estimate of β1 = (b1 − β1) ~ normal ( 0, σb1 )
This standard deviation is the standard error of the estimate,
where sx is the standard deviation of X. Since σ is unknown, we must replace it with an estimate from the data to obtain a numerical value for the standard error,
Example
The estimated error distribution gives in indication of how close our least squares estimate, b1 = 0.468, is likely to be to the population regression slope, β1.