The estimated mean response for the subpopulation corresponding to the value x* of the explanatory variable is found by substituting x=x* in the equation of the least-squares regression line:
estimated mean response =ˆy=b0+b1x*
The predicted value of the response y for a single observation from the subpopulation corresponding to the value x* of the explanatory variable is found in exactly the same way:
predicted individual response =ˆy=b0+b1x*
Confidence intervals for the mean response μy when x has the value x* have the form
ˆy±t*SEˆμ
Prediction intervals for an individual response y have a similar form with a larger standard error:
ˆy±t*SEˆy
In both cases, t* is the value for the t(n−2) density curve with area C between −t* and t*. Software often gives these intervals. The standard error SEˆy for an individual response is larger than the standard error SEˆμ for a mean response because it must account for the variation of individual responses around their mean.