SECTION 10.2 Summary

• The estimated mean response for the subpopulation corresponding to the value of the explanatory variable is found by substituting in the equation of the least-squares regression line:

• The predicted value of the response for a single observation from the subpopulation corresponding to the value of the explanatory variable is found in exactly the same way:

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• Confidence intervals for the mean response when has the value have the form

• Prediction intervals for an individual response have a similar form with a larger standard error:

  In both cases, is the value for the density curve with area between and . Software often gives these intervals. The standard error for an individual response is larger than the standard error for a mean response because it must account for the variation of individual responses around their mean.