Standard Error of the Estimate (3 of 3)
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One typically does not know the population parameters and therefore has to estimate from a sample. The symbol sest is used for the estimate of σest. The relevant formulas are:
and
where r is the sample correlation and Sy is the sample standard deviation of Y. (Note that Sy has a capital rather than a small "S" so it is computed with N in the denominator). The similarity between the standard error of the estimate and the standard deviation should be noted: The standard deviation is the square root of the average squared deviation from the mean; the standard error of the estimate is the square root of the average squared deviation from the regression line. Both statistics are measures of unexplained variation.
Next section: Partitioning the sums of squares