Standard Error of the Estimate (2 of 3)

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The regression line seeks to minimize the sum of the squared errors of prediction. The square root of the average squared error of prediction is used as a measure of the accuracy of prediction. This measure is called the standard error of the estimate and is designated as σ_est. The formula for the standard error of the estimate is:



where N is the number of pairs of (X,Y) points. For this example, the sum of the squared errors of prediction (the numerator) is 70.77 and the number of pairs is 12. The standard error of the estimate is therefore equal to:



An alternate formula for the standard error of the estimate is:



where is σ_y is the population standard deviation of Y and ρ is the population correlation between X and Y. For this example,