Computing Standard Error Of Estimate
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the estimate from a scatter plot Compute the standard error of the estimate based on errors of prediction Compute the standard error using Pearson's correlation Estimate the standard error of the estimate based on a sample
Standard Error Of Estimate In Regression
Figure 1 shows two regression examples. You can see that in Graph A, the the standard error of the estimate (for the regression) measures points are closer to the line than they are in Graph B. Therefore, the predictions in Graph A are more regression analysis standard error of estimate accurate than in Graph B. Figure 1. Regressions differing in accuracy of prediction. The standard error of the estimate is a measure of the accuracy of predictions. Recall that the regression line is the
Standard Error Of An Estimate Formula
line that minimizes the sum of squared deviations of prediction (also called the sum of squares error). The standard error of the estimate is closely related to this quantity and is defined below: where σest is the standard error of the estimate, Y is an actual score, Y' is a predicted score, and N is the number of pairs of scores. The numerator is the sum of squared
Standard Error In Regression
differences between the actual scores and the predicted scores. Note the similarity of the formula for σest to the formula for σ.  It turns out that σest is the standard deviation of the errors of prediction (each Y - Y' is an error of prediction). Assume the data in Table 1 are the data from a population of five X, Y pairs. Table 1. Example data. X Y Y' Y-Y' (Y-Y')2 1.00 1.00 1.210 -0.210 0.044 2.00 2.00 1.635 0.365 0.133 3.00 1.30 2.060 -0.760 0.578 4.00 3.75 2.485 1.265 1.600 5.00 2.25 2.910 -0.660 0.436 Sum 15.00 10.30 10.30 0.000 2.791 The last column shows that the sum of the squared errors of prediction is 2.791. Therefore, the standard error of the estimate is There is a version of the formula for the standard error in terms of Pearson's correlation: where ρ is the population value of Pearson's correlation and SSY is For the data in Table 1, μy = 2.06, SSY = 4.597 and ρ= 0.6268. Therefore, which is the same value computed previously. Similar formulas are used when the standard error of the estimate is computed from a sample rather than a
The slope and Y intercept of the regression line are 3.2716 and 7.1526 respectively. The third column, (Y'), contains the predictions http://davidmlane.com/hyperstat/A134205.html and is computed according to the formula: Y' = 3.2716X + 7.1526. The fourth column (Y-Y') is the error of prediction. It is simply the difference between what a subject's actual score was (Y) and what the predicted score is (Y'). The sum of the errors of prediction is zero. The last column, (Y-Y')², contains the squared errors of prediction.
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