Standard Error of Estimate

Let us consider yest as the estimated value of y for a given value of x. This estimated value can be obtained from the regression curve of y on x (see Linear regression ). From this, the measure of the scatter about the regression curve is supplied by the quantity:



The above equation is called the Standard Error of Estimate of y on x. It is important to note that this Standard Error of Estimate has properties analogous to those of standard deviation.

Example:

The regression line of y on x is given by the equation:

y = 35.82 + 0.476 x

The following table depicts the actual values of y and the estimated values of y (denoted by yest).

x 65 63 67 64
y 68 66 68 65
yest 66.76 65.81 67.71 66.28
y - yest 1.24 0.19 0.29 -1.28


Applying the formula for the Standard Error Estimate for this problem we have the solution as follows.