2.3.3. The Standard Error of the Estimate (syx)
Random variation which is the variation of the actual (observed) y values from the predicted y values (yi) is measured by the standard error of the estimate. The smaller the value of syx , the smaller the variation of the actual (observed) y values from the predicted y values (yi ), and hence better is the line of fit.
We will now compute the values for R2, r, and syx for the example problem on linear regression that we had solved earlier. As the independent variable in this example is t instead of x, we solve the above formulas for R2, r, and syx by substituting t for x. We have the following data from the example above.
n = 9, 
t = 45,
y = 592,
t*y = 3084,
t2 = 285,
y2 = 39226, a = 55.44, b = 2.067
All of the statistics indicate that the regression line obtained for example 1 is a very good line of fit.