June 2002 Vol. 4, No. 6
Quality Quiz from Professor Cleary

Congratulations!
You're right!

Donatello Mymuther should tell, not his mother, but his technicians, that he is unable to respond correctly to the question, and that the group should look up scatter diagrams in Practical Tools for Continuous Improvement and report back on what they find.

In fact, as Practical Tools will explain, the standard error of the estimate is a measure of variability of the observations around the regression line.

If it is large (as in Figure 1), then the observations are far from the regression line:

If the observations are close to the regression line, then it will be small:

The standard estimate of the error is calculated with the following formula:
Where

 an observation                                     the predicted value of y, given some value for x   sample size

Conceptually, this is similar to the formula for standard deviation:
Where

 an observation   the mean of the sample                               the size of the sample

The difference is that the standard error of the estimate measures the variability around a line, and the standard deviation measures the variability around a point ().