STANDARD ERROR OF ESTIMATE

Remember that the regression equation allows us to make predictions, but it doesn't tell us how accurate they are.

In essence, the regression line is the best fitting line.

To determine how well a line fits the data points, it is necessary to define the distance between the line and each data point.

For every X value, the linear equation will determine a Y value (the predicted Y, or Y')

The distance between the two (Y - Y') would show the error between the line and the actual data.

The best fitting line is the one that has the smallest total squared error S (Y - Y') ² .  This expression is essentially an average error over the entire scatterplot.

The standard error of the estimate s_esty  is useful in determining the range of potential Y' values for a particular X value.

The magnitude of the error is dependent on the degree of relationship between two sets of measures, as the following graph shows:

Figure 16-20  (p. 560)
(a) Scatterplot showing data points that perfectly fit the regression equation
Ŷ = 1.6X – 2. Note that the correlation is r = 1.00. (b) Scatterplot for the data from Example 16.14 Notice that there is error between the actual data points and the predicted Y values of the regression line.