326 Statistical Methods
This statistic will be covered more in depth in Chapter 9. Finally, the stan-
dard error measures the size of a typical deviation of an observed value
(x, y) from the regression line. Think of the standard error as a way of averag-
ing the size of the deviations from the regression line. The typical deviation
of an observed point from the regression line in this example is about 7.5447.
The observations value is the size of the sample used in the regression. In
this case, the regression is based on the values from 16 regions.Interpreting the Analysis of Variance Table
Figure 8-11 shows the ANOVA table output from the Analysis ToolPak
Regression command.Figure 8-11
Analysis of
Variance
(ANOVA)
tableThe ANOVA table analyzes the variability of the mortality index. The vari-
ability is divided into two parts: the fi rst is the variability due to the regres-
sion line, and the second is random variability.
The values in the df column of the table indicate the number of degrees of
freedom for each part. The total degrees of freedom are equal to the number of
observations minus 1. In this case the total degrees of freedom are 15. Of those
15 degrees of freedom, 1 degree of freedom is attributed to the regression, and
the remaining 14 degrees of freedom are attributed to random variability.
The SS column gives you the sums of squares. The total sum of squares
is the sum of the squared deviations of the mortality index from the over-
all mean. This total is also divided into two parts. The fi rst part, labeled in
the table as the regression sum of squares, is the sum of squared deviations
between the regression line and the overall mean. The second part, labeled
the residual sum of squares, is equal to the sum of the squared deviations of
the mortality index from the regression line. Recall that this is the value that
we want to make as small as possible in the regression equation. In this ex-
ample, the total sum of squares is 3,396.44, of which 2,599.53 is attributed
to the regression and 796.91 is attributed to error.
What percentage of the total sum of squares can be attributed to the re-
gression? In this case, it is 2,599.53/3,396.44 5 0.7654, or 76.54%. This is
equal to the R^2 value, which, as you learned earlier, measures the percentage
of variability explained by the regression. Note also that the total sum of
squares (3,396.44) divided by the total degrees of freedom (15) equals 226.43,
which is the variance of the mortality index. The square root of this value is
the standard deviation of the mortality index.