Conclusions from the Cumulative Residual SD Plot

We can make the following conclusions from the cumulative
residual standard deviation plot.
 The baseline model consisting only of the average
(\( \scriptsize \hat{Y} \)
= 110.6063) has a high residual standard deviation (95).
 The cumulative residual standard deviation shows a significant
and steady decrease as the following terms are added to the
average: X2, X7, X1*X3, X1,
X3, X2*X3, and X1*X2.
Including these terms reduces the cumulative residual standard
deviation from approximately 95 to approximately 17.
 Exclude from the model any term after X1*X2 as
the decrease in the residual standard deviation becomes
relatively small.
 From the effects plot, we see
that the average is 110.6063, the estimated X2 effect is
78.6126, and so on. (The model coefficients are one half of the
effect estimates.) We use this to from the following
prediction equation:
\( \begin{eqnarray*}
\hat{Y} & = & 110.6063  39.3063 X_2  39.0563 X_7 + \\
& & 35.00625 X_1 X_3 + 33.106245 X_1 +
31.90625 X_3  \\
& & 31.7313 X_1 X_5  29.781 X_1 X_2
\end{eqnarray*}
\)
Note that X1*X3 is confounded with
X2*X7 and X4*X6, X1*X5
is confounded with X2*X6 and X4*X7, and
X1*X2 is confounded with X3*X7 and
X5*X6.
From the above graph, we see that the residual standard
deviation for this model is approximately 17.
