Applied Statistics Using SPSS, STATISTICA, MATLAB and R

298 7 Data Regression
must ask which of the remaining variables, BPD or CP, has a higher correlation
with the predicted variable of the model that has already AP. The answer to this
question amounts to computing the partial correlation of a candidate variable, say
X2, with the predicted variable of a model that has already X1, r Y , X 2|
X . The
1
respective formula is:
2
rY , X 2|
X1
SSR(
X 2 | X 1)
SSE(
X 1)
− SSE(
X 1,
X
=
=
SSE(
X )
SSE(
X )
1
For the foetal weight dataset the computations with the values in Table 7.3 are
as follows:
2 SSR(
BPD | AP)
r FW, BPD|
AP =
= 0.
305 ,
SSE(
AP)
2 SSR(
CP | AP)
r FW, CP|
AP =
= 0.
167 ,
SSE(
AP)
resulting in the partial correlation values listed in Table 7.4. We therefore select
BPD as the next predictor to enter the model. This process could go on had we
more predictors. For instance, the partial correlation of the remaining variable CP
with the predicted variable of a model that has already AP and BPD is computed
as:
2
SSR(
CP | BPD,
AP)
r FW, CP|
BPD,
AP =
= 0.
014 .
SSE(
BPD,
AP)
Further details on the meaning and statistical significance testing of partial
correlations can be found in (Kleinbaum DG et al., 1988).
Table 7.4. Correlations and partial correlations for the foetal weight dataset.
Variables in
the model
Variables to
enter the model
1
2
)
Correlation Sample Value
(None) BPD rFW,BPD 0.731
(None) CP rFW,CP 0.743
(None) AP rFW,AP 0.847
AP BPD rFW,BPD|AP 0.552
AP CP rFW,CP|AP 0.408
AP, BPD CP rFW,CP|BPD,AP 0.119