Applied Statistics Using SPSS, STATISTICA, MATLAB and R

310 7 Data Regression
with s
2
= ∑ ∑
2
( d i1
− d1
) + ( d
n − 2
i2
− d
In the present case the computed t value is t * = –1.83 and the 0.975 percentile of
t412 is 1.97. Since |t * | < t412,0.975, we accept that the residual variance is constant.
Test of Fit
We now proceed to evaluate the goodness of fit of the model, using the method
described in 7.1.4, based on the computation of the pure error sum of squares.
Using SPSS, STATISTICA, MATLAB or R, we determine:
n = 414; c = 381; n – c = 33; c – 2 = 379 .
SSPE = 1846345.8; MSPE=SSPE/( n – c) = 55949.9 .
SSE = 34921109 .
Based on these values, we now compute:
SSLF = SSE − SSPE = 33074763.2; MSLF = SSLF/(c – 2) = 87268.5 .
Thus, the computed F * is: F * = MSLF/MSPE = 1.56. On the other hand, the 95%
percentile of F379, 33 is 1.6. Since F * < F379, 33, we do not reject the goodness of fit
hypothesis.
Detecting Outliers
The detection of outliers was already performed in 7.3.2.1. Eighteen cases are
identified as being outliers. The evaluation of the model without including these
outlier cases is usually performed at a later phase. We leave as an exercise the
preceding evaluation steps after removing the outliers.
Assessing Multicollinearity
Multicollinearity can be assessed either using the extra sums of squares as
described in 7.2.5.2 or using the VIF factors described in 7.3.2.2. This last method
is particularly fast and easy to apply.
Using SPSS, STATISTICA, MATLAB or R, one can easily obtain the
coefficients of determination for each predictor variable regressed on the other
ones. Table 7.8 shows the values obtained for our case study.
Table 7.8. VIF factors obtained for the foetal weight data.
r 2
2
)
2
.
BPD(CP,AP) CP(BPD,AP) AP(BPD,CP)
0.6818 0.7275 0.4998
VIF 3.14 3.67 2