THE APPLICATION OF EQUATION MODELS TO DETERMINE THE AGE OF PINK RIVER DOLPHIN SKULLS - Biology, Evolution and Conservation of River Dolphins Within South America and Asia - page 93

If we observed the absolute error values in table 6, we can see that the ages with the
highest errors were those near zero. For instance, the 27 and 57 individuals ages one and 0.5
years, respectively, present the highest absolute errors, with values of 1044.7 and 535.3.

Regression Using Distances

Such as in the previous analysis, 24 variables were employed for this procedure (those
significant for the linear regression analysis). For each one of the 5 distances used (Gower,
absolute Value, Mahalanobis, Minkowski with exponent 2 and 4), the coefficient of
determination, the residual sum of squares and the cross-validation statistic were considered.
These values can be observed in Table 7.

Table 7. Values of the coefficient of determination, sum of
residual squares, and cross-validation statistic for each one of the distances employed in
the distance regression analysis.

Coefficient of
determination

Sum of
residual squares

Cross-validation
statistic

Distance

Gower 0.81911 1938.2 58.815

Absolute value 0.93293 719.01 70.57

Mahalanobis 0.87981 1288.3 192.61

Minkowski exp 2 0.87984 1321.9 193.5

Minkowski exp 4 0.82288 2012.2 5580.6

The absolute distance was the best estimator of the real age. The determination
coefficient showed that 93 % of age variation was determined by the 24 variables employed.
This distance also yielded the lower sum of residual squares. Nevertheless, Gower distance
had the best cross-validation coefficient. The observed and estimated ages with the absolute
value distance are shown in table 8.
There was an excellent agreement between the observed and estimated ages for many
individuals. For instance, the individuals 10, 12, 31, 38, 42, 50, 55 and 64 the observed and
estimated ages were exactly the same. The individuals 5, 11, 16, 21, 24, 26, 29, 30, 33, 44,
49, 51, 56, 60, 63, 71 only differed in one year between the observed and the estimated ages.
The worst agreement was found in the set of individuals between the age range of less than
one year to two years. The estimated values for these cases were negative. However, these
animals were easier to recognize because of their calf or juvenile characteristics.
In addition to the linear and distances models, we used 24 other regression models and
polynomial regressions of third, fourth and fifth order to analyze the 24 variables which
showed the significant correlations with the linear regression. The different variables
presented diverse behavior with regard to these 24 regression models. Those which were up
to r = 0.50 are described here. Variable one (V1) showed an important correlation with age
using model 24 (r = 0.8324; r 2 = 0.6928) while V15 yielded a significant relationship with
model 21 (r = 0.6501; r 2 = 0.4226). Significant relationships were also found for other
variables with model 21 including: as V11 (r = 0.5887; r 2 = 0.3466), V12 (r = 0.5826; r 2 =
0.3394), V23 (r = 0.5088; r 2 = 0.2589), V26 (r = 0.5838; r 2 = 0.3408), V30 (r = 0.6313; r 2 =