Proceedings

very far away from the predicted value. In this regard, a large amount of error in the
NL-CD model is caused by a single case (n. 81). Size and effort for this case are 1127
and 23940, respectively. These values are approximately 3×Percentile 75 and
4×Percentile 75, respectively, so on a univariate basis we can consider case n. 81 as
an outlier with regard to both variables. Then, we removed this observation from the
sample and proceeded to the reestimation of the models. The results are detailed in
table 3.
Parameter estimates
A coefficient
(standard error)
t-statistic
A coefficient
(standard error)
t-statistic
A coefficient
(standard error)
t-statistic
Table 3. Estimation results after the deletion of case n. 81.
NL-CD LL-CD Linear
59.183
(48.720)
1.21
0.104
(0.094)
1.11
0.761
(0.141)
5.40
~ 689 ~
3.073
(0.739)
4.15
0.231
(0.155)
1.49
0.872
(0.136)
6.39
357.891
(752.083)
0.48
190.053
(245.508)
0.77
13.141
(3.457)
3.80
R 2 0.763 0.402 0.353
Accuracy measures (in-sample)
MMRE 0.676 0.600 0.710
MdMRE 0.314 0.341 0.318
Pred(25) 40.789% 38.157% 42.105%
ASREI 0.751 3.112 0.994
Accuracy measures (jackknife)
MMRE 6.159×10 10 1.799 2.139
MdMRE 0.980 0.527 0.322
Pred(25) 26.315% 30.263% 44.736%
ASREI 3532516.8 11.135 4.321
It is noticeable that the deletion of the outlier is more beneficial for the Cobb-Douglas
models than for the linear approach. This is especially true for the NL-CD model.
This result is not in accordance with findings of prior researchers, which suggest that
the Cobb-Douglas model is very stable with regard to outliers (see, e.g., Pickard et al.,
1999). However, even after dropping observation n. 81 the linear model still
outperforms the other two in terms of the most robust accuracy indicators. So, we can
conclude that the additive model with constant returns is superior.
5. SUMMARY, CONCLUSIONS AND DIRECTIONS FOR FUTURE
RESEARCH
The estimation of software development costs is an important task in the management
of software projects. In most cases the major cost factor is labor. For this reason
estimating development effort is central to the management and control of a software
project. However, these costs are not easy to anticipate. So, a series of models have
been proposed. Some of them are heuristic methods that solely rely on the use of
statistical / machine learning techniques.
However, these models can be complemented with others that incorporate theoretical
assumptions. Some of these systems are based on exponential functions which assume
the existence of decreasing returns to scale while others state that significant scale
economies do exist. Other models are linear systems which postulate that returns to