![](bg7.png)
4 CONCLUSIONS
The algorithm written in this paper yields a
bandwidth and some polynomial degrees for the
GWPolR model in optimal condition. It means that
the result is the best condition based on the used
criterion. However, computational programming
based on this algorithm still takes a long time. The
time will be longer when the number of variables
involved in model increases or the maximum degree
of polynomial is set greater. An efficient algorithm in
term of execution time is needed even though the
results may be only sub-optimal, for example, genetic
algorithm or neural network. Based on the goodness
of fit criteria(inter alia: CV, RSS, and R
2
) and
consideration of conformity with public opinion, we
can empirically conclude that the GWPolR model is
the best model among some models used here on
WQI dataset. Nevertheless, statistical tests between
spatial modelling need to be developed to determine
whether a GWPolR is significantly better than a
GWR or not.
ACKNOWLEDGEMENTS
The authors would like to thank Directorate General
of Science and Technology Resources and Higher
Education of The Ministry of Research, Technology
and Higher Education of Indonesia for scholarship
that be received by the first author throughout
undergoes doctoral program. The authors also thank
to Ministry of Environment and Forestry of Indonesia
and Statistics of Indonesia for kindly providing the
data.
REFERENCES
Al-Ahmadi, K., Al-Ahmadi, S., 2013. Rainfall-Altidude
Relationship in Saudi Arabia. Advances in Meteorology,
[Internet] [Citation: 25 January 2017]. Obtained from:
http://dx.doi.org/10.1155/2013/363029.
BPS, 2016. Jumlah Perusahaan Industri Mikro dan Kecil
Menurut Provinsi, 2013–2015. [Internet] [Citation: 20
June 2018]. Obtained from: https://bps.go.id.
BPS, 2017a. Kepadatan Penduduk menurut Provinsi, 2000–
2015. [Internet] [Citation: 20 June 2018]. Obtained
from: https://bps.go.id.
BPS, 2017b. Persentase Rumah Tangga Menurut Provinsi
dan Perlakuan Memilah Sampah Mudah Membusuk
dan Tidak Mudah Membusuk, 2013–2014. [Internet]
[Citation: 20 June 2018]. Obtained from:
https://webapi.bps.go.id.
Brunsdon, C., Fotheringham, A. S., Charlton, M., 1996.
Geographically Weighted Regression: A Method for
Exploring Spatial Nonstationarity. Geographical
Analysis, 28(4): 281–298.
Brunsdon, C., Fotheringham, A. S., Charlton, M., 1999.
Some Notes on Parametric Significance Tests for
Geographically Weighted Regression. Journal of
Regional Science, 38(3): 497–524.
Brunsdon, C., McClatchey, J., Unwin, D. J., 2001. Spatial
Variations in the Average Rainfall–Altitude
Relationship in Great Britain: An Approach using
Geographically Weighted Regression. International
Journal of Climatology, 21: 455–466.
Bhutiani, Faheem, A., Varun, T., Khushi, R., 2018.
Evaluation of water quality of River Malin using water
quality index (WQI) at Najibabad, Bijnor (UP) India.
Environment Conservation Journal, 19 (1&2): 191–201.
https://www.researchgate.net/publication/325986999
Chamidah, N., Saifuddin, T., Rifada, M., 2014. The
Vulnerability Modelling of Dengue Hemorrhagic Fever
Disease in Surabaya Based on Spatial Logistic
Regression Approach. Applied Mathematical Sciences,
8(28): 1369 – 1379.
Chiang, Y-H., Peng, T-C., Chang, C-O., 2015. The
nonlinear effect of convenience stores on residential
property prices: A case study of Taipei, Taiwan.
Habitat International, 46: 82–90.
Dhawde, R., Surve, N., Macaden, R., Wennberg, A.C.,
2018. Physicochemical and Bacteriological Analysis of
Water Quality in Drought Prone Areas of Pune and
Satara Districts of Maharashtra, India. Environment, 5,
61, doi: 10.3390/environments5050061. [Internet]
[Citation: 20 January 2018]. Obtained from:
http://dx.doi.org/10.3390/ environments5050061.
Fotheringham, A. S., Charlton, M. E., Brunsdon, C., 1998.
Geographically Weighted Regression: A natural
evolution of the expansion method for spatial data
analysis. Environment and Planning A, 30: 1905–1927.
Fotheringham, A. S., Charlton, M. E., Brunsdon, C., 2001.
Spatial Variation in School Performance: A Local
Analysis using Geographically Weighted Regression.
Geographical & Explanatory Modelling, 5(1): 43–66.
Fotheringham, A. S., Brunsdon, C., Chartlon, M., 2002.
Geographically Weighted Regression: The Analysis of
Spatially Varying Relationships. John Wiley and Sons,
USA.
Han, D., Gorman, D. M., 2013. Exploring Spatial
Associations between On-Sale Alcohol Availability,
Neighborhood Population Characteristic, and Violent
Crime in a Geographically Isolated City. Journal of
Addiction, [Internet] [Citation: 20 May 2017]. Obtained
from: http://dx.doi.org/10.1155/2013/ 356152.
Kementerian Lingkungan Hidup, 2015. Indeks Kualitas
Lingkungan Hidup Indonesia 2014. Kementerian
Lingkungan Hidup. [Internet] [Citation: 20 June 2018].
Obtained from: www.menlhk.go.id/downlot.php?file=
iklh2014.pdf.
Liyanage, C. P., Yamada, K., 2017. Impact of Population
Growth on the Water Quality of Natural Water Bodies.
Sustainability, 9, 1405. [Internet] [Citation: 20 January
Geographically Weighted Polynomial Regression:Selection of the Optimal Bandwidth and the Optimal Polynomial Degrees and Its
Application to Water Quality Index Modelling
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