An Application of Geographically Weighted Regression for Assessing Water Polution in Pontianak, Indonesia CAUCHY –Jurnal Matematika Murni dan Aplikasi Volume 7(2) (2022), Pages 186-194 p-ISSN: 2086-0382; e-ISSN: 2477-3344 Submitted: September 01, 2021 Reviewed: November 11, 2021 Accepted: January 05, 2022 DOI: http://dx.doi.org/10.18860/ca.v7i1.13266 An Application of Geographically Weighted Regression for Assessing Water Polution in Pontianak, Indonesia Dadan Kusnandar1, Naomi Nessyana Debataraja1,*, and Rossie Wiedya Nusantara2 1Department of Statistics, Universitas Tanjungpura, Indonesia 2Department of Soil Sciences, Universitas Tanjungpura, Indonesia *Corresponding Author Email: dkusnand@untan.ac.id, naominessyana@untan.ac.id*, rwiedyanusantara@gmail.com ABSTRACT Geographically weighted regression (GWR) is an exploratory analytical tool that creates a set of location-specific parameter estimates. The estimates can be analyzed and represented on a map to provide information on spatial relationships between the dependent and the independent variables. A problem that is faced by the GWR users is how best to map these parameter estimates. This paper introduces a simple mapping technique that plots local t-values of the parameters on one map. This study employed GWR to evaluate chemical parameters of water in Pontianak City. The chemical oxygen demand (COD) was used as the dependent variable as an indicator of water pollution. Factors used for assessing water pollution were pH (𝑋1), iron (𝑋2), fluoride (𝑋3), water hardness (𝑋4), nitrate (𝑋5), nitrite (𝑋6), detergents (𝑋7) and dissolved oxygen, DO, (𝑋8). Samples were taken from 42 locations. Chemical properties were measured in the laboratory. The parameters of the GWR model from each site were estimated and transformed using Geographic Information Systems (GIS). The results of the analysis show that 𝑋1, 𝑋2, 𝑋3, 𝑋5 and 𝑋7 influence the amount of COD in water. The resulting map can assist the exploration and interpretation of data. Keywords: Chemical Parameters; Geographically Weighted Regression; Modelling; T-Value Mapping INTRODUCTION In a residential area, human activities are one of the critical aspects that affect the quality of water resources. The more activities in the area, the higher the waste discharged into the environment. As the capital city of the West Kalimantan Province, the level of land use in Pontianak City has increased every year. This increase has resulted in a decrease in the carrying capacity of the city. One form of land use that has experienced a very rapid rise is the land for settlements. This condition is closely related to population growth. The total population of Pontianak City is estimated at 646,661 people, with a population density of 5,998 people/km2 and a population growth rate of 1.95% per year [1]. The quantity and quality of water in a region significantly affects the life of living things. Changes in the quality and quantity of water are strongly influenced by the patterns of land management that exist in the area. Waste generated from human http://dx.doi.org/10.18860/ca.v7i1.13266 mailto:dkusnand@untan.ac.idm mailto:naominessyana@untan.ac.idi mailto:rwiedyanusantara@gmail.com An Application of Geographically Weighted Regression for Assessing Water Polution in Pontianak, Indonesia Dadan Kusnandar 187 activities in daily life can cause deterioration in water quality. Discharged waste has different characteristics that determine the degree of water quality around it. Waste produced from the activities of human life is diverse both in type and content. The waste can be in the form of organic compounds degraded by microorganisms as well as inorganic compounds such as soap, detergent, shampoo, and other cleaning agents that can contaminate water [2]. Parameters in measuring water quality include physical, biological and chemical parameters. These parameters are essential variables for measuring the water quality [3]. However, this paper focused on chemical variables. Water pollution can also be seen from the amount of oxygen content dissolved in water, namely through the measurement of chemical oxygen demand [4]. Chemical oxygen demand (COD) is the total amount of oxygen needed to oxidize organic matter chemically. Household waste is the primary source of organic waste and is one of the leading causes of high COD concentrations. This condition has an impact on humans and the environment, one of which is that many aquatic biotas die because the level of oxygen dissolved in water is small. The criteria for proper water use are increasingly difficult to obtain. This research aimed to investigate the relationships among many variables and the COD in the research area. The samples were collected from several locations having different characteristics and types of land and environment. This sampling procedure could create a dependence between data measurements and their locations. Hence, it generates spatial data. Techniques of spatial analysis can then be applied to the collected data. This research utilized the Geographically Weighted Regression (GWR) to investigate the relationship between the dependent variable and the corresponding independent variables. As an exploratory method, GWR provides extra information for any spatial data set and should be useful across all disciplines in which spatial data are utilized. Applications of GWR include studies in a wide variety of demographic fields including but not limited to the analysis of health and disease (see for example [5, 6, 7, 8]), environmental equity [9], housing markets [10, 11], population density and housing [12], poverty mapping in Malawi [13], urban poverty [14], demography and religion [2], as well as environmental conditions [15]. Brown et al. [16] used GWR to investigate the relationships between land cover, rainfall, and surface water habitat in predominately agriculture regions in Southeast Australia. It was found that GWR provided a better estimate than the OLS method. In this study, GWR was applied to investigate the relationship among variables of chemical contained in the water samples. METHODS The research was carried out in Pontianak City (Lat. 0Β°02' N – 0Β°01' S, Long. 109Β°16' – 109Β°23 E). Pontianak is the Capital City of the West Kalimantan Province, Indonesia. It covers approximately 107.82 km2. Soil conditions in the City of Pontianak consist of soil types of Organosol, Gley, Humus, and Alluvial, each of which has different characteristics. The sampling method was carried out by stratified random sampling. Subsequent sub-populations called strata were formed based on the criteria of the area flowed by the same tributary. It is assumed that the level of water pollution is homogeneous. The sample units studied were rivers/ditches, with a total sample of 42 water samples from different locations, representing the six districts in the City of Pontianak. The sites were plotted into a map of Pontianak City in Figure 1 [17]. The samples were taken in the same An Application of Geographically Weighted Regression for Assessing Water Polution in Pontianak, Indonesia Dadan Kusnandar 188 conditions, namely when the water receded. In this study, the response variable is COD, while the independent variables used include pH (𝑋1), iron (𝑋2), fluoride (𝑋3), hardness (𝑋4), nitrate (𝑋5), nitrite (𝑋6), detergent (𝑋7), and dissolved oxygen, DO, (𝑋8). Figure 1. Map of sample locations Suppose we have a set of observations ijx for i = 1, 2, …, n cases and j = 1, 2, …, k independent variables, and a set of dependent variables  iy for each case. This notation is standard data set for a global regression model. Now suppose that in addition to this, we have a set of location coordinates   ,i iu v for each case. The underlying model for GWR is as follows [18]:    0 1 , , k i i i j i i ij i j y u v u v x  ο₯ ο€½ ο€½  οƒ₯ (1) where       0 1, , , , ,ku v u v u v   are k + 1 continuous functions of the location (u, v) in the geographical study area, and πœ€π‘– ∼ 𝑁(0, 𝜎 2). The log-likelihood for any particular set of estimates of the functions may be written as follows (see, for example [18]):            2 0 1 02 1 1 1 , , , , , | , , 2 n k k i i i ij j i i i j L u v u v u v D y u v x u v      ο€½ ο€½  οƒΆ ο€½ ο€­ ο€­  οƒ·  οƒΈ οƒ₯ οƒ₯ (2) where D is the union of the set  ijx ,  iy and   ,i iu v . Rather than attempting to maximize equation (2) globally, we consider the local likelihood. We consider the problem of estimating       0 1, , , , ,ku v u v u v   on a pointwise basis. That is, given a specific point in geographical space  0 0,u v , we attempt to estimate       0 1, , , , ,ku v u v u v   . The point  0 0,u v may or may not correspond to one of the observed  ,i iu v . If these functions are reasonably smooth, we can assume that a simple regression model 0 1 k i ij j i j y x  ο₯ ο€½ ο€½  οƒ₯ (3) holds close to the point  0 0,u v , where each j is a constant valued approximation of the An Application of Geographically Weighted Regression for Assessing Water Polution in Pontianak, Indonesia Dadan Kusnandar 189 corresponding  ,j u v in Eq. (1). We can calibrate a model of this sort by considering observations close to the point  0 0,u v . An obvious way to do this is to use weighted least squares; this is to choose  0 1, , , k   to minimize   2 0 0 1 1 n k i i ij j i j w d y x  ο€½ ο€½  οƒΆ ο€­  οƒ·  οƒΈ οƒ₯ οƒ₯ (4) where d0i is the distance between the points  0 0,u v and  ,i iu v . This result gives us the standard GWR approach. We simply set  0 0Λ† ,j u v as Λ† j to obtain the familiar GWR estimates. At this stage, it is worth noting that Eq. (4) maybe multiplied by 2 1  ο€­ and be considered as a local log-likelihood expression:      0 0 0 1 | | n k i k i WL D w d L D    ο€½ ο€½ οƒ₯ (5) where  0 |kWL D  is an empirical estimate of the expected log-likelihood at the point of estimation GWR employs a weighted distance decay function for model calibration. The GWR assumes that observations closer together will have more impact on each other than on observations further apart. The weighting function for including related samples can be calculated using the exponential distance decay function: 2 2 exp ij ij d b   οƒΆο€­ ο€½  οƒ·  οƒ·  οƒΈ (6) where ij is the weight of observation j for observation i, dij is the distance between observation i and j and b are the kernel bandwidth When the distance between observations is greater than the kernel bandwidth, the weight rapidly approaches zero. Fixed bandwidth kernel calculates a bandwidth that is held constant over space, whereas the adaptive bandwidth kernel can adapt bandwidth distance in relation to variable- density; bandwidths are smaller where data are dense and more abundant when data are sparse. In this study, all GWR models used the adaptive kernel bandwidth as sample densities varied spatially. The optimal bandwidth distance was determined automatically in GWR using the Akaike information criterion (AIC). RESULTS AND DISCUSSION Tests on spatial aspects consist of two stages, namely the analysis of spatial dependency and spatial heterogeneity test. The spatial dependency test performed using the Moran's I test, whereas the spatial heterogeneity test used the Breusch-Pagan test. The test results are presented in Table 1. Table 1. Test on spatial aspects Tests p-value Decision Moran’s I 9,763e-08 Reject H0 Breusch-Pagan 0,1375 Do not reject H0 Moran’s I test indicated the existence of dependency spatial in the model. Whereas the results of Breush-Pagan showed there are no differences in characteristics among An Application of Geographically Weighted Regression for Assessing Water Polution in Pontianak, Indonesia Dadan Kusnandar 190 observation points. The next step is the selection of bandwidth that will be used in GWR modeling. Bandwidth selection can be made by examining the Cross-Validation (CV) value between weighting functions. The weighting function used were Fixed Gaussian, Fixed Bisquare, and Fixed Tricube (Table 2). Table 2. Cross-validation values and the bandwidth for each model. Model CV Bandwidth Gaussian 19,587.93 0.020963 Bisquare 20,381.45 0.07239735 Tricube 20,260.00 0.07239735 Table 2 shows that the Fixed Gaussian model gives a minimum value of the CV with the bandwidth of 0.020963. The Fixed Gaussian model was then used to obtain the weighting matrix for each location. Models obtained by the GWR was compared to that of the Ordinary Least Squares (OLS) Method in term of their SSE. The results showed that GWR performed better than that of the OLS (Table 3). Table 3. Comparison between the GWR and the OLS Methods. SSE Df F p-value OLS 17,330.621 33,000 GWR 5,195.428 16,602 3.3357 0.005773 Models for all 42 locations of the COD on the eight dependent variables are presented in Table 4. The coefficient of determination (R2) also showed in the table. Table 4. Regression model for the 42 locations No Location R2 Model 1 S. Raya Dalam 1 .78 y=190-8.9x1-13.4x2+70.3x3-+0.02x4-16.3x5-11.6x6-8682x7+0.9x8 2 S. Raya Dalam 2 .82 y=174-9.0x1-12.2x2+76x3+0.34x4-19.3x5-15.2x6-9011x7+0.1x8 3 Jl. Sepakat 2 .75 y=249-12.2x1-14.0x2-73x3-0.72x4-11.1x5-11.5x6+10665x7-3.9x8 4 Jl. Parit H. Husin 2 .95 y=181-12.2x1-6.1x2-8.2x3+0.92x4-20.4x5+29.3x6+19033x7+3.6x8 5 Jl. Parit H. Husin 1 .82 y=173-9.6x1-11.6x2-84x3+0.35x4-19.5x5-15.4x6+9350x7-0.2x8 6 Jl. Imam Bonjol .83 y=174-10.1x1-10.9x2-92x3+0.31x4-19.4x5-14.8x6-9693x7-0.7x8 7 Jl. Media .83 y=190-11.6x1-10.2x2-97x3+0.14x4-18.2x5-12.9x6-10117x7-1.9x8 8 Jl. Perdana .81 y=241-14.3x1-11.5x2+88x3-0.38x4-14.2x5-12.2x6-11432x7-3.4x8 9 Jl. Purnama .84 y=275-17.2x1-10.1x2+81x3-0.65x4-13.2x5-10.9x6-12776x7-3.2x8 10 Jl. Tebu .89 y=172-13.6x1-6.3x2+69x3-0.17x4-10.1x5-11.8x6-3942x7+3.0x8 11 Jl. Karet .93 y=222-21.5x1-5.9x2+53x3-0.01x4-7.0x5-6.9x6-3448x7+3.2x8 12 Jl. Ampera .90 y=340-37.1x1-5.0x2-27x3+0.07x4-3.7x5+22.8x6-4795x7-3.9x8 13 Jl. Wahidin .88 y=283-27.8x1-5.6x2+56x3-0.03x4-8.2x5+4.4x6-5345x7+0.3x8 14 Jl. Purnama Jaya .84 y=264-17.3x1-9.7x2+86x3-0.45x4-14.0x5-10.9x6-12128x7-3.7x8 15 Jl. Uray Bawadi .86 y=260-19.5x1-7.8x2+82x3-0.25x4-13.6x5-6.3x6-10159x7-3.3x8 16 Jl. HM Suwignyo .86 y=259-21.5x1+6.8x2+74x3-0.17x4-12.0x5-2.6x6-8077x7-2.2x8 17 Ujung Suwignyo .85 y=143-6.6x1-8.8x2+91x3-0.10x4-16.3x5-11.9x6-7250x7-0.9x8 18 Jl. Gst Hamzah .86 y=223-17.1x1-7.2x2+78x3-0.13x4-13.0x5-5.4x6-7484x7-2.0x8 19 Jl. Hasanuddin .85 y=122-4.1x1-9.2x2+94x3-0.11x4-17.0x5-13.8x6-6912x7-0.2x8 An Application of Geographically Weighted Regression for Assessing Water Polution in Pontianak, Indonesia Dadan Kusnandar 191 No Location R2 Model 20 Jl. K Yos Sudarso .86 y=141-8.4x1-6.9x2+79x3-0.21x4-12.3x5-14.1x6-4619x7+2.3x8 21 Jl. WR. Supratman .85 y=171-9.5x1-8.8x2+95x3-0.03x4-17.1x5-11.3x6-8755x7-2.3x8 22 Pasar Flamboyan .84 y=180-10.6x1-9.3x2+98x3+0.09x4-18.2x5-12.5x6-9767x7-2.4x8 23 Depan Ramayana .84 y=163-10.6x1-9.4x2+100x3+0.15x4-19.1x5-13.7x6-9544x7-1.9x8 24 Jl. Flora Siantan .95 y=178-15.8x1-6.5x2+65x3-0.17x4-8.3x5-16.3x6-2715x7+5.7x8 25 Jl. Teluk Selamat .84 y=82+0.4x1-8.9x2+97x3-0.21x4-17.4x5-19.7x6-5497x7+2.4x8 26 Jl. Parit Makmur .84 y=91+0.1x1-10.0x2+101x3-0.09x4-19.7x5-17.9x6-6875x7+0.8x8 27 Jl. Puring 1 .85 y=105-1.5x1-9.8x2+101x3-0.04x4-19.6x5-16.5x6-7557x7-0.2x8 28 Jl. Selat Sumba 2 .84 y=97-0.4x1-9.9x2+102x3+0.01x4-20.8x5-18.4x6-7735x7+0.9x8 29 Parit Pangeran .84 y=85+1.2x1-9.9x2+99x3+0.01x4-22.0x5-21.1x6-7593x7+0.9x8 30 Jl. Keb. Nasional .83 y=85+1.3x1-9.7x2+91x3+0.12x4-23.1x5-23x6-8678x7+1.7x8 31 Jl. Selat Panjang .84 y=86+1.1x1-9.7x2+95x3+0.11x4-22.9x5-22.5x6-8431x7+1.2x8 32 Jl. Tritura .84 y=110-2.1x1-9.7x2+102x3+0.15x4-21.4x5-18.4x6-8714x7-0.5x8 33 Tanjung Hilir .84 y=116-3x1-9.6x2+102x3+0.14x4-21x5-17.4x6-8751x7-0.8x8 34 Tanjung Raya 1 .84 y=128-4.8x1-9.7x2+100x3+0.27x4-21.4x5-17.5x6-9334x7-0.6x8 35 Tanjung Raya 2 .84 y=132-5.3x1-9.9x2+99x3+0.32x4-21.4x5-17.6x6-9445x7-0.5x8 36 Jl. Panglima Aim .84 y=120-4x1-10.1x2+95x3+0.39x4-22.4x5-19.7x6-9562x7+0.4x8 37 Jl. Ya’ M Sabran .83 y=96-0.6x1-10.2x2+86x3+0.37x4-23.6x5-22.3x6-9998x7+2.2x8 38 Jl. Tani .83 y=120-3.9x1-10.6x2+82x3+0.53x4-23.1x5-21.2x6-10021x7+1.7x8 39 Tj. Raya 2 Ujung .83 y=163-7.9x1-11.8x2+59x3+0.54x4-21.6x5-16.8x6-9212x7+1.2x8 40 Jl. Tabrani Ahmad .87 y=216-19.0x1-6.2x2+64x3-0.08x4-9.5x5-4.7x6-4688x7+1.0x8 41 Jl. Harapan Jaya .85 y=281-17.1x1-10.0x2+65x3-0.86x4-11.3x5-3.0x6-13148x7+0.1x8 42 Jl. Merdeka .85 y=162-9.0x1-8.5x2+89x3-0.10x4-15.6x5-10.4x6-7406x7-1.4x8 y = COD; x1 = pH; x2 = iron; x3 = fluoride; x4 = water hardness; x5 = nitrate; x6 = nitrite; x7 = detergents; x8 = DO The coefficient of determination of the model varied between 75% (Location 3) to 95% (Location 4 and 24). Partial significance tests were carried out to examine which parameters are significant. The t-statistic was used for the tests. The values of the t- statistics for each parameter are presented in Figure 2 (a) to (h). (a) t value for 1 (b) t value for 2 An Application of Geographically Weighted Regression for Assessing Water Polution in Pontianak, Indonesia Dadan Kusnandar 192 (c) t value for 3 (d) t value for 4 (e) t value for 5 (f) t value for 6 (g) t value for 7 (h) t value for 8 Notes: ●: |t| < 1.64; : 1.64 ≀ |t| < 1.96; +: 1.96 ≀ |t| < 2.33; ο‚«: |t| > 2.33 Figure 2. (a) to (h) are the plot of t values for each 𝛽 in every location The sample locations marked with ● indicate that the corresponding coefficient of 𝛽i is not significant (the |t| value is smaller than 1.64). The symbol  is used to indicate that the coefficient of 𝛽 i is almost significant (1.64 ≀ |t| < 1.96). Whereas the symbols + and ο‚« are used to indicate that the coefficient of 𝛽 i are significant (|t| β‰₯ 1.96). The values of t for 𝛽1 are generally small for the samples located close to the rivers (Fig. 2 (a)). The variable pH (X1) for those locations is not significant, hence it does not contribute to modeling the COD. However, variable pH appeared to be significant for the sample located at some distance from the river (there were 18 sample locations). In general, the t values for 𝛽2, 𝛽3, 𝛽5, and 𝛽7 are significant (Fig. 2 (b), (c), (e), (g)). These results indicate that the contents of the variable of iron, fluoride, nitrate, and detergent have a great influence in An Application of Geographically Weighted Regression for Assessing Water Polution in Pontianak, Indonesia Dadan Kusnandar 193 modeling the COD. High nitrogen compounds in the form of oxidized nitrogen, such as nitrate, tend to reduce the level of dissolved oxygen in water through the oxidation of ammonia [13, 10]. Likewise, detergent, where one of the integral ingredients is phosphate compound, has a major role in the occurrence of eutrophication in the water body [22]. The t value for 𝛽4, 𝛽6, and 𝛽8 (Fig.2 (d), (f), and (h)) are generally small, indicating that water hardness (𝑋4), nitrite (𝑋6), and DO (𝑋8) are not significant in the whole samples. The three variables are, therefore, not important in predicting the COD of the samples. Plotting the t value of the regression coefficients of the sample location in a map enables the researcher to identify the importance of the variables to the regression models in each sample location. The application of GWR allows getting a different model in each location. CONCLUSIONS This study has demonstrated the superiority of GWR to model the spatially varying relationship between variables over OLS regression. GWR 42 samples point can result in 42 regression models that accommodate the characteristics of the location. The variable pH (X1) generally small for the samples located close to the rivers, however it is significant for the samples located at some distances from the river. 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