1. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 2, February (2014), pp. 156-162, © IAEME
156
WATER QUALITY OF BUDHABALANGA RIVER IN THE VICINITY OF
BALASORE TOWN BY CORRELATION AND REGRESSION METHOD
Nibedita Pattnayak
Associate Professor, Department of Chemistry, OEC, Bhubaneswar, Orissa, India
ABSTRACT
In industrial zone different types of industries emits highly concentrated polluted water. The
concentrated of pollution depends upon the situation of point with respect to the industries that emits
the polluted water. As there are large number of variables, the only statistical methods are useful for
prediction of concentration of pollutants. This study aims to calculate the various parameters by
correction and regression techniques.
Key words: Pollutants, Water Quality Index, Correlation and Regression Method.
INTRODUCTION
Water is one of the abundantly available substances in nature. Pollution of land, water and air
through water generated as a result of increasing is a challenge of serious dimensions. The main
purpose of water analysis is to evaluate methods of treatments of ground water with to reuse or
dispose, ascertain quality of water. Correlation among water quality parameters in specific
environmental condition have been shown to be useful [1]. Utilization of such methodology will thus
greatly facilitate the task of rapid monitoring of the status of pollution of water body or waste waters
or effluents and achieve economy in matters of collection and analysis of samples [2]. The water
quality of ground water can be predicted with sufficient accuracy just by the measurement of EC
alone. This provides a means for easier and faster monitoring of water quality in a location [3]. The
correlation study and correlation coefficient values can help in selecting treatments to minimize
contaminates in ground water [4].
Water quality index has been regarded as one of the most effective way to communicate
water quality [5].
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING
AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 5, Issue 2, February (2014), pp. 156-162
© IAEME: www.iaeme.com/ijaret.asp
Journal Impact Factor (2014): 4.1710 (Calculated by GISI)
www.jifactor.com
IJARET
© I A E M E

2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 2, February (2014), pp. 156-162, © IAEME
157
The WQI value [8] indicate the overall pollution of drinking water:
0 – 25 Excellent
25 – 50 Good
50 – 75 Poor
75 – 100 Very poor
> 100 Unfit for drinking.
MATERIAL AND METHOD
Water samples were collected from Budhabalanga river of Balasore. The water samples were
collected in every months. The correlation coefficient (r) among 23 water quality parameters, such as
Chloride, Nitrate, sulfate, sulfide, phosphate, Nickel, Lead, Chromium, Cobalt, Zinc, Manganese,
Iron, Turbidity, pH, electrical conductivity, Total alkalinity, Total hardness, calcium, magnesium,
TDS, Sodium, Potassium, DO. of different categories of waters samples were calculated. The
sampling of water was carried out during the period of one year (December-2012 to November-
2013). The water samples were collected by holding glass stoppered sterile bottle near its base in the
hand and plugging it and transported in the laboratory in an ice-box to avoid unpredictable changes
in physico-chemical characteristic after measuring temperature. Physico-chemical analysis for water
were done following the standard methods by APHA[6].
Correlation coefficient and Linear regression
Correlation coefficient ‘r’ has been calculated between each pair of parameters by using
experimental data [7]. Let X and Y be the two variables, then the correlation ‘r’ between the
variables X and Y is given by
2 2
Σ
Σ Σ
XY
r
X Y
=
×
where, X X X= − and
ΣX
X
n
=
Y Y Y= − and
ΣY
Y
n
=
n = no. of samples.
If the values of correlation coefficient ‘r’ between two variables X and Y are fairly large it
implies that these two variables are highly correlated. In such cases it is feasible to try linear relation
of the form :Y = AX + B to correlate X and Y, where A and B are the constants.
For high ‘r’ values linear equation is found for two variables X and Y i.e. the concentration
of certain parameters can be predicted when one is determined.
RESULT AND DISCUSSION
1. The value of ‘r’ in positive correlation was between 0 to 0.99 and for negative correlation 0 to
0.99.
2. For Budhabalanga river, there was a negative correlation between sulfide and zinc
(r= –0.864). There was some positive correlation between sulfide and pH (r=0.807), E.C. and
TDS (r = 0.831), total alkalinity and TDS (r=0.831), total hardness and calcium (r=0.891).

3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 2, February (2014), pp. 156-162, © IAEME
158
3. Least square fitting for linear relation Y = AX+B (X and Y = Parameters, A and B =
regression coefficient, r = correlation coefficient
OPTIMUM PROCEDURE OF PREDICTING CONCENTRATION OF EACH
CONTAMINANT
This method aims to predict the concentration of all parameters when one is used to calculate
all parameters[fig 1 to 4].
1. Calculate Zinc from equation:
Zinc = –0.1297 (Sulfide) + 0.060
2. Calculate pH from equation:
pH=1.4872 (Sulfide)+ 7.150
3. Calculate TDS from equation:
TDS =0.4976 (EC) + 8.8538
4. Calculate TDS from equation:
TDS = 0.6072 (Total alkalinity) + 8.8432
5. Calculate Calcium from equation:
Calcium = 0.627 (Total hardness) + 1.3729
Category of
water sample
X Y A B r
Regression
equation
Y=AX+B
Budhabalanga
river water
Sulfide Zinc -0.1297 0.060 -0.864
Zinc = –0.1297
(Sulfide) +
0.060
Sulfide pH 1.4872 7.150 0.807
pH=1.4872
(Sulfide)+
7.150
EC TDS 0.4976 8.853 0.831
TDS =0.4976
(EC) + 8.8538
Total
alkalinity
TDS 0.6072 8.8432 0.831
TDS = 0.6072
(Total alkalinity
+ 8.8432
Total
hardness
Calcium 0.627 –1.3729 0.891
Calcium =
0.627 (Total
hardness) +
1.3729

4. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 2, February (2014), pp. 156-162, © IAEME
159
Table -1
Correlation coefficient ‘r’ among various parameters of Bhudhabalanga river water of Balasore
Chlorid
e
Nitrat
e
Sulfat
e
Sulfid
e
Phosphat
e
Nicke
l Lead
Chromiu
m
Cobal
t Zinc
Mangane
se Iron
Turbidit
y pH
Ele.
Cond
Total
Alkal.
Total
Hard
Calciu
m
Magnesiu
m TDS
Sodiu
m
Potassiu
m DO
Chloride 1.000
Nitrate 0.248 1.000
Sulfate 0.585 0.173 1.000
Sulfide -0.367
-
0.060
-
0.293 1.000
Phosphate -0.098
-
0.192
-
0.301 0.076 1.000
Nickel -0.401 0.195 0.101
-
0.076 0.001 1.000
Lead 0.149 0.070 0.197
-
0.620 -0.316 0.288 1.000
Chromium -0.100
-
0.117
-
0.020
-
0.368 -0.071
-
0.149 0.192 1.000
Cobalt -0.312
-
0.480
-
0.273
-
0.185 0.311 0.199
-
0.073 0.158 1.000
Zinc 0.374 0.310 0.496
-
0.864 -0.194 0.273 0.690 0.144
-
0.195 1.000
Manganes
e -0.099
-
0.025
-
0.086 0.299 0.288
-
0.352
-
0.012 0.137 0.005
-
0.315 1.000
Iron -0.005 0.140 0.424
-
0.179 0.121 0.097
-
0.122 0.231 0.387 0.143 0.323 1.000
Turbidity 0.040 0.736 0.133 0.422 -0.243 0.020
-
0.287 -0.296
-
0.765
-
0.054 0.055
-
0.118 1.000
pH -0.313
-
0.002
-
0.175 0.807 0.303
-
0.161
-
0.569 -0.325
-
0.421
-
0.607 0.392
-
0.185 0.550 1.000
Ele. Cond -0.515 0.394
-
0.416
-
0.199 -0.072 0.430 0.393 -0.094 0.079 0.273 0.050
-
0.016 0.160
-
0.114 1.000
Total
Alkal. -0.515 0.394
-
0.416
-
0.199 -0.072 0.430 0.393 -0.094 0.078 0.273 0.050
-
0.016 0.161
-
0.114 1.000 1.000
Total
Hard 0.331 0.491 0.068
-
0.542 -0.466
-
0.008 0.267 -0.052
-
0.177 0.506 -0.561
-
0.218 0.196
-
0.477 0.368 0.368 1.000
Calcium 0.008 0.229
-
0.238
-
0.377 -0.522
-
0.032 0.282 -0.006
-
0.014 0.251 -0.490
-
0.367 0.028
-
0.403 0.487 0.487 0.891 1.000
Magnesiu
m 0.663 0.671 0.480
-
0.564 -0.200 0.030 0.140 -0.096
-
0.340 0.670 -0.439 0.083 0.359
-
0.394 0.051 0.051 0.760 0.381 1.000
TDS -0.604 0.036
-
0.313
-
0.316 0.096 0.570 0.511 0.070 0.144 0.371 -0.066
-
0.094 -0.118
-
0.095 0.831 0.831 0.169 0.325 -0.121 1.000
Sodium -0.120
-
0.220 0.391
-
0.210 -0.334 0.174 0.127 0.581 0.239 0.127 -0.216 0.455 -0.340
-
0.315 -0.243 -0.243 -0.066 -0.014 -0.115 0.002 1.000
Potassium -0.318 0.135 0.061 0.082 -0.276 0.261 0.230 -0.104 0.320
-
0.022 0.354 0.593 -0.077
-
0.169 0.430 0.430 -0.141 -0.025 -0.251 0.206 0.256 1.000
DO -0.161
-
0.560
-
0.242 0.572 -0.004
-
0.112
-
0.414 -0.043 0.441
-
0.790 0.035
-
0.137 -0.347 0.133 -0.507 -0.507 -0.461 -0.225 -0.616
-
0.477 0.146 0.022
1.00
0
Fig. 1: Linear plot between Sulfide and Zinc values
y = -0.1297x +0.0606
R =-0.864
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0 0.1 0.2 0.3 0.4 0.5
[Sulfide], mg/l
[Zinc],mg/l

5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 2, February (2014), pp. 156-162, © IAEME
160
Fig.2: Linear plot between E.C. and TDS values
Fig. 3: Linear plot between Total Alkalinity and TDS values
Fig. 4: Linear plot between Total Hardness and Calcium values
y = 0.6072x + 8.8432
R = 0.831
0
10
20
30
40
50
60
70
80
90
95 100 105 110 115 120
[Total Alkalinity], mg/l
[TDS],mg/l
y = 0.627x - 1.3729
R = 0.891
0
2
4
6
8
10
12
14
16
18
0 5 10 15 20 25 30
[Total Hardness], mg/l
[Calcium],mg/l

6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 2, February (2014), pp. 156-162, © IAEME
161
METHOD OF CALCULATION OF WATER QUALITY INDEX (WQI)
Water quality indices were calculated using the method proposed by Tiwari and Mishra [5].
In this method following equations have been used.
(i) Quality rating, [ ]100 ( )/( )n n i s iq V V V V= − − .
where, Vn = Actual amount present in polluted water on nth
parameter.
Vi = The ideal value of this parameter.
Vi = 0 for the suitable water except pH and DO
Vi = 7.0 mg/l for pH and Vi = 14.6 mg/l for DO.
Vs = Its standard.
(ii) Unit weight for various parameters is inversely proportional to the recommended standard
(Sn) for the corresponding parameters.
n
n
Kw
S
= ( nw = Unit weight)
11
1
1n
Si
K
V=
=
∑
( iSV = Standard value of its parameters)
K = constant of proportionality which is determined from the condition and K=1 for sake of
simplicity
(iii) Sub-indices, ( ) ( ) nw
n nSI q= .
(iv) The overall WQI was calculated by taking geometric mean of these sub-indices (SI)n.
WQI
21 21
=1 =1
Π ( ) Π ( )n n n
n n
SI q w= =
or,
WQI = Antilog10
21
10
1
logn n
n
w q
=
 
 
 
∑
Categories Water Quality Index
S1 Budhabalang river : 25.187 > 25

7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 2, February (2014), pp. 156-162, © IAEME
162
CONCLUSION
In this case study the relation between various parameters has been derived by using
correlation coefficient. As this is a statistical calculation there are more or less errors present, in spite
of errors this method is very important, because analysis of all parameters is very time consuming
and costly. To determine pollution load, it is a tough task every day. This method gives better
alternative. It reduces cost analysis as well as time. The important application of WQI could be
(i) identification and ranking of different activities for environmental degradation (ii) prioritization of
pollution prevention resources (iii) determination of seasonal changes in environmental indices[9].
REFERENCE
1. Patnaik, N., P.K. Mohapatra and G. Mishra, Correlations among water quality parameters of a
textile mill effluent, Indian Jour. Env. Protection, 10(6): 418-423 (1990).
2. Tewari, T.N. and Manzoor Ali, Correlations among water quality parameters of industrial
waters, Indian J. Env. Prot. 8(1): 44 (1988).
3. Kalyanaraman, S.B. and G. Geetha, Correlation analysis and prediction of characteristics
parameters and water quality index of ground water, Pollution Resource, 24(1): 197-200
(2005).
4. Achuthan Nair, G.I. Mohamad Abdullah and Moholy Fadiel Mahamoud, Physico-chemical
parameters and correlation coefficients of ground water on North-East Libya, Pull. Res.
24(1): 1-6 (2005).
5. T.N. Tiwari and M. Mishra, A preliminary assessment of WQI to major India rivers. Ind. J.
Env. Prot. 5(4): 276-279 (1985).
6. American Public Health Association, Standard Methods for the Examination of water and
waste water, 14th
ed. Washington, DC. American Water Works Association, 1976, p. 131.
7. A.D. Gavos, P.B. Lokhande and H.A. Mujawar, Charcterisation of waste water by correlation
and regression method, Ind. J. Env. Prot. 27(12), 1117-1128 (2007).
8. R.K. Patel and P.C. Mishra, Some aspects of the quality of water in and around Rourkela
(2005).
9. Alaka Panda and Nibedita Pattnayak, Costal Water Pollution Index-a tool assessing coastal
water quality along the North East Coast of India, IJSER, Vol.4, ISSUE 6, June-2013.
10. R. S. Sapkal and Dr. S. S. Valunjkar, “Development and Sensitivity Analysis of Water Quality
Index for Evaluation of Surface Water for Drinking Purpose”, International Journal of Civil
Engineering & Technology (IJCIET), Volume 4, Issue 4, 2013, pp. 119 - 134, ISSN Print:
0976 – 6308, ISSN Online: 0976 – 6316.