Association rules and regression linear model of the groundwater population by the evaluation of uranium

. The uranium available more on groundwater samples of certain types on the total alkalinity were relatively the same. But, the content of the uranium was higher in the samples. The multiple linear regression for pH as a dependent variable showed that the pH negatively correlated to the uranium, but the uranium was not significant for the linear regression model. The data of groundwater population from the samples of 127 with 12 variables of measurement of the Energy Department of the United States of America resulted in those association rules and linear regression models. The data has five factors of Producing horizon namely Ogallala Formation (TPO), Dockum Formation (TRD), Quartermaster Group (POQ), Whitehorse and Cloud Chief Group (PGWC), El Reno Group and Blaine Formation (PGEB). The step-wise linear regression for each of the five producing horizon codes was fitted to the data. Then, the regression models for each variable of producing horizon were obtained if pH was the dependent variable. If the Uranium was a dependent variable, then the regression models obtained were four only, with the model for PGEB was not able to be made. When pH as a dependent variable, it was depended upon Boron, Total alkalinity, and Bicarbonate.


Introduction
Uranium is a naturally occurring alpha-emitting radionuclide and plausible human carcinogen [1]. Uranium is a radioactive metal that occurs in low concentration in nature [2]. It is present in certain types of soils and rocks, especially granites [2]. The interim maximum acceptable concentration of uranium in drinking in Health Canada's Guidelines for Canadian Drinking Water Quality is 0.020 mg/L (milligrams perlitre) [2]. Rural areas are depended heavily on groundwater sources approximately 40% of South Carolina (SC) residents regularly use ground-water as their primary drinking water sources [3]. Results from ecological investigation [4] suggested that colorectal, breath, kidney, and total cancer incidences may be elevated in areas with frequent groundwater use and elevated groundwater uranium. Uranium persists in the groundwater at former mining sites [5].

Methodology
The methodology of association rules and stepwise regression were applied for data analysis. Association rules are an important class of regularities that exist in databases. Since association rules were first introduced by [6], the problem of mining associations has received a great deal of attention. The classic application is market basket analysis, it is analysis how the items purchased by customers are associated. An example of an association rule is as follows: Roticanai ---> tehtarik [sup = 10%, conf = 80 %] This rule says that 10% of customers buy roticanai and tehtarik together, and those who buy roticanai also buy tehtarik 80% of the time [7].
Stepwise regression is a semi-automated process of building a model by successively adding or removing variables based solely on the t-statistics of their estimated coefficients. Properly used, the stepwise regression [8] option in Statgraphics (or other stat packages) puts more power and information at your fingertips than does the ordinary multiple regression option, and it is especially useful for sifting through large numbers of potential independent variables and/or fine-tuning a model by poking variables in or out. Improperly used, it may converge on a poor model while giving you a false sense of security. It's like doing carpentry with a chainsaw: you can get a lot of work done quickly, but it leaves rough edges and you may end up cutting off your own foot if you don't read the instructions, remain sober, engage your brain, and keep a firm grip on the controls. It is not a tool for beginners or a substitute for education and experience. The association rules could not uncover the relation between uranium and other variables [9], and also it mentioned that pH had correlated negatively to uranium, and in the linear regression when pH is a dependent variable, the existence of uranium was not significant [9]. However, Uranium much more available on groundwater samples of PGEB > POQ > TRD > PGWC > TPO, where PGEB was El Reno Group and Blaine Formation, POQ was Quartermaster Group, TRD was Dockum Formation, the lay out of the data is as follows [10] In [11]: PGWC was Whitehorse and Cloud Chief Group, and TPO was Ogallala Formation. In this paper, the step-wise linear regression was applied where the independent variables were pH and Uranium. The association rules were also applied.
Where P_GC is Producing Horizon, U is Uranium, AS is Arsenic, B is Boron, BA is Barium, MO is Molybdenum, SE is Selenium, V is Vanadium, SO4 is Sulfate, T_AK is Total Alkaninity, BC is Bicarbonate, CT is Conductivity, pH is an indicator for solution, whether acid or alkaline. The association rules on Table 2 was not uncover the involvement of Uranium. As seen on  The five regression models on Table 3 and 4 are as follows: All the models have its pH as dependent variable, the first model is for producing code of TPO as follows: The regression model indicated that the pH in the groundwater samples of the Producing Horizon code of TPO (Ogallala Formation) is depended upon the element of Boron. The second for producing code of TRD as follows: indicated that the pH in the groundwater samples of Producing horizon code of TRD is depended upon Boron and Conductivity (CT). However, pH and CT are negatively correlated. It can be seen in the equation (2) that if the CT increased in one unit, then the pH will decrease by 0.261.
The third is for POQ as follows: The equation (4) indicated that pH is negatively correlated either to CT or to T_Ak. However, pH is positively correlated to either Boron or Bicarbonate (BC) as it can be seen on the coefficients of B (Boron) and BC.
The fifth is for PGEB as follows: The equation (5) indicated that the pH is negatively correlated to the T_Ak (total alkanity). The equation (1) until (5)   The coefficient of T_AK is -3.95, it meant the it has a negative correlation to the pH. Moreover, if we take a look at the Model which also stratified by it producing horizon codes when the Uranium as an independent variable, and After operating the step-wise regression onto the data, then the results is as seen on the Table 6.  The Uranium regression model of Producing Horizon of PGEB was not created by the SPSS Software. Perhaps, the data related to this PGEB suffered singularity in its variancecovariance matrix, then it could not be found the coefficients of each parameter.
As seen on Table 7 and 8 that all four models were significant for every code of Producing horizon where the adjusted R square is different in accordance with the producing horizon code. However, biggest and involving more variables, such as: Constant, MO, SO4, T_AK, B.
Where, U is Uranium. MO is Molybdenum. SO4 is Sulfate. T_AK is Total Alkalinity. B is Boron. The interpretation of equation (8) is that the Uranium was depended upon the existence of Molybdenum, Sulfate, Total Alkalinity, and Boron. However, the Uranium has negative correlation with Boron. Over the last halfcentury, uranium has become one of the most sought-after minerals on the planet due to from energy to healthcare, this revolutionary substance has applications in a variety of industries. As such, let's take a few moments to consider the uranium mining and extraction process as well as its immense value throughout the world [10].
In Canada [12], Uranium was available in Natural and fortified water as the trace elements in water as also available [12] in Natural Sediments and Soils as trace elements in sediments along with Molybdenum. Most volcanogenic uranium deposits are deeply buried and very hard to locate. A prospecting method using geoelectrochemical probes has been proven in practice to be an effective way of pinpointing the locations of these hidden deep uranium deposits. The efficacy of the method has been verified through analyses of two carefully selected known uranium deposits: the Xiangshan and Shenyuan uranium deposits in southeastern China [13].
Analyses of geoelectrochemical probe samples presented in transections crossing the ore bodies revealed distinct anomalies of U and Mo distribution [13]. A recent study led by scientists at the Department of Energy's SLAC National Accelerator Laboratory helps describe how the contaminant cycles through the environment at former uranium mining sites and why it can be difficult to remove. Contrary to assumptions that have been used for modeling uranium behavior, researchers found the contaminant binds to organic matter in sediments. The findings provide more accurate information for monitoring and remediation at the sites. Decades after a uranium mine was shuttered, the radioactive element can stills persists in groundwater at the site, despite cleanup efforts [5].