Predictive Modelling of Air Quality Index at Various Locations in Vishakhapatnam City, India

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1. Introduction

Air pollution had become one of the most important problems that the environment and general health is facing, as it is caused by the growing urbanisation and industrialisation around the world (Ghorani-Azam et al., 2016; Hilal & Rao, 2025) [7, 35]. Exposure to air pollutants causes both short-term and long-term health effects (Simu et al., 2020; Mathew et al., 2023) [28, 20]. Every year, obvious threats are caused to human health and the environment due to the air pollution, which costs in many lives lose (Manisalidis et al., 2020) [19]. In order to control air pollution, it is important to understand the nature of the pollutants and their sources. Based on the pollutant’s nature, the air pollutants could be classified into three categories: natural contaminants, aerosols, and gases and vapours. Natural fog, pollen, grains, and product of volcanic eruption are examples of natural contaminants, while, dust, smoke, mists, and fog, are examples of aerosols, and as an example for gases and vapours, Sulphur compounds, Nitrogen compounds, Oxygen compounds, could be included (Mitchell & Sweeney, 2018) [21]. Another classification based on the source of these pollutants is found, where the pollutants split into two types: primary, and secondary pollutants (Singh et al., 2025; Hilal & Rao, 2025) [29, 35]. The pollutants that are directly released from certain processes, and remain in the same form tat they are released in, are called primary pollutants, such as vehicle exhaust emissions. In the other hand, the pollutants that are generated due to chemical reactions including primary pollutants, are called secondary pollutants, for example the photochemical smog which is due to chemical reactions between weather factors and some air pollutants (Simu et al., 2020; Singh et al., 2025) [28, 29]. Every day a huge number of pollutants, such as CO, CO2, Particulate Matter (PM), NO2, SO2, O3, NH3, and Pb, which have a negative effect on the health of humans, animals, and plants, are released. These chemicals and pollutants are considered to be an important component of air pollution (Ghorani-Azam et al., 2016; Kumar & Pande, 2023) [7, 16]. The Air Quality Index (AQI) is designed to be a standard tool, aims to simplify the scientific information related to air pollution, and converts it into clearly and easily formula for public. Where this index is considered to be a useful tool to connect the complex quantitative data with the levels of potential health impact on human and environment (Beig. et al., 2010) [5]. It simplifies the complex data collected for various pollutants by transforming them into a single numerical value, a descriptive label, and a corresponding colour (Abas et al.,2024) [2]. According to the Andhra Pradesh Pollution Control Board, air quality refers to how suitable the air is for humans, plants, and animals to breathe. Poor air quality can harm health, the environment, the economy, and a city’s livability, affecting both current and future generations. Outdoor air pollution is an important environmental health problem impacting people in low-, middle-, and high-income countries. A healthy environment is an essential aspect of the right, for both humans and other animals, to live, which leads to the importance of the quality of outdoor air for well-being.

To get better outcomes and to understand the air quality metric, the components of air pollution and their interactions in the atmosphere must be understood. Tiny airborne particles together form the fine particulate matter, which can cause harm to health, such as respiratory diseases (Harrison, 2020) [9]. These particles can be classified due to their size into two groups: PM2.5 and PM10 (Kim et al., 2015) [13]. In addition to particulate matter, different gaseous pollutants such as nitrogen oxides (NOX), sulfur dioxide (SO2), carbon monoxide (CO), and VOCs also cause respiratory and environmental damage. Pollutants form from various human activities, such as daily, industrial, and commercial activities (Abas et al.,2024) [2].

In environmental studies, due to its complex interactions, machine learning becomes a very wide-ranging tool used for its analytical capabilities, especially in predicting air quality fields. Therefore, the handling and processing of large and heterogeneous dataset’s ability of machine learning makes it proper for forecasting the air quality index, besides capturing changes over time and area (Kang et al., 2018) [11]. ML models are chosen based on data and work requirements, where there are many kinds of ML methods, such as linear regression, decision trees, random forests, support vector machines, and neural networks (Saravanan & Sujatha, 2018) [27]. The air quality index measures air pollution based on different parameters using historical and real-time data, for example, PM2.5, PM10, NO2, and SO2. Therefore, for protecting public health and helping policy decision makers, ML methods have been used to forecast AQI accurately (Kumar & Pande, 2023) [16].

Since human health and the environment have become very essential in recent years. Thus, to know the effects of what one breathes, a lot of studies have discussed their effects on the health. West et al. (2016) [33] concentrated on the negative effects of pollutants emitted from several sources into the air, especially in developing countries. As well as the researchers must have a better understanding of the sophisticated physical and chemical characteristics of air pollutants. Studies by Ravindiran et al. (2023) [26] and Natarajan et al. (2024) [22] forecast AQI using different machine learning models in Indian cities, and compare the effectiveness of these models. Different researchers use the SPSS program and apply several models to predict air quality based on historical and real-time data of different factors, capturing the relationship between AQI and its influencing parameters (Ma et al., 2020; Abdullah et al., 2020) [3]. This study tests machine learning models (e.g., multivariate linear, nonlinear regression) for predicting AQI levels using various data, including meteorological and pollutant datasets. The performance of each model is compared with the official, calculated, and published AQI values by the government agencies. The study aimed to establish a predictive model in order to forecast the air quality index in the study area (the city of Visakhapatnam) by using historical and real time data, involving the pollutant concentrations (e.g., PM2.5, NO₂, CO), meteorological factors (e.g., temperature, precipitation and wind speed), and official and government-calculated AQI values. For assessing the models’ performance several metrics were used, and they are R-squared (R²), Adjusted R-squared, Standard Error of Estimate, Significance of Predictors (p-values), and Multicollinearity Check.

2. Study Area and Sampling

Visakhapatnam (also known as Vizag) is considered to be the largest and most populous metropolitan city in the Andhra Pradesh state, it takes a place between the Eastern Ghats and the coast of the Bay of Bengal, which gives it a special geographical location that combines both mountainous and costal properties (Rani, 2016) [25]. It is considered to be the second biggest city on the east coast of India after Chennai and the fourth in South India (Rani, 2016) [25]. The city coordinates lie between 17.7041 N and 83.2977 E. The city's area is 682 km². The average elevation is 45 meters (Tanuja & Sreenivasulu, 2023) [32]. Visakhapatnam is situated in the Coastal Andhra Region. It has a tropical climate with hot, humid summers and moderate winters. The year is divided into the following seasons: • Winter: includes of the months from December to February • Summer: includes of the months from March to May • Monsoon: includes of the months from June to September • Autumn: includes of the months from October to November By studying the city climate history, it is found that May is the hottest month of the city with average highs of 35°C and lows of 28°C. In contrast, December is the coldest month with average highs of 27°C and lows of 20°C. The officially calculated and reported Air Quality Index (AQI) values along with its affecting parameters, which were used as sample data from 2018 to 2024, were collected from available air quality datasets provided by government monitoring stations, which are the Andhra Pradesh Pollution Control Board (APPCB) and the Central Pollution Control Board (CPCB) websites. The data were from six manual and one continuous monitoring stations, and the GVMC is the continuous monitoring station. While the manually monitored stations include: • Industrial Estate, Autonagar • Mindi Gudivada Appanna Kalyanamandapam • Seethammadhar • Gnanapuram • Peda Gantyada • Raitu Bazar The data consisted of an average of 7,960 samples for each station, while the GVMC station consisted of 38,355 samples. The data was split into a 70:30 ratio as training and test data, respectively. The data was gathered from the government website and measured on an hourly basis. The data is converted into daily measurements in order to facilitate the calculation and analysis process by taking its average. The stations’ variables are SO2, NOx, PM10, PM2.5, NH3, Temperature, Precipitation, and Wind Speed. Meanwhile, the GVMC station contained extra parameters besides what were listed earlier, are NO, NO2, CO, O3, Benzene, and Toluene. The study was conducted to detect a predictive Air Quality Index (AQI) equation established from gathered data, which was converted into daily averages, and then divided into a 70:30 ratio as training and testing sets. According to the studies by Ma et al. (2020); Kumar & Pande, (2023) [16]; Ravindiran et al. (2023) [26]; Natarajan et al. (2024) [22], which used the same technique, the AQI values used in this study are officially calculated and reported by the relevant regulatory authorities, and are treated as reference values for evaluating the performance of the prediction models. This was done in order to achieve approximate with the highest possible accuracy.

3. Methodology

Out of SPSS statistical and machine learning characteristics, it was successfully used for the Air Quality Index prediction. In simple terms, SPSS (Statistical Package for the Social Sciences) can be defined as a statistical analysis, data mining, and management software tool. As well as, the program provides a simple interface that help users with minimal programming experience to perform different statistical tasks (Kaurav et al., 2020) [12]. SPSS supports data entry, preparation, visualization, and modelling, all these features make it suitable for all users whereas beginners or experienced researchers. According to that it is commolnly used in different fields, such as social science, business, and research (Keith et al., 2020; Kaurav et al., 2020) [12]. It also simplifies data preparation tasks like managing missing values by giving easy to apply features and commands (e.g., PM2.5, PM10, NO2). Different models, such as regression, decision trees, and neural network models, are supported to analyse relationships between air pollutants and weather variables (Keith et al., 2020).

Figure 1 spotlights the key steps included in the methodology.

Fig 1: The Methodology Flow Chart

3.1. Multivariate Linear Regression

Regression analysis is one of the important analytical models used to study and estimate the relationship between variables. This analyse aims to modeling the relationship in order to explain the variables attitude and predict its future values. It is widely use over different fields, such as engineering, physical and chemical sciences (Douglas et al., 2012). Multiple linear regression is an extend to simple linear regression, which aims to analyse the relationship between one dependent variable and multiple independent ones. This model is based on the basic principles of simple linear regression. But the main difference is to include more than one independent variables in the model, this allows for deeper understanding of the effect of each independent variable on the dependent variable, and controlling the impact of other variables (Song, 2018; Ma et al., 2020) [30]. The linear relationship between a single independent variable X and a dependent variable Y is described using a simple linear regression model, where the relationship is illustrated by a straight line (Douglas et al., 2012; Abdullah et al., 2020; Ma et al., 2020) [3]. The following equation represents the simple linear regression model:

➢ Y: Represents the value of dependent variable ➢ X: Represents the value of independent variable ➢ β0: Represents the regression line intercept ➢ β1: Represents the regression line slope ➢ ε: Represents the random error component, which accounts for the model failure of precisely fitting the data.

To extend simple linear regression, which uses a single independent variable, by incorporating multiple predictors, we get the Multiple Linear Regression (MLR) (Ma et al., 2020). The objective of it is to develop a mathematical model that captures the relationship between the dependent variable and the independent variables, enabling predictions of the dependent variable based on the values of the predictors (Song, 2018; Darman & Abd Hamid, 2024) [30, 6]. The general equation for multiple linear regression is provided below:

In formula (2), x1, x2,.., xp represent independent variables. Here, x1 represents for the value of SO2, x2 for NOX, x3 for PM10, x4 for PM2.5, x5 for NH3, x6 for Temperature, x7 for Precipitation, and x8 for Wind Speed.

If there are N samples, it is more appropriate to deal with multiple regression models if they are conveyed in matrix notation (Douglas et al., 2012; Song, 2018) [30], as shown by formula (3):

Therefore, the equation that represents the multivariate linear regression in a matrix form is as follows:

In multiple linear regression (sometimes called multivariate linear regression when involving one dependent variable and multiple independent variables), the error term Ɛ must meet specific assumptions to ensure the regression results are valid and meaningful (Ma et al., 2020).

3.2. Polynomial Regression Models

Since the relationship between AQI and pollutants, along with meteorological factors, does not always follow a linear pattern, we should seek an alternative model to develop a better equation for predicting AQI. The regression analyses that include more than one independent variable are known as Multiple regression. Polynomial regression technique is one type of Multiple regression; in this kind, the dependent variable is regressed against different powers of the independent variables (Ostertagová, E. 2012) [23]. The linear regression method, which is expressed by the simple equation y = βx + Ɛ, works as a general frame for fitting relationships that are linear in the unknown parameters β. This includes the significant category of polynomial regression models (Douglas et al., 2012). For example, a quadratic polynomial model in a single variable demonstrates this approach.

Which is also a linear regression model. Polynomials are extensively applied in scenarios where the response shows a curvilinear pattern, as they can effectively model even complicated nonlinear relationships within relatively narrow ranges of the x variables (Douglas et al., 2012).

3.3. Exponential Regression Models

An exponential model assumes that the dependent variable (e.g., AQI) grows or decays at a rate proportional to its current value (Douglas et al., 2012). A typical form might be:

• AQI: Dependent variable (Air Quality Index). • x: Independent variable (e.g., PM2.5, temperature). • β0: Base value • β1: Growth/decay rate. • ε: Random error.

In SPSS, the formula should be written in a simple exponential model, for example: b0 * EXP (b1 * PM2.5), where b0 represents β0 and b1 represents β1, and so on. In the parameter box, set the initial values for each parameter; this assists SPSS in starting the iteration process. After running the analysis, SPSS will estimate the parameters and provide output, including parameter estimates, standard errors, and fit statistics, so these results can be used to assess how much this model can fit the data and explain the relation between the variables. The analysis process would be rerun until a negative or positive variable estimations is found. This analysis supports the use of an exponential model, in order to understand and explain the nonlinear relationship between the air quality index (AQI) and its impacting factors. The use of this model is suitable in the cases that the variables show nonlinear correlation, and this enable the researcher to represent the cumulative or accelerated changes in the AQI as a response to the changes in the meteorological variables, such as, temperature, humidity, wind speed, etc. (Douglas et al., 2012).

3.4. Model Comparison

The final stage of the methodology is the systematic comparison between the analysis models after completing the analysis and estimating the variables. This stage is aimed to detect the most accurate and efficient model to interpret the relationship between variables. The comparison depends on analysing a group of statistical indicators that used for assessing the models and their suitability for the data, which helped in choosing the best model among all models. The used indicators for comparing include the following: First, R² shows the proportion of variance in AQI explained by the predictors (e.g., pollutants like PM2.5, NO2, etc.). Higher R² (closer to 1) indicates a better fit (Joseph et al.,2019). Secondly, the Standard Error of Estimate, which shows the average distance between the reference AQI values and the predicted values. A smaller standard error means more accurate prediction (Douglas et al., 2012). Thirdly, Significance of Predictors (p-values): Check it for each independent variable. If p < 0.05, the predictor is statistically significant (contributes meaningfully to AQI prediction)

(Pallant, 2020) [24]. Finally, the Multicollinearity Check (Variance Inflation Factor) should be less than 5 to be generally acceptable (Pallant, 2020) [24].

4. Results and Discussion

The predicted AQI values were compared with the official reference values using, calculated and published using standard statistical measures, to evaluate the predictive ability of the different models (Linear, Polynomial, and Exponential) used in this study, for predicting the Air Quality Index (AQI) over the monitoring stations in the city of Vishakhapatnam. For the illustrative and comparing purposes, Table 1 shows the equations of each model developed for each station.

The results of R-squared (R2), Adjusted R-squared (Adj. R2), Standard Error, significance levels (p-value), and VIF are the metrics used for the compression approach, are shown in Table 2.

Table 2: The comparison metrics of the models. Station Models R2 Adj. R2 Std. Error p-value VIF Industrial Estate, Autonagar Mindi Gudivada Appanna Kalyanamandapam Seethammadhara Gnanapuram Peda Gantyada Raitu Bazar GVMC Across the monitoring stations, and based on the comparison metrics, the polynomial model was found to give the best performance, holding the highest R2 and lowest standard errors compared with Linear and Exponential models. In contrast, the Exponential model has the weakest predictive ability.

Seethammadhara station has the strongest fit with the values of R2 = 0.944, Adj. R2 = 0.943, and std. error = 5.073. While GVMC shows the weakest performance with the values of R2 = 0.662, Adj. R2 = 0.660, and std. error = 32.204. VIF values for all the models were below 5, which means there are no multicollinearity problems, and p-values for all stations and for all models were below 0.05, which means all the predictors are statistically significant and contribute meaningfully to AQI.

These results point to the suitability of the Polynomial model to predict AQI and explain its variations across the stations.

5. Conclusion and Recommendations

This study aimed to improve a predictive model in Visakhapatnam for the Air Quality Index (AQI) using historical and real-time data acquired from pollution control websites of the Andhra Pradesh Pollution Control Board (APPCB) and the Central Pollution Control Board (CPCB). The objectives were to identify the key indicators affecting air quality. The relationships and interactions between these parameters and the AQI were analysed.

The analysis was built using SPSS software, and the model performance was compared using statistical indicators such as R-squared (R²), Adjusted R-squared, Standard Error of Estimate, significance levels (p-values), and multicollinearity tests. From the results gained earlier, the following conclusions were drawn.

The polynomial model was found to be the most effective model among the tested ones. This model detected that the relationship between AQI and its predictors is not completely linear and differs with seasonal changes, influenced by meteorological conditions. The selection of the best model was based on its ability to give a realistic and accurate estimation when compared to reference AQI values. The values of R² were as follows: (0.889, 0.937, 0.944, 0.900, 0.931, 0.703, and 0.662) respectively for the stations, while the adjusted R² values for the stations respectively were as follows: (0.888, 0.937, 0.943, 0.899, 0.930, 0.701, 0.660), which indicate a better fit.

6. Funding Declaration

There is no fund has received for any part of this research