A Time Series Study of PM10 Pollutant in Ghaziabad City Using Multiple Linear Regression

A Time Series Study of PM10 Pollutant in Ghaziabad City Using Multiple Linear Regression | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Time Series Study of PM10 Pollutant in Ghaziabad City Using Multiple Linear Regression Lokesh kumar, Gaurav Kumar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3897109/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Air pollution has grown to be a serious issue in Ghaziabad, Uttar Pradesh. PM10, SO2, and NO2 are a few examples of air pollution constituents. The forecasting of these pollutants can help in the formulation of a strategy to decrease air pollution. This study analyzes the air toxin PM10 for the Khora Colony of Ghaziabad, Uttar Pradesh, utilizing data from previous years produced by the Uttar Pradesh Pollution Control Board. Multiple linear regression (MLR) is used for the analysis. Particulate Matter Air Pollution MLR Figures Figure 1 Figure 2 I. INTRODUCTION Poor air quality is one of the biggest environmental problems in urban areas around the world, especially in developing countries (Comrie, 1997 & Bhavsar, 2019). Since people's awareness of the potential dangers presented by chemical pollutants and their effects on the environment and human health have increased, air pollution has become a major concern in recent decades (Zaefizadeh et al, 2011 & Guo et al, 2020). Air pollution is the presence of one or more pollutants in the atmosphere over an extended period of time and in a quantity that is detrimental to the welfare or health of humans, animals, or plants (Gardner and Dorling, 1999). It could also refer to the atmospheric discharge of hazardous substances. There are many different types of air pollution. These substances are referred to as air pollutants (Shi et al, 1997 & Jef et al, 2005). Freeman (1974) created techniques for evaluating environmental resources including air pollution. The Indian Air Pollution Control Board keeps an eye on PM10, NO2, and SO2 levels. PM10 is the most hazardous of these three since it is the tiniest (Kumar, 2018). The government can use time series analysis to help create a plan to lower PM10. We have analyzed the PM10 applying time series in this paper. Time series define the study's ordering on a time scale. This may be used to environmental economics and financial forecasts, although it is most commonly utilized in scientific domains like signal processing and statistics. Time series analysis may be done using a variety of methods, such as the moving average approach, regression, the ANN method, and more (Kumar 2018). The regression approach is used in this study to create the time series model for PM10 prediction. II. METHODOLOGY One way to define the MLR model is as follows: $$Y={\beta }_{0}+{\beta }_{1}{X}_{1}+{\beta }_{2}{X}_{2}+{\beta }_{3}{X}_{3}+\dots +{\beta }_{p}{X}_{p}+\epsilon \left(1\right)$$ Where \(Y\) is dependent variable and \({X}_{1}\), \({X}_{2}\), \({X}_{3}\),…, \({X}_{p}\) are independent variables. Also \(\epsilon\) is the error term. Let \(X=\left({X}_{1},{X}_{2},{X}_{3},\dots ,{X}_{p}\right)\). Here, the following assumptions are made: Error distribution is normal. The error term's mean is zero. \(When j=1, 2, 3,\dots ,p\) then there is no correlation between \({X}_{j}\) and \(\epsilon .\) \(\text{F}\text{o}\text{r}\) non-random variable X the variance is finite. \(When j=\text{1,2},3,\dots ,p\) then there is no direct relationship between the independent variables \({X}_{j}\) The least squares method is used to evaluate the parameters \({ \beta }_{0}\), \({\beta }_{1}\), \({\beta }_{2}\), …,\({ \beta }_{p}\). 2.1 Calculation of Multiple Regression Let Y be the dependent variable and assume that \(q\) perceptions are accessible. Then let \({X}_{j} where j=\text{1,2},3,\dots ,p\) have \(p\) indicators. Assume that \({X}_{ij}\) is the \(i\) th level of indicator \({X}_{j}\) and \({Y}_{i}\) to be the \(i\) th reaction level of Y and after that, we can deal with our sample data, which includes \(q\) perceptions, as shown in Table 1 below: Table 1 Reaction Level and Indicators Perception No. \(i\) Reaction Level Y (\(p\)) Indicators \({X}_{1}\) \({X}_{2}\) … \({X}_{p}\) 1 \({Y}_{1}\) \({X}_{11}\) \({X}_{12}\) … \({X}_{1p}\) 2 \({Y}_{2}\) \({X}_{21}\) \({X}_{22}\) … \({X}_{2p}\) . . . . . . . . . . . . . . . . . . \(q\) \({Y}_{q}\) \({X}_{q1}\) \({X}_{q2}\) … \({X}_{qp}\) Using Eq. (1), we have $${Y}_{i}={\beta }_{0}+{\beta }_{1}{X}_{i1}+{\beta }_{2}{X}_{i2}+{\beta }_{3}{X}_{i3}+\dots +{\beta }_{p}{X}_{ip}+{\epsilon }_{i} , i=1, 2, 3,\dots , q$$ The least squares method may be used to determine the parameters. The dependent variable Y exhibits two different forms of variability: (1) explained and (2) unexplained. Sum of squares by regression (SSR) may also be used to determine the explained variability: SSR (Sum of squares by regression) =\(\sum _{i=1}^{q}{(\widehat{{y}_{i}}-\stackrel{-}{y})}^{2}\) Sum of squares by error (SSE) may be used to determine the unexplained variability: SSE (Sum of squares by error) =\(\sum _{i=1}^{q}{({y}_{i}-\widehat{y})}^{2}\) Hence, total variability (SST) in dependable variable Y ca be defined as: SST (Total variability) = SSR + SSE Hence, coefficient of determination \({R}^{2}\) =\(\frac{SSR}{SST}\)= \(\frac{SST-SSE}{SST}\) = 1-\(\frac{SSE}{SST}\) It implies that 0≤\({R}^{2}\)≤1 Now we can see that \({R}^{2}\) approaches 1 at the moment where SSR assumes values that are closer to SST. It suggests that the regression specifies the best model and accounts for a significant amount of the variability in Y. \({R}^{2}\)approaches 0 at the moment where SSE adopts values that are closer to SST. It indicates that the model is not very good and suggests that regression doesn't explain much of the variation in Y. When an independent variable is incorporated into the model, its value rises. This rise occurs independent of the additional explanatory (independent) variable's contribution. Because \({R}^{2}\)may be misleading, adjusted \({R}^{2}\)is supplied. Adjusted \({R}^{2}\) may be defined by: \({R}_{adj}^{2}=\) 1-\(\frac{SSE/(q-p-1)}{SST/(q-1)}\) Where \(p\) denotes the number of (explanatory) independent variables. One way to define standard error is \({S}_{YX}=\sqrt{SSE/(q-p-1)}\) III. TIME SERIES STUDY The time series analysis is completed using multiple linear regression and is defined as follows: $${A}_{q+1}=f({A}_{q}, {A}_{q-1},\dots ,{A}_{1})$$ Where \({A}_{1}\) , \({A}_{2}\) , \({A}_{3}\) , …, \({A}_{q}\) are regarded as inputs and \({A}_{q+1}\) is the output. The form of \(f\) above is created using multiple linear regression. The fourth information point is classified as the output, whereas the first three are considered the input. 3.1 Analyzing Data The Uttar Pradesh State Pollution Control Board gathers data for its website pertaining to the state's several metropolitan regions by screening information on three elements of air pollution: SO2, PM10 and NO2. At the Ghaziabad city's Khora colony, PM10 levels are estimated. The level has been crucial for the last few years. The city of Ghaziabad's air quality would also deteriorate with an increase in PM10 pollutant. For Khora colony in Ghaziabad, PM10 data from January 2019 to June 2023 has been collected for analysis. Summary of the data is shown in Fig. 1 : 3.2 Analysis of Regression Using SPSS software, we have created a linear regression model for the city of Ghaziabad. This study uses 47 information points in total. There are 44 groupings created from these data points. Each group has four information points. The fourth PM10 data point was taken as the output, while the first three were used as the input. Again, Neglecting the first information point, the next three information points are inputs and next in series is outputs. While P_OUTPUT is the designation for the output information point, P_A, P_B, and P_C are the initial three information points. The time series model that is shown below has been created: Table 2 Summary for the model b Model R R Square Adjusted R Square Standard Error of the Estimate Durbin-Watson 1 0.496 0.246 0.190 64.65752 1.883 a. Predictors are Constant, P_C, P_A, P_B b. Dependent Variable is P_OUTPUT Table 2 indicates that the variability of the independent variables is 49.6%. ANOVA results are displayed in Table 3 . Table 3 ANOVA a Model Sum of Squares df Mean Square F Sig. 1 Regression 54647.328 3 18215.776 4.357 .010 b Residual 167223.819 40 4180.595 Total 221871.147 43 a. Dependent Variable is P_OUTPUT b. Predictors are Constant, P_C, P_A, P_B Regression coefficients and t-test results are given in Table 4 . Table 4 Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B B Standard Error Beta Lower Bound Upper Bound 1 Constant 148.218 38.944 3.806 .000 69.508 226.927 P_A − .170 .154 − .171 -1.104 .276 − .481 .141 P_B − .075 .173 − .075 − .430 .669 − .425 .276 P_C .499 .157 .497 3.180 .003 .182 .816 a. Dependent Variable: P_OUTPUT Using Table 4 , the regression model may be defined as P_OUTPUT = 148.218 − 0.170*P_A-0.075*P_B + 0.499*P_C. Below Fig. 2 shows the actual and estimated values of PM10. IV. CONCLUSION Time series analysis is used to forecast the PM10 value for Ghaziabad, Uttar Pradesh, India. The time series model is produced using multiple linear regression. The independent factors were assessed as having 49.6% changeability, indicating that future PM10 levels may be somewhat predicted from past values. The model exhibits non-linearity. This problem may be solved using a variety of regression techniques, including log-linear and log-log. To deal with non-linearity, an ANN model can be created. Declarations * Ethics approval and consent to participate -Yes, i approve and give consent * Consent for publication -Yes, i give consent * Availability of data and material - http://www.uppcb.com/ambient_quality.htm * Competing interests -Not applicable * Funding -No funds, grants, or other support was received Author Contribution Mr. Lokesh Kumar wrote the manuscript and Dr. Gaurav Kumar has made the corrections. References Bhavsar R. (2019) “ Air Pollution Monitoring Using Artificial Neural Network”, International Journal of Scientific & Engineering Research , 10 (12), pp. 515-519 Comrie A.C. (1997) “Comparing Neural Networks and Regression Models for Ozone Forecasting”, Air & Waste Management Association , 47, pp. 653- 663. Freeman A. M. III , “Air pollution and property values, a further comment”, Review of Economics and Statistics , vol. 56, pp. 554– 556, Nov. 1974 Gardner M.W. and Dorling S.R. (1999) “Neural network modelling and prediction of hourly NOx and NO2 concentrations in urban air in London”, Atmospheric Environment , 33, pp. 709-719 Guo C., Liu G. and Chen C.H. (2020) “ Air Pollution Concentration Forecast Method Based on the Deep Ensemble Neural Network”, Hindawi Wireless Communications and Mobile Computing , Vol. 2020, Article ID 8854649, 13 pages Jef H., Clemens M., Gerwin D., Frans F. and Olivier B. (2005) “A neural network forecast for daily average PM10 concentrations in Belgium” Atmospheric Environment , 39, pp. 3279-3289 Kumar G. (2018) “Time series analysis of PM10 for Bulandhshahr Industrial Area in NCR using Multiple Linear Regression”, International Journal of Engineering Research and Development , 14 (3), pp. 56-62 Kumar G. (2018) “Time series analysis of PM10 for Noida Sector 1 Industrial Area in NCR using Multiple Linear Regression”, Bulletin of Pure and Applied Sciences, Section E-Math. & Stat ., 37 (2), pp. 273-277 Shi J. P. and Harrison R.M. (1997) “Regression modelling of hourly NOx and NO2 concentrations in urban air in London”, Atmospheric Environment , 31, pp. 4081-4094 Zaefizadeh M., Khayatnezhad M. and Gholamin R. (2011) “ Comparison of Multiple Linear Regressions (MLR) and Artificial Neural Network (ANN) in Predicting the Yield Using its Components in the Hulless Barley”, American-Eurasian Journal of Agricultural & Environmental Sciences , 10 (1), pp. 60-64 SPSS27 software , SPSS Inc., http://www.spss.com. Additional Declarations No competing interests reported. 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INTRODUCTION","content":"\u003cp\u003ePoor air quality is one of the biggest environmental problems in urban areas around the world, especially in developing countries (Comrie, 1997 \u0026amp; Bhavsar, 2019). Since people's awareness of the potential dangers presented by chemical pollutants and their effects on the environment and human health have increased, air pollution has become a major concern in recent decades (Zaefizadeh et al, 2011 \u0026amp; Guo et al, 2020). Air pollution is the presence of one or more pollutants in the atmosphere over an extended period of time and in a quantity that is detrimental to the welfare or health of humans, animals, or plants (Gardner and Dorling, 1999). It could also refer to the atmospheric discharge of hazardous substances. There are many different types of air pollution. These substances are referred to as air pollutants (Shi et al, 1997 \u0026amp; Jef et al, 2005). Freeman (1974) created techniques for evaluating environmental resources including air pollution. The Indian Air Pollution Control Board keeps an eye on PM10, NO2, and SO2 levels. PM10 is the most hazardous of these three since it is the tiniest (Kumar, 2018). The government can use time series analysis to help create a plan to lower PM10. We have analyzed the PM10 applying time series in this paper. Time series define the study's ordering on a time scale. This may be used to environmental economics and financial forecasts, although it is most commonly utilized in scientific domains like signal processing and statistics. Time series analysis may be done using a variety of methods, such as the moving average approach, regression, the ANN method, and more (Kumar 2018). The regression approach is used in this study to create the time series model for PM10 prediction.\u003c/p\u003e"},{"header":"II. METHODOLOGY","content":"\u003cp\u003eOne way to define the MLR model is as follows:\u003c/p\u003e\n\u003cdiv id=\"Equa\"\u003e\n \u003cdiv id=\"FileID_Equa\" name=\"EquationSource\"\u003e$$Y={\\beta }_{0}+{\\beta }_{1}{X}_{1}+{\\beta }_{2}{X}_{2}+{\\beta }_{3}{X}_{3}+\\dots +{\\beta }_{p}{X}_{p}+\\epsilon \\left(1\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhere \\(Y\\) is dependent variable and \\({X}_{1}\\), \\({X}_{2}\\), \\({X}_{3}\\),\u0026hellip;, \\({X}_{p}\\) are independent variables. Also \\(\\epsilon\\) is the error term. Let \\(X=\\left({X}_{1},{X}_{2},{X}_{3},\\dots ,{X}_{p}\\right)\\). Here, the following assumptions are made:\u003c/p\u003e\n\u003col\u003e\n \u003cli\u003e\n \u003cp\u003eError distribution is normal.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThe error term\u0026apos;s mean is zero.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003e\\(When j=1, 2, 3,\\dots ,p\\) then there is no correlation between \\({X}_{j}\\) and \\(\\epsilon .\\)\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003e\\(\\text{F}\\text{o}\\text{r}\\) non-random variable X the variance is finite.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003e\\(When j=\\text{1,2},3,\\dots ,p\\) then there is no direct relationship between the independent variables \\({X}_{j}\\)\u003c/p\u003e\n \u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThe least squares method is used to evaluate the parameters \\({ \\beta }_{0}\\), \\({\\beta }_{1}\\), \\({\\beta }_{2}\\), \u0026hellip;,\\({ \\beta }_{p}\\).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.1 Calculation of Multiple Regression\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eLet Y be the dependent variable and assume that \\(q\\) perceptions are accessible. Then let \\({X}_{j} where j=\\text{1,2},3,\\dots ,p\\) have \\(p\\) indicators. Assume that \\({X}_{ij}\\) is the \\(i\\)\u003csup\u003eth\u003c/sup\u003e level of indicator \\({X}_{j}\\) and \\({Y}_{i}\\) to be the \\(i\\)\u003csup\u003eth\u003c/sup\u003e reaction level of Y and after that, we can deal with our sample data, which includes \\(q\\) perceptions, as shown in Table 1 below:\u003c/p\u003e\n\u003cdiv\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 1\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eReaction Level and Indicators\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003ePerception No.\u003c/p\u003e\n \u003cp\u003e\\(i\\)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eReaction Level\u003c/p\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003e(\\(p\\)) Indicators\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\\({X}_{1}\\)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\\({X}_{2}\\)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026hellip;\u003c/strong\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\\({X}_{p}\\)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({Y}_{1}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({X}_{11}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({X}_{12}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026hellip;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({X}_{1p}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({Y}_{2}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({X}_{21}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({X}_{22}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026hellip;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({X}_{2p}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\(q\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({Y}_{q}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({X}_{q1}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({X}_{q2}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026hellip;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\\({X}_{qp}\\)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eUsing Eq.\u0026nbsp;(1), we have\u003c/p\u003e\n\u003cdiv id=\"Equb\"\u003e\n \u003cdiv id=\"FileID_Equb\" name=\"EquationSource\"\u003e$${Y}_{i}={\\beta }_{0}+{\\beta }_{1}{X}_{i1}+{\\beta }_{2}{X}_{i2}+{\\beta }_{3}{X}_{i3}+\\dots +{\\beta }_{p}{X}_{ip}+{\\epsilon }_{i} , i=1, 2, 3,\\dots , q$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe least squares method may be used to determine the parameters.\u003c/p\u003e\n\u003cp\u003eThe dependent variable Y exhibits two different forms of variability: (1) explained and (2) unexplained.\u003c/p\u003e\n\u003cp\u003eSum of squares by regression (SSR) may also be used to determine the explained variability:\u003c/p\u003e\n\u003cp\u003eSSR (Sum of squares by regression) =\\(\\sum _{i=1}^{q}{(\\widehat{{y}_{i}}-\\stackrel{-}{y})}^{2}\\)\u003c/p\u003e\n\u003cp\u003eSum of squares by error (SSE) may be used to determine the unexplained variability:\u003c/p\u003e\n\u003cp\u003eSSE (Sum of squares by error) =\\(\\sum _{i=1}^{q}{({y}_{i}-\\widehat{y})}^{2}\\)\u003c/p\u003e\n\u003cp\u003eHence, total variability (SST) in dependable variable Y ca be defined as:\u003c/p\u003e\n\u003cp\u003eSST (Total variability)\u0026thinsp;=\u0026thinsp;SSR\u0026thinsp;+\u0026thinsp;SSE\u003c/p\u003e\n\u003cp\u003eHence, coefficient of determination \\({R}^{2}\\) =\\(\\frac{SSR}{SST}\\)= \\(\\frac{SST-SSE}{SST}\\) = 1-\\(\\frac{SSE}{SST}\\)\u003c/p\u003e\n\u003cp\u003eIt implies that 0\u0026le;\\({R}^{2}\\)\u0026le;1\u003c/p\u003e\n\u003cp\u003eNow we can see that \\({R}^{2}\\) approaches 1 at the moment where SSR assumes values that are closer to SST. It suggests that the regression specifies the best model and accounts for a significant amount of the variability in Y. \\({R}^{2}\\)approaches 0 at the moment where SSE adopts values that are closer to SST. It indicates that the model is not very good and suggests that regression doesn\u0026apos;t explain much of the variation in Y. When an independent variable is incorporated into the model, its value rises. This rise occurs independent of the additional explanatory (independent) variable\u0026apos;s contribution. Because \\({R}^{2}\\)may be misleading, adjusted \\({R}^{2}\\)is supplied.\u003c/p\u003e\n\u003cp\u003eAdjusted \\({R}^{2}\\) may be defined by:\u003c/p\u003e\n\u003cp\u003e\\({R}_{adj}^{2}=\\) 1-\\(\\frac{SSE/(q-p-1)}{SST/(q-1)}\\)\u003c/p\u003e\n\u003cp\u003eWhere \\(p\\) denotes the number of (explanatory) independent variables.\u003c/p\u003e\n\u003cp\u003eOne way to define standard error is \\({S}_{YX}=\\sqrt{SSE/(q-p-1)}\\)\u003c/p\u003e"},{"header":"III. TIME SERIES STUDY","content":"\u003cp\u003eThe time series analysis is completed using multiple linear regression and is defined as follows:\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$${A}_{q+1}=f({A}_{q}, {A}_{q-1},\\dots ,{A}_{1})$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({A}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({A}_{2}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({A}_{3}\\)\u003c/span\u003e\u003c/span\u003e, \u0026hellip;, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({A}_{q}\\)\u003c/span\u003e\u003c/span\u003e are regarded as inputs and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({A}_{q+1}\\)\u003c/span\u003e\u003c/span\u003e is the output.\u003c/p\u003e \u003cp\u003eThe form of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(f\\)\u003c/span\u003e\u003c/span\u003e above is created using multiple linear regression.\u003c/p\u003e \u003cp\u003eThe fourth information point is classified as the output, whereas the first three are considered the input.\u003c/p\u003e \u003cp\u003e \u003cb\u003e3.1 Analyzing Data\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe Uttar Pradesh State Pollution Control Board gathers data for its website pertaining to the state's several metropolitan regions by screening information on three elements of air pollution: SO2, PM10 and NO2. At the Ghaziabad city's Khora colony, PM10 levels are estimated. The level has been crucial for the last few years. The city of Ghaziabad's air quality would also deteriorate with an increase in PM10 pollutant. For Khora colony in Ghaziabad, PM10 data from January 2019 to June 2023 has been collected for analysis. Summary of the data is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e3.2 Analysis of Regression\u003c/b\u003e \u003c/p\u003e \u003cp\u003eUsing SPSS software, we have created a linear regression model for the city of Ghaziabad. This study uses 47 information points in total. There are 44 groupings created from these data points. Each group has four information points. The fourth PM10 data point was taken as the output, while the first three were used as the input. Again, Neglecting the first information point, the next three information points are inputs and next in series is outputs. While P_OUTPUT is the designation for the output information point, P_A, P_B, and P_C are the initial three information points. The time series model that is shown below has been created:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary for the model \u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR Square\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAdjusted R Square\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eStandard Error of the Estimate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDurbin-Watson\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e64.65752\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.883\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003ea. Predictors are Constant, P_C, P_A, P_B\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eb. Dependent Variable is P_OUTPUT\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e indicates that the variability of the independent variables is 49.6%.\u003c/p\u003e \u003cp\u003eANOVA results are displayed in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eANOVA \u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSum of Squares\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMean Square\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003eSig.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRegression\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e54647.328\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e18215.776\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.357\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e.010\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eResidual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e167223.819\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4180.595\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e221871.147\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003ea. Dependent Variable is P_OUTPUT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c8\" namest=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003eb. Predictors are Constant, P_C, P_A, P_B\u003c/p\u003e \u003cp\u003eRegression coefficients and t-test results are given in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c8\" namest=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCoefficients \u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eUnstandardized Coefficients\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eStandardized Coefficients\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003et\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSig.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e95% Confidence Interval for B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStandard Error\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBeta\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eLower Bound\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eUpper Bound\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eConstant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e148.218\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e38.944\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e69.508\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e226.927\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP_A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.170\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.154\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.171\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.104\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.276\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.481\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.141\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP_B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.173\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.669\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.425\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.276\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP_C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.499\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.157\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.182\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.816\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003ea. Dependent Variable: P_OUTPUT\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eUsing Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the regression model may be defined as\u003c/p\u003e \u003cp\u003eP_OUTPUT\u0026thinsp;=\u0026thinsp;148.218\u0026thinsp;\u0026minus;\u0026thinsp;0.170*P_A-0.075*P_B\u0026thinsp;+\u0026thinsp;0.499*P_C.\u003c/p\u003e \u003cp\u003eBelow Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the actual and estimated values of PM10.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"IV. CONCLUSION","content":"\u003cp\u003eTime series analysis is used to forecast the PM10 value for Ghaziabad, Uttar Pradesh, India. The time series model is produced using multiple linear regression. The independent factors were assessed as having 49.6% changeability, indicating that future PM10 levels may be somewhat predicted from past values. The model exhibits non-linearity. This problem may be solved using a variety of regression techniques, including log-linear and log-log. To deal with non-linearity, an ANN model can be created.\u003c/p\u003e"},{"header":"Declarations","content":" \u003cp\u003e \u003cb\u003e* Ethics approval and consent to participate -Yes, i approve and give consent\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e* Consent for publication -Yes, i give consent\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e* Availability of data and material -\u003c/b\u003e \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://www.uppcb.com/ambient_quality.htm\u003c/span\u003e\u003cspan address=\"http://www.uppcb.com/ambient_quality.htm\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e \u003cb\u003e* Competing interests -Not applicable\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e* Funding -No funds, grants, or other support was received\u003c/b\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eMr. Lokesh Kumar wrote the manuscript and Dr. Gaurav Kumar has made the corrections.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003e\u003cstrong\u003eBhavsar R. (2019) \u0026ldquo;\u003c/strong\u003eAir Pollution Monitoring Using Artificial Neural Network\u0026rdquo;, \u003cem\u003eInternational Journal of Scientific \u0026amp; Engineering Research\u003c/em\u003e, 10 (12), pp. 515-519\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eComrie A.C. (1997)\u003c/strong\u003e \u0026ldquo;Comparing Neural Networks and Regression Models for Ozone Forecasting\u0026rdquo;, \u003cem\u003eAir \u0026amp; Waste Management Association\u003c/em\u003e, 47, pp. 653- 663.\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eFreeman A. M. III\u003c/strong\u003e, \u0026ldquo;Air pollution and property values, a further comment\u0026rdquo;, \u003cem\u003eReview of Economics and Statistics\u003c/em\u003e, vol. 56, pp. 554\u0026ndash; 556, Nov. 1974\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eGardner M.W. and Dorling S.R. (1999)\u003c/strong\u003e \u0026ldquo;Neural network modelling and prediction of hourly NOx and NO2 concentrations in urban air in London\u0026rdquo;, \u003cem\u003eAtmospheric Environment\u003c/em\u003e, 33, pp. 709-719\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eGuo C., Liu G. and Chen C.H. (2020) \u0026ldquo;\u003c/strong\u003eAir Pollution Concentration Forecast Method Based on the Deep Ensemble Neural Network\u0026rdquo;, \u003cem\u003eHindawi Wireless Communications and Mobile Computing\u003c/em\u003e, Vol. 2020, Article ID 8854649, 13 pages\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eJef H., Clemens M., Gerwin D., Frans F. and Olivier B. (2005)\u003c/strong\u003e \u0026ldquo;A neural network forecast for daily average PM10 concentrations in Belgium\u0026rdquo; \u003cem\u003eAtmospheric Environment\u003c/em\u003e, 39, pp. 3279-3289\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eKumar G. (2018)\u003c/strong\u003e \u0026ldquo;Time series analysis of PM10 for Bulandhshahr Industrial Area in NCR using Multiple Linear Regression\u0026rdquo;, \u003cem\u003eInternational Journal of Engineering Research and Development\u003c/em\u003e, 14 (3), pp. 56-62\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eKumar G. (2018)\u003c/strong\u003e \u0026ldquo;Time series analysis of PM10 for Noida Sector 1 Industrial Area in NCR using Multiple Linear Regression\u0026rdquo;, \u003cem\u003eBulletin of Pure and Applied Sciences, Section E-Math. \u0026amp; Stat\u003c/em\u003e., 37 (2), pp. 273-277\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eShi J. P. and Harrison R.M. (1997)\u003c/strong\u003e \u0026ldquo;Regression modelling of hourly NOx and NO2 concentrations in urban air in London\u0026rdquo;, \u003cem\u003eAtmospheric Environment\u003c/em\u003e, 31, pp. 4081-4094\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eZaefizadeh M., Khayatnezhad M. and Gholamin R. (2011) \u0026ldquo;\u003c/strong\u003eComparison of Multiple Linear Regressions (MLR) and Artificial Neural Network (ANN) in Predicting the Yield Using its Components in the Hulless Barley\u0026rdquo;, \u003cem\u003eAmerican-Eurasian Journal of Agricultural \u0026amp; Environmental Sciences\u003c/em\u003e, 10 (1), pp. 60-64\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eSPSS27 software\u003c/strong\u003e, SPSS Inc., http://www.spss.com.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Particulate Matter, Air Pollution, MLR","lastPublishedDoi":"10.21203/rs.3.rs-3897109/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3897109/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAir pollution has grown to be a serious issue in Ghaziabad, Uttar Pradesh. PM10, SO2, and NO2 are a few examples of air pollution constituents. The forecasting of these pollutants can help in the formulation of a strategy to decrease air pollution. This study analyzes the air toxin PM10 for the Khora Colony of Ghaziabad, Uttar Pradesh, utilizing data from previous years produced by the Uttar Pradesh Pollution Control Board. Multiple linear regression (MLR) is used for the analysis.\u003c/p\u003e","manuscriptTitle":"A Time Series Study of PM10 Pollutant in Ghaziabad City Using Multiple Linear Regression","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-08 16:38:59","doi":"10.21203/rs.3.rs-3897109/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bd676e83-641b-4170-b067-aa4688ed6220","owner":[],"postedDate":"March 8th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-03-25T14:12:08+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-08 16:38:59","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3897109","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3897109","identity":"rs-3897109","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}