Predicting PM2.5 in Urban and Suburban Beijing: A Comparative

Study of Random Forest and Linear Regression Models

Zhuoyang Zhou

Beijing Normal - Hong Kong Baptist University, Zhuhai, 519000, China

Keywords: PM2.5, Regression Model, Random Forest, Prediction Model.

Abstract: This study evaluates the performance of multiple linear regression (MLR) and random forest regression (RFR)

models in predicting PM2.5 concentrations across twelve air quality monitoring stations in Beijing, China,

using hourly meteorological and pollution data from 2013 to 2017. The analysis reveals that RFR significantly

outperforms MLR, with R² values improving from 0.11 to 0.22 (MLR) to 0.29–0.41 (RFR), demonstrating

better handling of non-linear interactions. However, both models exhibit critical limitations, particularly in

predicting extreme pollution events (PM2.5 > 300 µg/m³), where systematic underprediction occurs.

Geographical disparities in model accuracy are evident, with suburban stations (e.g., Dingling, Huairou)

exhibiting lower errors than urban-industrial sites (e.g., Dongsi, Aotizhongxin), likely due to the complexity

of emission sources and microclimates. Dew point temperature emerges as the most influential predictor,

while precipitation shows limited impact. These findings underscore the challenges in air quality forecasting

and advocate for localised, hybrid modelling approaches integrating real-time emission data to enhance

predictive reliability for public health applications.

1 INTRODUCTION

Air pollution, particularly that 2.5 microns or smaller

(PM2.5), seriously threatens the environment and

people's health worldwide. Air pollution, including

PM2.5, directly impacts people's health, which may

cause heart problems and breathing difficulties

(Brook et al., 2010). Additionally, it harms the setting

and the essence (Li et al., 2019). To better formulate

recommendations for cleaner environments and

lessen the damaging effects of air pollution, people

must be aware of how these issues impact PM2.5.

PM2.5 deposition in the air significantly impacts

weather conditions, such as temperature, humidity,

and wind speed. For instance, higher temperatures

can increase PM2.5, while higher humidity can make

it easier to create tiny antigens (Li et al., 2019; Perrino

et al., 2011). The drizzle of pollutants depends on

wind speed. PM2.5 particles are typically higher

because the air doesn't mix well when the wind blows

(Tai et al., 2010). PM2.5 costs may be accurately

predicted because of how connected these elements

are. Besides weather conditions, personal activities,

especially retreat-related, can drastically change

https://orcid.org/0009-0001-6098-6604

PM2.5. Individuals move more during holidays,

corporations may work differently, and more

situations take place, which may affect air quality.

For example, during major festivals like Chinese New

Year, there are fewer factory activities and cars on the

road, which makes the air fresh for a short time

(Wang et al., 2014; Wang et al., 2017).

On the other hand, trips that involve more travel

and tourism may produce more pollutants from

transportation and places to stay, leading to higher

levels of PM2.5 (Zhang et al., 2015). It is crucial to

understand how PM2.5 costs and air quality change.

Using this data, better air quality management

strategies can be created during the lively holidays.

Some studies have examined how PM2.5 prices,

weather conditions, and actions are connected in

various locations worldwide. In a study conducted in

Beijing, China, the wind's temperature, humidity, and

wind speed significantly impacted the amount of

PM2.5 provided. When the weather and the wind

were cooler, PM2.5 costs increased (Zhang et al.,

2017). A study in the United States found that

weather conditions played a key role in modifying

PM2.5 levels, with temperature and wind speed being

Zhou, Z.

Predicting PM2.5 in Urban and Suburban Beijing: A Comparative Study of Random Forest and Linear Regression Models.

DOI: 10.5220/0013825300004708

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy (IAMPA 2025), pages 331-336

ISBN: 978-989-758-774-0

331

the most important aspects (Perrino et al., 2011). Due

to the large number of people using lights and

increased traffic on the roads, a study in India found

that during the Diwali festival, the levels of harmful

PM2.5 in the air significantly increased (Guo et al.,

2014). When measuring PM2, these analyses

demonstrate that. 5, both weather conditions and

specific activities should be taken into account.

Despite numerous studies, People still aren't

aware of the relationship between PM2.5 levels,

temperature, and holidays. Most studies focused on

PM2's impact on a single cultural problem (Pope and

Dockery, 2006). Not many studies have examined

how various weather conditions interact with one

another to alter it (Pope & Dockery, 2006).

Moreover, people don't understand how weather

conditions and breaks affect PM2.5 (Wang et al.,

2017).

To remove these deficiencies, this study will

examine how PM2.5 charges relate to weather

conditions and falls in a particular area. The

assessment uses information on air quality and

weather conditions to observe how PM2.5 (a type of

air pollution) rates change over weather changes. To

improve air quality management and develop better

rules and regulations, the research may utilise

multiple linear regression analysis to examine the

effects of weather conditions.

Complex components, like the environment and

the lives of women, are affected by PM2.5 exposure.

Knowing how these factors affect PM2.5 rates is

crucial to making effective air quality management

strategies. This research hopes to raise the

consciousness by understanding how PM2.5 rates,

temperature, and holidays relate to a specific area.

Policymakers and professionals can comprehend

these issues because of this (Tai et al., 2010; Zhang et

al., 2015).

2 METHODOLOGY

2.1 Data Source and Description

The dataset used in this study was obtained from

Kaggle, comprising hourly air quality measurements

from twelve monitoring stations in Beijing, China,

spanning from March 1st, 2013, to February 28th,

2017.

2.2 Indicator Selection and Description

Meteorological variables-TEMP, DEWP, PRES, and

RAIN-were chosen as independent variables for their

established influence on PM2.5 dispersion and

formation (as showing in Table 1). For instance,

PM2.5 concentrations exhibit considerable

variability, with hourly readings ranging from 3 to

500 µg/m³, highlighting the severity of pollution

episodes. Temperature and dew point display

seasonal trends, while precipitation events are

sporadic but critical for pollutant scavenging. Table 1

lists all the variable names and their descriptions, and

ranges.

Table 1: Descriptions and ranges of variables

Variable Description Range

PM2.5 Fine particulate matter

concentration

(µg

/m³

)

2.0 to 999.0

TEMP Temperature (°C) -19.9 to 42.6

DEWP Dew point temperature (°C) -43.3 to 29.1

PRES Atmospheric pressure (hPa) 982.4 to 1042.8

RAIN Precipitation (mm) 0.0 to 72.5

2.3 Methodology

The analysis employs two regression techniques:

multiple linear regression (MLR) and random forest

regression (RFR).

Multiple Linear Regression (MLR): MLR

establishes baseline relationships between PM2.5 and

meteorological factors, providing interpretable

coefficients for each predictor. The model is

formulated as: PM2.5 = 𝛽



+ 𝛽



TEMP + 𝛽



DEWP + 𝛽



PRES + 𝛽



RAIN + 𝜖 , where 𝛽



the intercept, 𝛽



to 𝛽



are coefficients, and 𝜖 is the

error term.

Random Forest Regression (RFR): RFR, a

machine learning approach, captures non-linear

interactions and improves predictive accuracy. The

model uses bootstrap aggregation and random feature

selection, with hyperparameters (e.g., ntree = 500)

tuned via cross-validation to prevent overfitting. Key

advantages include handling non-linearity and

robustness to outliers. Normalisation was included to

address scale differences and remove missing values

(na.omit).

The analytical workflow began with a stratified

data approach. Each station's dataset was divided into

training (70%) and testing (30%) subsets. Both MLR

and RFR models were then trained on the training

subsets. This study used three evaluation indices (the

coefficient of determination (R²), root mean squared

error (RMSE) and mean absolute error (MAE)) to

compare the performance of MLR and RFR models

in predicting PM2.5 concentrations across Beijing's

monitoring stations.

IAMPA 2025 - The International Conference on Innovations in Applied Mathematics, Physics, and Astronomy

332

3 RESULTS AND DISCUSSION

3.1 Multiple Linear Regression

By using the R code, this paper constructs the

multiple linear regression model of the 12 stations.

The regression coefficients are shown in Table 2.

Table 2: Multiple Linear Regression Coefficients by

Station

Statio

Interc

PRES TEMP DEW

RAIN

Aotizh

ongxi

1407.

088

-1.243 -5.819 4.005 -3.686

Chang

1039.

030

-0.903 -4.621 3.260 -4.126

Dingli

1016.

191

-0.885 -4.611 3.342 -3.747

Dongs

2048.

266

-1.858 -6.647 4.300 -6.038

Guany

uan

1335.

387

-1.172 -5.770 4.047 -5.724

Guche

1373.

740

-1.208 -5.801 3.843 -6.324

Huair

490.3

-0.379 -3.600 2,885 -3.180

Nongz

hangu

1886.

982

-1.698 -6.840 4.300 -6.392

Shuny

1258.

115

-1.100 -5.488 3.907 -4.653

Tianta

1935.

161

-1.755 -6.278 3.960 -5.063

Wanli

1341.

457

-1.182 -5.534 3.722 -2.901

Wans

houxi

1889.

810

-1.705 -6.570 3.939 -6.647

From the results provided by the R code, this paper

can summarise the coefficient ranges and offer some

possible explanations for these results. The summary

will be shown in Table 3 below.

As table 3 shows, RAIN (mm) -6.65 to -3.18

Rainfall significantly reduces PM2.5, with urban

stations (e.g., Wanshouxigong) showing stronger

effects. This is possibly due to rain efficiently

depositing PM2.5.

Urban stations (e.g., Dongsi, Nongzhanguan)

exhibit larger coefficients for PRES, TEMP, and

RAIN, suggesting that meteorological factors play a

more pronounced role in PM2.5 variability in densely

populated areas. Suburban stations (e.g., Huairou,

Dingling) show weaker relationships, possibly due to

fewer local emissions and greater influence of

regional transport. Huairou Station has the smallest

coefficients (e.g., PRES: -0.38, TEMP: -3.60). This is

possibly because of its location in a rural,

mountainous area, which reduces the sensitivity of

PM2.5 to local weather.

Table 3. MLR Coefficient Ranges and Interpretations

Variables Range Explanation

Intercept 490.35

2048.27

Intercepts of PM2.5 are

significantly different from

station to station. Urban sites

(e.g., Dongsi, Nongzhanguan)

have higher intercepts, likely

due to more substantial local

emissions.

PRES

(hPa)

-1.86 to

-0.38

Higher atmospheric pressure

will lead to lower PM2.5. This

is possible because stable

weather conditions suppress

vertical spread. But the effect is

weaker in suburban stations.

TEMP

(°C)

-6.84 to

-3.60

Temperature has a negative

effect. This is possible because

warmer conditions enhance

atmospheric mixing, and

seasons have higher

temperatures, like summer

reduce coal heatin

emissions.

DEWP

(°C)

2.89 to

4.30

Higher dew point strongly

increases PM2.5. This is

possibly caused by moisture-

enhanced secondary aerosol

formation and stagnant air

masses.

RAIN

(mm)

-6.65 to

-3.18

Rainfall significantly reduces

PM2.5, with urban stations

(e.g., Wanshouxigong) showing

stronger effects. This is

possibly due to rain efficiently

depositing PM2.5.

Dongsi Station shows the strongest negative effect of

TEMP (-6.647), potentially linked to its central urban

setting, where temperature inversions trap pollutants.

The negative RAIN coefficients align with Beijing’s

observed "post-rain blue sky" phenomenon, where

precipitation removes particulate matter. The stronger

effect at urban stations (e.g., coefficient of -6.65 at

Wanshouxigong) may reflect higher initial PM2.5

concentrations available for wet deposition.

3.2 Random Forest Regression

This study also uses R code to construct a random

forest regression model (RFR) and calculate the

importance score (IncMSE) of these variables.

Predicting PM2.5 in Urban and Suburban Beijing: A Comparative Study of Random Forest and Linear Regression Models

333

Table 4: Variable Importance Score (IncMSE)

Variable

RAIN

(%)

DEWP

(%)

TEMP

(%)

PRES

(%)

Aotizhongxin 42.5 24.5 18.6 14.4

Changping 33.9 29.1 19.2 17.7

Din

lin

39.9 30.2 16.6 13.3

Don

si 38.3 24.2 19.2 18.3

Guan

uan 39.6 23.3 17.9 19.2

Gucheng 36.2 25.1 18.7 20

Huairou 32.9 26.5 20.9 19.8

Nongzhanguan 39.1 21.9 18.2 20.7

Shun

i 33.9 24.7 19.1 22.3

Tiantan 31 29.7 22.3 17

Wanliu 44.9 23 17.9 14.2

Wanshouxigong 40.9 24.4 18.5 16.2

The variable importance scores (IncMSE) from

Random Forest Regression reveal distinct patterns in

how meteorological factors influence PM2.5

concentrations across Beijing's monitoring stations

(Table 4). The results highlight both consistent trends

and notable spatial variations in atmospheric

processes affecting air quality. RAIN emerges as the

most important predictor at all stations (31.0-44.9%

importance), particularly at Wanliu (44.9%) and

Aotizhongxin (42.5%). This reflects Beijing's

reliance on wet deposition for particulate removal,

where precipitation effectively scavenges aerosols

from the atmosphere. The stronger effect at urban

stations suggests higher initial PM2.5 loading

available for removal. DEWP shows moderate

importance (21.9-30.2%), peaking at Dingling

(30.2%) and Tiantan (29.7%). This importance likely

represents moisture-enhanced secondary aerosol

formation and stagnant conditions during high

humidity episodes. TEMP (16.6-22.3%) and PRES

(13.3-22.3%) show more variable importance across

stations. For example, Tiantan station shows

unusually high TEMP importance (22.3%), possibly

due to its location near parks where temperature

inversions may trap pollutants.

Urban stations (Dongsi, Nongzhanguan) show

balanced importance across all variables. Suburban

stations (Huairou, Shunyi) display elevated PRES

importance (19.8-22.3%), suggesting the greater

influence of synoptic weather patterns. Wanliu

Station shows extreme RAIN dominance (44.9%)

with low DEWP importance (23.0%), possibly due to

its location near water bodies enhancing rain effects.

Tiantan Station has unusually high TEMP importance

(22.3%), potentially reflecting the urban heat island

effect in this cultural landmark area. Huairou Station

demonstrates the most balanced distribution,

consistent with its rural location, where no single

factor dominates.

The strong RAIN importance suggests that

weather modification (e.g., cloud seeding) could be

particularly effective during pollution episodes. High

DEWP importance indicates that humidity control

measures might help reduce secondary aerosol

formation. Urban stations may benefit most from

emission controls before forecasted precipitation

events. Suburban stations require more attention to

pressure systems and temperature variations.

The IncMSE results demonstrate that while

rainfall universally dominates PM2.5 variability

across Beijing, the relative importance of other

factors varies substantially by location. This spatial

heterogeneity underscores the need for tailored air

quality management strategies that account for local

meteorological sensitivities. The outlier behaviour at

stations like Wanliu and Tiantan suggests that

microclimate effects may significantly modify

pollution-weather relationships in specific urban

contexts. Future work should incorporate finer-scale

topographic and land-use data to better explain these

station-level differences.

3.3 Model Performance Metrics

Table 5 lists all the R², RMSE and MAE of the 12

stations. The evaluation metrics reveal several key

patterns in the performance of MLR and RFR models

across Beijing's air quality monitoring stations.

Both models show limited predictive power

overall, with test R² values ranging from 0.112-0.225

for MLR and 0.287-0.411 for RFR, indicating that

meteorological factors alone explain less than half of

PM2.5 variability. This suggests that additional

predictors like wind patterns, emission sources, or

temporal factors may be necessary for improved

accuracy. The RFR models consistently outperform

MLR in training data (R² 0.425-0.509 vs 0.117-

0.220), but this advantage diminishes in test data,

revealing moderate overfitting, particularly at stations

like Aotizhongxin where the train-test R² gap exceeds

0.12. This overfitting likely stems from the RFR's

complexity of capturing noise in the training data.

Spatial patterns in model performance reflect

Beijing's air pollution dynamics. Urban stations

(Dongsi, Nongzhanguan) show the highest R² values

for both models, with Nongzhanguan's RFR

achieving the best test performance (R²=0.406). This

urban advantage may result from stronger, more

consistent relationships between meteorological

conditions and local emissions in built-up areas. In

contrast, suburban stations like Huairou demonstrate

the poorest performance (test R²=0.287 for RFR),

IAMPA 2025 - The International Conference on Innovations in Applied Mathematics, Physics, and Astronomy

334

likely because regional transport of pollutants

weakens local weather-PM2.5 correlations.

Table 5: Model Performance Metrics (R²/RMSE/MAE)

Stati

del

rai

est

SE_

Trai

SE_

Test

E_T

rain

E_T

est

Aoti

zho

ngxi

0.1

74.0

74.5

53.9

53.

836

0.4

0.3

65.1

69.1

47.4

49.

970

Cha

ngpi

0.1

65.9

67.9

48.4

49.

303

0.4

0.3

56.2

61.5

41.0

44.

279

Din

glin

0.1

67.1

65.4

48.6

48.

192

0.4

0.3

56.7

59.0

40.9

43.

165

Don

gsi

0.2

76.7

55.8

55.

340

0.5

0.4

67.2

70.5

48.9

51.

219

Gua

nyu

0.1

73.0

72.5

52.9

52.

631

0.4

0.3

64.9

67.0

47.1

49.

145

Guc

hen

0.1

75.2

74.9

53.9

53.

742

0.4

0.3

65.9

68.7

47.5

49.

774

Hua

irou

0.1

67.2

66.2

49.2

48.

953

0.4

0.2

57.3

60.3

41.6

44.

030

Non

gzha

ngu

0.2

76.3

75.5

55.2

55.

291

0.5

0.4

67.0

69.7

48.3

51.

138

Shu

nyi

0.1

74.0

73.6

53.6

53.

561

0.4

0.3

64.3

67.3

46.4

48.

655

Tian

tan

0.2

72.2

71.3

52.2

52.

236

0.4

0.3

63.7

66.2

46.4

48.

765

Wan

liu

0.1

75.0

74.2

54.6

54.

362

0.4

0.3

66.8

68.8

48.6

50.

350

Wan

shou

xigo

0.2

76.7

76.6

54.9

55.

165

The models' relative performance varies spatially too-

at Dingling, RFR reduces test RMSE by 9.8%

compared to MLR, while at Wanshouxigong the

improvement is just 6.1%.

Notable anomalies include Dongsi station, where

MLR unexpectedly matches RFR's test performance

(R²=0.219 vs 0.411), suggesting linear relationships

may suffice at this urban location. Meanwhile,

Wanliu shows unusually poor RFR performance

despite its urban setting, possibly due to microclimate

effects from nearby water bodies. The consistent

MAE values (45-55 μg/m³ across stations) indicate

both models struggle with extreme PM2.5 events, a

critical limitation for pollution warning systems.

These results underscore that while RFR generally

outperforms MLR, its advantages are modest and

station-specific, highlighting the need for localised

model tuning in Beijing's heterogeneous airshed. The

persistent low R² values across all stations suggest

that effective PM2.5 forecasting requires

incorporating non-meteorological predictors like

real-time emission data.

4 CONCLUSION

This comprehensive evaluation of MLR and RFR

models for PM2.5 prediction across Beijing's

monitoring network yields several important insights

with significant implications for air quality

management. The analysis reveals that while both

models demonstrate limited predictive capability

using only meteorological variables, the Random

Forest approach consistently outperforms traditional

linear regression, albeit with notable spatial variations

in performance. The urban stations, particularly

Nongzhanguan and Dongsi, show relatively better

model performance (test R² up to 0.41), likely due to

a stronger coupling between local emissions and

meteorological conditions in densely populated areas.

In contrast, suburban stations like Huairou exhibit

poorer performance, suggesting that regional

pollutant transport and other non-local factors play a

more dominant role in these locations. The consistent

gap between training and test performance in RFR

models (average ΔR² of 0.12) indicates moderate

overfitting, emphasising the need for more robust

regularisation or inclusion of additional relevant

predictors.

The spatial patterns in model performance reflect

Beijing's complex air pollution dynamics, where

urban-scale processes appear more predictable than

regional-scale phenomena. The superior performance

of RFR models, particularly in urban settings,

Predicting PM2.5 in Urban and Suburban Beijing: A Comparative Study of Random Forest and Linear Regression Models

335

suggests that nonlinear relationships between

meteorological factors and PM2.5 concentrations are

important to capture. However, the modest absolute

performance levels (R² < 0.5 even for the best

models) strongly indicate that meteorological

variables alone are insufficient for accurate PM2.5

prediction. This limitation is particularly evident

during extreme pollution events, as shown by the

consistently high MAE values (45-55 μg/m³). The

station-specific variations in model performance,

such as the unexpectedly strong showing of MLR at

Dongsi or the poor RFR performance at Wanliu,

highlight the importance of localised model

development that accounts for microclimate effects

and unique station characteristics.

These findings have several important

implications for both research and air quality

management. First, they underscore the need to

incorporate additional predictors beyond basic

meteorological variables, particularly emission-

related indicators and wind pattern data. Second, they

suggest that different modelling approaches may be

warranted for different parts of the metropolitan area,

with more sophisticated techniques like RFR being

prioritised for urban core stations. Finally, the results

indicate that current models have limited capability in

predicting extreme pollution events, which should be

a focus area for future model improvement. Future

research directions should include testing more

advanced machine learning architectures,

incorporating real-time emission data, and

developing ensemble approaches that combine the

strengths of different modelling paradigms.

Ultimately, while meteorological factors provide a

useful foundation for PM2.5 prediction in Beijing,

significant improvements in forecasting accuracy will

require a more comprehensive approach that accounts

for the full range of physical and chemical processes

governing air pollution in this complex urban

environment.

REFERENCES

Brook, R. D., Rajagopalan, S., Pope, C. A., Brook, J. R.,

Bhatnagar, A., Diez-Roux, A. V., Holguin, F., Hong,

Y., Luepker, R. V., Mittleman, M. A., Peters, A.,

Siscovick, D., Smith, S. C., Whitsel, L., Kaufman, J. D.

2010. Particulate matter air pollution and

cardiovascular disease: An update to the scientific

statement from the American Heart Association.

Circulation, 121(21), 2331-2378.

Guo, H., Zhang, Q., Cheng, Y., He, K. 2014. The impact of

the Chinese New Year on air quality in China: A

review. Atmospheric Environment, 98, 647-656.

Li, J., Zhang, Y., Wang, X., Li, Z. 2019. The impact of the

Spring Festival on air quality in China: A review.

Environmental Pollution, 245, 707-718.

Perrino, C., Tiwari, S., Catrambone, M., Dalla Torre, S.,

Rantica, E., Canepari, S. 2011. Chemical

characterization of PM2.5 during the Diwali festival in

Delhi, India. Atmospheric Environment, 45(34), 6123-

6130.

Pope, C. A., Dockery, D. W. 2006. Health effects of fine

particulate air pollution: Lines that connect. Journal of

the Air & Waste Management Association, 56(6), 709-

742.

Tai, A. P. K., Mickley, L. J., Jacob, D. J. 2010. Correlations

between fine particulate matter (PM2.5) and

meteorological variables in the United States:

Implications for the sensitivity of PM2.5 to climate

change. Atmospheric Environment, 44(32), 3976-3984.

Wang, G., Zhang, R., Wang, L., Li, Z. 2014. Impact of

meteorological conditions on PM2.5 concentrations in

Beijing, China. Atmospheric Chemistry and Physics,

14(22), 12307-12322.

Wang, Y., Zhang, Q., Wang, L., Zhang, R., Li, Z. 2017. The

impact of meteorological factors on PM2.5

concentrations in urban areas: A case study in Beijing,

China. Atmospheric Environment, 165, 52-63.

Zhang, Q., Quan, J., Tie, X., Cao, J., Han, S., Wang, Z.,

Zhao, D., Li, J., Liu, X. 2015. The impact of

meteorological conditions on PM2.5 concentrations in

China: A review. Atmospheric Environment, 122, 823-

833.

Zhang, R., Wang, G., Zhang, Q., Li, Z. 2017. The impact of

holidays on air quality in China: A review.

Environmental Pollution, 231, 1234-1245.

IAMPA 2025 - The International Conference on Innovations in Applied Mathematics, Physics, and Astronomy

336