RPubs link information

• Rpubs link: https://rpubs.com/fernandojt13/1357141

Introduction

• Air pollution is a major global health concern.
• Economic development often correlates with industrialization and energy consumption.
• This project investigates the relationship between a country’s economic development (GDP) and its average air pollution (PM2.5) levels.
• Understanding this relationship can help navigate environmental policies and sustainable development strategies.

Introduction Cont.

• Fine particulate matter (PM2.5) is a widely used indicator of air pollution.
• Common sources of PM2.5 particles include car and truck exhausts, coal-fired power stations, industry, smoke from fires and smoke from wood heaters.
• World Health Organization (WHO) recommends an annual average of no more than \(5\) \(g/m^{3}\) and a 24-hour average not to exceed \(15\) \(g/m^{3}\) for more than 3-4 days a year.
• GDP (Gross Domestic Product) is a widely used indicator of global wealth/development.
• Countries can be grouped as low GDP (below $200 billion), medium GDP ($200 billion – $1 trillion), and high GDP (above $1 trillion) based on the total value of goods and services produced annually.
• We explore whether countries with higher PM2.5 exposure tend to differ in development, evaluated by GDP (constant 2015 US$).
• The goal of the project is to use open data to statistically analyze the link between a country’s wealth/development (measured by GDP) and its environmental quality (measured by PM2.5 exposure).

Problem Statement

• We aim to answer two primary questions:

1. Regression Analysis: Is there a significant linear relationship between a country’s GDP and its mean annual PM2.5 exposure?
2. Hypothesis Testing: Is the mean air pollution level significantly different between countries with high GDP and those with low GDP?

Data

• The data was sourced from the World Bank’s open data platform, where GDP and PM2.5 variables were manually filtered and extracted for analysis.
• Secondary data collection is used, as the study relies on pre-existing global datasets from the World Bank rather than collecting primary samples.
• Data are country-level aggregates compiled from national agencies.
• The data can be obtained from : https://databank.worldbank.org/source/world-development-indicators#

Data Cont.

• Dataset Details:
  • Year of Analysis: We will focus on the data for 2020 as it is the most recent year with complete data for both variables of interest across the widest range of countries.
• Variables:

1. GDP (constant 2015 US$) : This is a numerical variable representing a country’s economic output, adjusted for inflation. It is our measure of economic development.
2. PM2.5 air pollution, mean annual exposure (\(\mu\text{g/m}^3\)) : This is a numerical variable representing the average concentration of fine particulate matter (PM2.5) that a country’s population is exposed to. It is our measure of air pollution.

Data Preprocessing

read_csv("dataset.csv") %>%
  filter(`Series Code` %in% c("NY.GDP.MKTP.KD", "EN.ATM.PM25.MC.M3")) %>%
  mutate(v2020 = readr::parse_number(na_if(`2020 [YR2020]`, ".."))) %>%
  select(`Country Name`, `Country Code`, `Series Code`, v2020) %>%
  pivot_wider(names_from = `Series Code`, values_from = v2020) %>%
  filter(!is.na(`Country Code`) & grepl("^[A-Z]{3}$", `Country Code`)) ->
  data2020_ready

• Filtered Dataset to 2020: Focused analysis on data from the year 2020 only.

• Selected Key Indicators: Retained GDP (constant 2015 US$) and PM2.5 air pollution (µg/m³).

• Removed Irrelevant Columns: Dropped unused year columns (2018–2024) and metadata.

• Handled Missing Values: Replaced “..” with NA and removed incomplete records.

• Converted Data Types: Transformed 2020 values from text to numeric.

• Reshaped Data using pivot_wider(): Created one row per country with GDP and PM2.5 as separate columns.

• Removed Aggregates and Duplicates: Excluded regional aggregates (e.g., “World”) and kept unique country entries.

Descriptive Statistics

GDP_mean <- mean(data2020_ready$NY.GDP.MKTP.KD, na.rm = TRUE)
PM25_mean <- mean(data2020_ready$EN.ATM.PM25.MC.M3, na.rm = TRUE)
GDP_median <- median(data2020_ready$NY.GDP.MKTP.KD, na.rm = TRUE)
PM25_median <- median(data2020_ready$EN.ATM.PM25.MC.M3, na.rm = TRUE)
GDP_sd <- sd(data2020_ready$NY.GDP.MKTP.KD, na.rm = TRUE)
PM25_sd <- sd(data2020_ready$EN.ATM.PM25.MC.M3, na.rm = TRUE)
GDP_min <- min(data2020_ready$NY.GDP.MKTP.KD, na.rm = TRUE)
PM25_min <- min(data2020_ready$EN.ATM.PM25.MC.M3, na.rm = TRUE)
GDP_max <- max(data2020_ready$NY.GDP.MKTP.KD, na.rm = TRUE)
PM25_max <- max(data2020_ready$EN.ATM.PM25.MC.M3, na.rm = TRUE)
descriptive_stats <- data.frame(
  Statistic = c("Mean", "Median", "Min", "Max", "Range", "Standard Deviation"),
  GDP_2015_USD = c(GDP_mean, GDP_median, GDP_min, GDP_max, GDP_max - GDP_min, GDP_sd),
  PM25_ug_m3 = c(PM25_mean, PM25_median, PM25_min, PM25_max, PM25_max - PM25_min, PM25_sd)
)
knitr::kable(descriptive_stats, digits = 3)

Descriptive Statistics Cont.

• Mean:
  • Average GDP = 3.96 × 10¹¹ US$ - shows huge global economic disparity.
  • Average PM2.5 = 23.53 µg/m³ - above the WHO safe limit (10–15 µg/m³).
• Median:
  • Median GDP much lower than mean - right-skewed (few rich nations dominate).
  • PM2.5 median close to mean - distribution fairly balanced.
• Min–Max:
  • GDP ranges from 4.4 × 10⁷ to 1.97 × 10¹³ US$.
  • PM2.5 ranges from 4.89 to 85.12 µg/m³ - large environmental gap between nations.
• Range:
  • GDP range extremely wide - economic inequality.
  • PM2.5 range also wide - pollution disparity.
• Standard Deviation:
  • GDP SD = 1.78 × 10¹² - very high variation among countries.
  • PM2.5 SD = 14.99 - moderate variation in pollution levels.

Visualisation

op <- par(mfrow = c(1, 2), mar = c(4, 4, 2, 1))  # 1 row, 2 plots; tidy margins
hist(data2020_ready$EN.ATM.PM25.MC.M3,
     main = "PM2.5 (µg/m³), 2020",
     xlab = "PM2.5 (µg/m³)",
     breaks = 20)
hist(log10(data2020_ready$NY.GDP.MKTP.KD),
     main = "log10(GDP, 2015 US$), 2020",
     xlab = "log10(GDP)",
     breaks = 20)

par(op)

Visualisation Cont.

plot(EN.ATM.PM25.MC.M3 ~ log10(NY.GDP.MKTP.KD),
     data = data2020_ready,
     xlab = "log10(GDP, 2015 US$)",
     ylab = "PM2.5 (µg/m³)",
     main = "PM2.5 vs log10(GDP), 2020")

Visualisation Cont.

• GDP Histogram:
  • Strong right-skew — most countries have low GDP, while a few are extremely wealthy.
  • Indicates large global economic inequality.
• PM2.5 Histogram:
  • Moderately skewed — many countries fall between 15–35 µg/m³, while a few face very high pollution levels (>70 µg/m³).
  • Reflects uneven environmental conditions across the world.
• Scatter Plot (GDP vs PM2.5):
  • The scatter plot displays each country’s GDP (log-scaled) against its PM2.5 concentration for 2020.
  • The points appear widely scattered without a strong visible trend, suggesting that any relationship between GDP and PM2.5 is not visually obvious.
  • The log₁₀ transformation of GDP was applied to reduce the extreme spread between small and large economies.
  • A formal regression analysis will later be used to test whether a relationship exists statistically, even if it is not visually evident.

Hypothesis Testing

• Determine whether the average global PM2.5 (2020) is significantly higher than the WHO safe limit (15 µg/m³).
• Assumptions:
  • Independence: Each country’s PM2.5 is a separate observation and air quality levels are not dependent on one another.
  • Scale of Measurement: PM2.5 values are continuous, allowing meaningful mean & variance.
  • Normality: Sample size n > 30 ⇒ Central Limit Theorem ≈ normal sampling distribution. Histogram and QQ plot has also been implemented to verify this.
  • Appropriate test: one-sample t-test.
• Hypotheses:
  • \[H_0: \mu_1 = 15 \]
  • \[H_A: \mu_1 \ne 15\]
  • Significance level α = 0.05

Hypthesis Testing Cont.

pm25 <- na.omit(data2020_ready$EN.ATM.PM25.MC.M3)
par(mfrow = c(1,2))
hist(pm25, main = "PM2.5 Distribution", xlab = "µg/m³")
qqnorm(pm25); qqline(pm25, col = 2)

par(mfrow = c(1,1))

Hypthesis Testing Cont.

t.test(pm25, mu = 15)

## 
##  One Sample t-test
## 
## data:  pm25
## t = 8.049, df = 199, p-value = 7.443e-14
## alternative hypothesis: true mean is not equal to 15
## 95 percent confidence interval:
##  21.44257 25.62372
## sample estimates:
## mean of x 
##  23.53315

• Mean = 23.53 µg/m³, t = 8.049, p = 7.443e-14
• 95 % CI = (21.44 , 25.62)
• All assumptions are satisfied.
• p < 0.05 ⇒ Reject H₀.
• Mean PM2.5 significantly > 15 µg/m³.
• Global air pollution in 2020 was statistically above the WHO safe limit.

Regression Testing

• Assess whether economic development (GDP) predicts air pollution (PM2.5) across countries (2020).

model_pm25 <- lm(EN.ATM.PM25.MC.M3 ~ log10(NY.GDP.MKTP.KD),
                 data = data2020_ready)
plot(EN.ATM.PM25.MC.M3 ~ log10(NY.GDP.MKTP.KD),
     data = data2020_ready,
     xlab = "log10(GDP, 2015 US$)",
     ylab = "PM2.5 (µg/m³)",
     main = "PM2.5 vs log10(GDP)")
abline(model_pm25,col = "red")

Regression Testing Cont.

par(mfrow = c(2, 2))
plot(model_pm25)

par(mfrow = c(1, 1))

Regression Testing Cont.

summary(model_pm25)

## 
## Call:
## lm(formula = EN.ATM.PM25.MC.M3 ~ log10(NY.GDP.MKTP.KD), data = data2020_ready)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -18.450 -11.436  -3.408   5.273  61.693 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)  
## (Intercept)           24.09276   11.06626   2.177   0.0307 *
## log10(NY.GDP.MKTP.KD) -0.06564    1.04756  -0.063   0.9501  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.16 on 193 degrees of freedom
##   (22 observations deleted due to missingness)
## Multiple R-squared:  2.034e-05,  Adjusted R-squared:  -0.005161 
## F-statistic: 0.003926 on 1 and 193 DF,  p-value: 0.9501

confint(model_pm25)

##                           2.5 %    97.5 %
## (Intercept)            2.266428 45.919087
## log10(NY.GDP.MKTP.KD) -2.131771  2.000489

Regression Testing Cont.

• Model Summary: PM2.5 = 24.09 − 0.066 × log10 (GDP)
• R² = 2.034e-05 - GDP explains virtually none of PM2.5 variation.
• F(1, 193) = 0.003926, p = 0.9501 - Model not statistically significant.
• 95% CI for slope: (−2.13, 2.00): Includes 0 - confirms insignificance.
• Assumptions:
  • Linearity: Scatter plot shows no clear linear trend between GDP and PM2.5.
  • Normality: Residuals approximately normal (n > 30 ⇒ CLT valid; confirmed via histogram and Q–Q plot).
  • Homoscedasticity: Residuals show roughly constant variance across fitted values.
  • Independence: Each country’s data point is independent of others.
• The regression analysis found no significant linear relationship between GDP and PM2.5 levels in 2020 (p = 0.9501).
• This suggests that economic development did not reliably predict air pollution across countries for that year.

Discussion

• Findings:
  • No significant linear relationship between GDP and PM₂.₅ (p = 0.95).
  • Economic growth alone does not explain global variation in air pollution.
  • Wide disparities in GDP and PM₂.₅ levels reflect global inequality.
• Strengths:
  • Reliable World Bank dataset ensures data accuracy.
  • Clear preprocessing and assumption checks performed.
• Limitations:
  • Analysis limited to one year (2020) — lacks temporal trends.
  • Only one predictor (GDP) used; other key factors excluded.
• Future Directions:
  • Use multi-year data to study trends over time.
  • Extend to multiple regression including population, energy, and policy variables.
• Conclusion
  • Economic development alone does not ensure clean air — sustainable growth requires environmental policies and technological innovation.

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