#gapminder

Source code:

STEP 1: univariate graphs.

selected variables:

Life Expectancy

Income per Person

Alcohol Consumption

Life Expectancy:

Center: The distribution is centered at approximately 70-75 years.

Spread: The data is left-skewed, meaning most countries have high life expectancy, but there is a long tail towards the left representing countries with lower health outcomes (ranging down to 45 years).

Income per Person:

Center: The center of the data is located at the very low end of the scale (below $5,000).

Spread: This variable is highly right-skewed. There is a massive concentration of countries at low income levels and a very long "tail" that extends to the right, showing a few outlier countries with extremely high GDP per capita.

Alcohol Consumption:

Center: The distribution is centered around 5-6 liters per capita.

Spread: The data is relatively spread out across the entire range (0 to 15+ liters), but it shows a higher frequency of countries with low-to-moderate consumption levels.

STEP 2: bivariate graph

For the bivariate analysis, Income per Person has been selected as the explanatory variable to investigate its relationship with Life Expectancy, which serves as the response variable.

The goal of this visualization is to determine if a country's economic wealth (represented by GDP per capita) acts as a significant predictor of its population's longevity. By plotting these two variables together, we can observe whether higher income levels correlate with improved health outcomes and identify the strength and direction of this association.

To examine the association between the variables, It has been defined them as follows:

Explanatory Variable (X-axis): incomeperperson. This is the independent variable used to explain the variation in health outcomes. Hypothesis: the country's economic capacity influences its population's longevity.

Response Variable (Y-axis): lifeexpectancy. This is the dependent variable. It represents the outcome or "response" that changes based on the level of income per person.

To meet the requirements for this second assignment, we must incorporate a third variable from the Gapminder dataset: alcconsumption.

STEP 1: Run your first program.

Source Code:

Step 2: Run frecuency / Output.

Rubric items:

Program output: The output is organized into clear frequency tables with descriptive headers. Each table includes the calculated frequency and percentage for each interval, including a 'TOTAL' row to confirm the sample size.

Each of the three selected variables is displayed in its respective frequency table: Life Expectancy, Income per person and alcohol consumption.

Each table displays the selected intervals (values), including columns for frequency and percentage to show how often these values occur. Furthermore, row selection was performed to filter out countries with missing data (Step 3 in the code), and a final 'TOTAL' row is included to verify the complete sample size.

Data Interpretation: In this preliminary analysis, Life Expectancy shows a balanced distribution across all intervals because quartiles were used to divide the data (each group representing approximately 25% of the sample). In contrast, the majority of countries fall into the lower levels for both income per person and alcohol consumption.

STEP 1: Data Set Selection I have chosen to work with the Gapminder dataset to explore global trends in health and economics.

STEP 2: Identify a Specific Topic of Interest After looking through the codebook for the Gapminder dataset, I decided that I am particularly interested in public health, specifically life expectancy.

STEP 3: Prepare a Personal Codebook (First Topic) Since Gapminder provides a clear, single indicator for this topic, I added the lifeexpectancy variable to my personal codebook:

Variable Name: lifeexpectancy

Description: 2011 life expectancy at birth (years). The average number of years a newborn child would live if current mortality patterns were to stay the same.

STEP 4: Identify a Second Topic While life expectancy is a good starting point, I needed to determine what factors might influence how long people live across different countries. It strikes me that nations with higher economic resources generally seem to have better healthcare systems and living conditions. Therefore, I decided that I am most interested in exploring the association between a country's wealth and its life expectancy.

STEP 5: Add Second Topic to Personal Codebook I added to my personal codebook the variable reflecting economic development (incomeperperson):

Variable Name: incomeperperson

Description: 2010 Gross Domestic Product per capita in constant 2000 US$. The inflation but not the differences in the cost of living between countries has been taken into account.

STEP 6: Literature Review To understand the existing research on this topic, I conducted a brief literature review:

Search Terms Used: I used Google Scholar with the exact search terms: "GDP per capita and life expectancy", "economic development and mortality rates", and "income inequality and public health".

Summary of Findings: The literature consistently shows a strong, positive relationship between national income and life expectancy, a pattern famously known as the "Preston Curve". Researchers highlight that higher income per capita allows countries to invest more heavily in healthcare infrastructure, sanitation, and nutrition. Interestingly, studies also show that this relationship is non-linear: gains in life expectancy are massive when moving from extreme poverty to middle-income, but the curve flattens out among the wealthiest nations, where lifestyle factors play a larger role.

References Used:

Preston, S. H. (1975). The changing relation between mortality and level of economic development. Population Studies, 29(2), 231-248.

Deaton, A. (2003). Health, inequality, and economic development. Journal of Economic Literature, 41(1), 113-158.

STEP 7: Research Question & Hypothesis

Research Question: Is there a direct and positive association between a country's income per person (incomeperperson) and the life expectancy of its inhabitants at birth (lifeexpectancy)?

A k-means cluster analysis was conducted to identify latent groupings among countries based on multiple quantitative socioeconomic indicators drawn from the Gapminder dataset. Variables were numerically encoded, and missing data was imputed using the median for each feature. Given the dataset's moderate size, all observations were included to maximize subgroup detection.

K-means partitioned countries into three clusters according to shared patterns across indicators. This approach minimizes within-cluster variation and highlights differences between subpopulations.

Results

The clustering algorithm assigned:

112 countries to Cluster 1

72 countries to Cluster 2

29 countries to Cluster 0

Summary statistics for each cluster show distinct profiles:

Clusters are differentiated by combinations of high income, technology adoption, urbanization, and health outcomes. Higher income and longer life expectancy are concentrated in Cluster 0, while lower values are observed in Cluster 2.

Interpretation

Three subgroups emerged, each characterized by similar socioeconomic profiles. Cluster analysis identified countries with higher income, better health, and more urbanized populations in one group, compared to countries with distinctly lower scores in another. The approach reveals meaningful geographic and developmental differences without relying on predefined labels.

Appendix: Python Syntax

This analysis evaluates how national indicators contribute to the classification of countries by income level. The dataset was numerically encoded, and missing values were filled by the median of each feature. The binary response variable reflects whether a country’s income per person is above the sample median.

A Random Forest classifier was fitted to the data, utilizing an ensemble of decision trees to provide robust classification and importance measures for each predictor variable.

Results

The model achieved perfect classification performance on the available data, with an accuracy score of 1.0. The confusion matrix confirms that all instances were classified correctly:

importance values, showing which variables most influenced the classification, are visualized below. Internet user rate, life expectancy, and urbanization rate had the highest impact in distinguishing between high- and low-income countries.

Interpretation

The analysis demonstrates that only a few socioeconomic features are needed to classify countries by income group with high certainty. Variables such as internet user rate and urbanization provide the most predictive power, as seen in their relative importance scores and the perfect model accuracy. Ensemble methods like Random Forests are effective at capturing feature interactions without overfitting when variables are properly preprocessed.

Appendix: Python Syntax

A quantitative analysis was conducted to investigate the association between various demographic and economic indicators and life expectancy across countries. The dataset comprises multiple predictors, including numeric variables from health, consumption, and social domains. Prior to modeling, missing values were addressed using median imputation to maintain consistency and completeness in the sample.

The approach used Lasso regression, which introduces a regularization parameter to enforce sparsity in the model, automatically reducing certain coefficients to zero and thus simplifying the set of explanatory variables. This penalty parameter was optimized via five-fold cross-validation. All available observations were included in the modeling phase without a train-test split due to the moderate data size.

Results

After regularization, only a subset of predictors were retained by the model. The cross-validated alpha parameter converged to approximately 0.26. Predictors such as armedforcesrate, breastcancerper100th, hivrate, internetuserate, polityscore, relectricperperson, suicideper100th, employrate, and urbanrate exhibited non-zero coefficients. The intercept for the optimized model reached 70.10, with an R-squared value of 0.71, indicating that the selected variables explained a substantial proportion of the variance in life expectancy.

Interpretation of the resulting model shows that internetuserate, urbanrate, and employrate impact life expectancy positively, while variables such as hivrate and suicideper100th act in the opposite direction. The Lasso regression delivers an interpretable model by excluding predictors with negligible association, focusing analysis on a limited and influential subset of features.

Appendix: Python Syntax

A cross-country dataset was analyzed to assess the association between urbanization rate and the probability of having above-median life expectancy. The binary outcome variable was defined as 1 for countries whose life expectancy exceeded the median value and 0 otherwise. After converting the relevant columns to numeric and removing missing values, the final sample allowed a straightforward logistic regression with urbanization rate as sole predictor.

A logistic regression model was fitted, providing the following parameter estimates: the regression coefficient for urbanrate was 0.052, translating into an odds ratio of 1.054. The model intercept was estimated at -3.221. These results indicate that for each percentage point increase in urbanization, the odds of belonging to the “high life expectancy” group increase by approximately 5%. The uncertainty in coefficient estimation and odds ratio implies that urbanization has a meaningful positive association with binary life expectancy status.

Model performance was evaluated using the area under the ROC curve (AUC), which reached 0.795, reflecting strong discrimination between the two categories. The ROC curve visualizes the tradeoff between true positive and false positive rates, and the confusion matrix quantifies classification accuracy at the conventional threshold.

The analysis supports the hypothesis that countries with higher urbanization rates are more likely to exhibit higher life expectancy. All diagnostic steps confirmed stable estimation, and no major limitations arose in residuals or classification metrics.

Regression Results Table

Figure 1. ROC curve for logistic regression model

Figure 2. Confusion matrix at threshold 0.5

Appendix: Code