Untitled

A Lasso regression analysis was conducted to identify a subset of variables from a small pool of socioeconomic and digital access indicators that best predicted life expectancy across countries. The response variable was life expectancy. Three predictor variables were initially included in the model: income per person, urbanization rate, and internet usage rate. These variables were selected to represent key dimensions of economic development, population structure, and technological access.

To run the analysis, the following syntax were used

The following results were obtained

Interpretation of the results

A Random forest analysis was performed to evaluate the importance of a set of explanatory variables in predicting a binary categorical response variable, high versus low life expectancy. The explanatory variables included in the model were income per person, urban rate, and internet use rate.

To run the analysis, we applied the following syntax in Spyder.

The analysis run successfully and the results obtained are presented below.

The Results indicate that, internet use rate had the highest relative importance score, followed by income per person and urban rate. This indicates that internet access was the strongest contributor to distinguishing between countries with high and low life expectancy, while income and urbanization also played meaningful but smaller roles in prediction.

Decision tree analysis was performed to examine nonlinear relationships among a set of explanatory variables and a binary categorical response variable. The following syntax was used to generate the classification tree for the variables under investigation.

Below is a picture of the results obtained including the classification tree.

Interpretation of the Results

Decision tree analysis was conducted to examine nonlinear relationships among a set of explanatory variables and a binary categorical response variable, life expectancy (classified as High vs. Low). All possible separations (for categorical variables) and cut points (for continuous variables) were evaluated. For the present analysis, a Gini impurity criterion was used to identify optimal splits, and a cost–complexity pruning algorithm was applied to reduce the full tree to a parsimonious final sub-tree. The explanatory variables included in the classification tree model were internet use rate, urban rate, and income per person.

Internet use rate emerged as the first and most influential variable separating the sample into two major subgroups. Countries with an internet use rate ≤ 26.6% were more likely to be classified as having Low Life Expectancy, whereas countries with higher internet penetration were more likely to exhibit High Life Expectancy. Among countries with low internet use (≤ 26.6%), a further subdivision was made based on urban rate. Countries with an urbanization level ≤ 53.8% were overwhelmingly classified as having Low Life Expectancy, with very low node impurity, indicating a high degree of homogeneity in this group. Within this subgroup, countries with very low urbanization (≤ 21.1%) showed an almost pure classification toward Low Life Expectancy.

For countries with higher internet use (> 26.6%), life expectancy outcomes were predominantly classified as High. A further split based on urban rate (≤ 59.8%) refined this classification, with higher urbanization consistently associated with higher life expectancy. At the terminal nodes, countries with urbanization levels exceeding 71.4% formed highly homogeneous groups classified as High Life Expectancy. The final pruned decision tree classified approximately 76% of cases correctly, with stronger performance in identifying countries with High Life Expectancy (higher sensitivity) than those with Low Life Expectancy (moderate specificity).

To further investigate the factors associated with life expectancy, we fitted a logistic regression model using a binary indicator of life expectancy (high vs. low) as the response variable. Income per person was specified as the primary explanatory variable, with urban rate and internet use rate included to assess their independent effects and potential confounding. The Python syntax below shows how the model was estimated.

The model output were as follows:

Interpretation of the results: The overall model fit was strong (Pseudo R² = 0.53; likelihood ratio test p < 0.001), indicating that the explanatory variables jointly explain a substantial proportion of the variation in life expectancy.

Among the explanatory variables, internet use rate was significantly and positively associated with the odds of having a high life expectancy. Specifically, each one-unit increase in internet use rate was associated with a 7.2% increase in the odds of high life expectancy (OR = 1.07, 95% CI [1.04, 1.11], p < 0.001). In contrast, income per person showed a marginal, non-significant positive association with life expectancy (OR = 1.00, 95% CI [1.00, 1.00], p = 0.079), while urban rate was not significantly associated with life expectancy after adjustment (OR = 1.02, 95% CI [0.99, 1.05], p = 0.163).

Our primary hypothesis was that higher income per person would be associated with higher life expectancy. Although the estimated odds ratio for income per person was greater than 1, the association did not reach conventional levels of statistical significance. Therefore, the results did not fully support our hypothesis in the multivariable logistic regression model.

We examined the relationship between life expectancy and income per person using a multiple linear regression framework. In addition to income, urban rate and internet use rate were included in the model to evaluate their independent associations with life expectancy and to assess potential confounding effects.

The analysis was performed in python using the following syntax:

Results

Summary Interpretation

We tested the association between income per person and life expectancy from the gapminder dataset using the simple linear regression model. The syntax used to run this analysis include:

The results were

Interpretation of the results:

I worked with the Gapminder dataset. This dataset focuses on global development patterns across countries and over time.

The Sample

The gapminder dataset consists of countries around the world. Each observation represents a single country rather than an individual person. The data summarize national-level indicators related to population health, economic conditions, and urban development. The level of analysis for this study is aggregate (country-level). All variables describe characteristics of entire countries, such as average income or national life expectancy. The Gapminder dataset includes about 213 countries. For my analysis, I included countries that had complete data on life expectancy, income per person (GDP per capita), and urban rate. Countries with missing values for any of these variables were excluded so that comparisons across countries would be consistent and reliable.

Data Collection Procedures

The data were generated through secondary data reporting. Gapminder compiles existing data from multiple international sources. The original purpose of the data collection was to monitor and compare global trends in health, economic development, population dynamics, and living conditions across countries. Data were collected by international organizations such as the World Bank, United Nations, and World Health Organization using national censuses, household surveys, administrative records, and statistical modeling. Gapminder harmonized these data to ensure consistency across countries and years. The dataset includes data collected over multiple decades, generally from the 1960s to the most recent year available, depending on the indicator. Data were collected globally, with each country contributing information through its national statistical systems and reporting agencies. The data analytic sample for this study was restricted to countries with complete information on the variables of interest. This ensured comparability across observations and reduced bias associated with missing data.

Description of Variables

We tested a potential moderator using the gapminder data. we asked the question " Does the relationship between income per person and life expectancy depend on urban rate?". To do this, we used the following syntax:

Results obtained

Association between income and life expectancy for low urban rate countries

Association between income and life expectancy for medium urban rate countries

Association between income and life expectancy for high urban rate countries

Interpretation of the results

When we look at the relationship between income per person and life expectancy across countries grouped by urbanization level:

High Urban Rate Countries (n = 59) show a strong positive correlation (r = 0.695, p < 0.00000001). This means that in highly urbanized countries, higher income is strongly associated with longer life expectancy.

Medium Urban Rate Countries (n = 58) have a moderate positive correlation (r = 0.496, p < 0.0001). Here, income still matters for life expectancy, but the effect is smaller than in high urbanized countries.

We used the following syntax to assess the relationship between income per person and urban rate from gapminder dataset.

The following results were obtained

Interpretation of the results

The analysis shows a moderate positive correlation between income per person and urban rate (r = 0.49). This means that, countries with higher average incomes tend to have a larger share of their population living in urban areas. The relationship is statistically significant (p<0.001).

We used the following syntax

We had the following results

Interpretation of the results

The Chi-square test of independence revealed a statistically significant association between income per person and urban rate. Specifically, the distribution across low, medium, and high urban rate categories differed by income group (χ² = 9.95, df = 4, p = 0.041).

Post-hoc pairwise Chi-square comparisons with Bonferroni adjustment were conducted to determine which income categories differed in their distribution of urbanization levels.

The post-hoc analysis revealed that:

Low-income and medium-income countries differed significantly in their urbanization distributions (Bonferroni-adjusted p = 0.038).

Low-income and high-income countries showed no statistically significant difference.

Medium-income and high-income countries also showed no statistically significant difference.

The mean of urbanization rate across three income categories were assessed using the following functions in Spyder (Python 3.12).

The results of ANOVA are displayed below.

The results were interpreted as follows:

Since p < 0.05, we reject the null hypothesis and conclude that there is a statistically significant difference in mean urbanization rates among at least two income categories.

A one-way ANOVA revealed a statistically significant effect of income-per-person category on urbanization rate, F(2, 186) = 14.47, p < 0.0001. Countries in the medium-income category exhibited substantially higher levels of urbanization compared to low-income countries, with urbanization rates that were markedly greater for medium-income countries (SD = 11.22) than for low-income countries (SD = 22.26).

The syntax for creating univariate graphs are shown below

This graph is unimodal and is highly right-skewed as they are higher frequencies in the lowest income ranges. The highest peak is at the first category of -1.27USD to 21112.51USD.

This graph is unimodal, with it highest peak in the category of 65 and 80 years life expectancy. It seems to be skewed to the left but the skewness is not pronounced.

This graph is unimodal and seems to be skewed to the left. The highest peak is at the category of 60 and 80% urban rate ranges.

The data was called in as shown on the picture below

The results obtained are displayed on the pictures below

Using the Gapminder dataset (213 countries), I examined how countries are distributed across different ranges of income per person, life expectancy, and urbanization rate using frequency distributions. These tables show how many countries fall into each interval and what percentage of the total they represent. Some countries, however, had missing data for certain variables, so the totals in the tables do not always sum to the full 213 countries. The cumulative frequency in each table reflects only the countries with available data, making it easy to see the overall distribution patterns.

I asked the question:

“What proportion of countries falls within each interval of income per person, life expectancy, and urbanization rate, and what percentages do they represent?”

The analysis reveals:

Income per Person (USD): Most countries (n = 153, 80.53%) fall within the lowest income interval of –1.27 to 15,110 USD per person. Countries with higher income (>60,000 USD) represent less than 3% of the total.

Life Expectancy (years): More than half of the countries (~67.5%) have life expectancy above 68 years, while only around 10% fall below 53 years.

I have chosen the Gapminder dataset for my project. This dataset provides information on global social, economic, and health indicators across different countries and years. After reviewing the codebook, I became interested in exploring the relationship between economic development and human health, particularly focusing on GDP per capita and life expectancy.

Topic of Interest: The relationship between economic development and human health

The main question I would like to study is: Is GDP per capita associated with life expectancy across countries?

This question examines whether wealthier nations tend to have longer life expectancies, reflecting how economic progress can influence public health outcomes. I also expect that in countries with larger populations, the positive effect of GDP per capita on life expectancy may be weaker, as economic and health resources could be more unevenly distributed among citizens.

Second Topic: Population dynamics

While GDP and life expectancy form the core of my study, I am also curious about population size. Does having a very large or small population influence how wealth translates into health outcomes?

A quick literature review conducted on Google Scholar shows that this relationship has been studied for decades:

Preston (1975): First described the positive GDP–life expectancy link.

Deaton (2003): Showed that income gains improve health but unevenly across regions.

Pritchett & Summers (1996): Argued that “wealthier is healthier” — higher incomes allow for better health infrastructure and living standards.

These studies support the idea that national wealth plays a major role in shaping health outcomes, but local and demographic factors can complicate this relationship.