RPubs Link

This presentation can be found here: http://rpubs.com/mckipa/Math1324_LifeExpectancyvsGDP

Introduction

Do people from rich countries live longer? In this report I attempt to apply statistical testing techniques to that question.

Using two datasets from the World Bank, I evaluate the relationship between

• GDP: Gross Domestic Product per capita (per person) of a country and
• Life Expectancy at Birth in that country.

I used the most recent year with conplete statistics for both variables - 2017.

Introduction Cont.

• In the 21st century life expectancies increased in our world. This result was not uniform across the globe.

• If we can find a relationship between wealth and life expectancy perhaps we can suggest a level below which coutries are supported by more wealthier countries. These countries could be given favourable trading status to bring capital and investment and - if we prove it - longer livespans to the citizens of that country.

Problem Statement

• Examine the realtionship between Wealth - GDP per capita (per person) and Life Expectancy.
  
• Provide statistical evidence of any relationship between GDP per capita and Life Expectency

Data

• The data was collected as two daatsets from the World Banks open data source. Datasets were provided in csv format.
• only observations with a value for both GDP per capita and Life Expectancy were retained. No imputation for missing values could be justified.
  
• The first three rows of each dataset contained titles and dates of publication which were removed to produce easily loadable csv files.
• To repeat this exercise:

1. download the datasets linked on the references page of this report
2. remove the top three lines from the csv files
3. keep only the country code column and the values for the year 2017
4. label the year value as GDP or LIfe as appropriate.
5. combine the datasets into one csv file for loading.
6. remove entire entries with no value of either Life expectancy or GDP.

Data Cont.

• 233 observations were loaded
• No factors were utilised in this analysis
• GDP (per capita GDP) was provided in $US and is in numeric format to four decimal places.
• Life (life Expectancy at birth in years) was provided in numeric format to five decimal places
• Both GDP and Life are continuous variables

Descriptive Statistics

• Summaries of the the GDP pr capita (GDP) and Life Expectancy (Life) for 2017 are provided below.

• Note:

1. Mean life Expectancy is 72 in the 233 coutries assessed
2. Mean GDP per person is US $13,188

data <- summary(Life_GDP)
knitr::kable(data[0:-1 ,2:3])

Boxplot of Life Expectancy

• Maximum 84.68, No outliers.

Life_GDP$Life %>% boxplot(ylab = "Life Expectancy")

normality of Life Expectancy

• Note: normal distribution

Life_GDP$Life %>% qqPlot(dist="norm", ylab="Life Expectancy", xlab="Quantiles", 
                               main = "Q-Q plot - Life Expectancy by country - 2017", ylim=range(40:90,  na.rm=TRUE))

## [1] 183  30

Boxplot of GDP per capita

• Note the wide range/
• Many outliers. No valid reason to remove from the data.

Life_GDP$GDP %>% boxplot(ylab = "Gross Domestic Product - per capita", ylim=range(0:50000,  na.rm=TRUE))

# normality of GDP per capita - Note: Increased Variation from normal as wealth increases

Life_GDP$GDP %>% qqPlot(dist="norm", ylab="GDP per capita",
                               main = "Q-Q plot - GDP per capita  by country - 2017",xlab="Quantiles", ylim=range(0:50000,  na.rm=TRUE))

## [1] 127 129

Plot of Life Expectancy versus GDP per capita

• Note: Visual Evidence of linear realtionship when GDP per capita greater than 5000.

plot(Life ~ GDP, data = Life_GDP, xlim=range(0:50000,  na.rm=TRUE) , ylim=range(50:85,  na.rm=TRUE), 
     ylab="Life Expectancy - Years", xlab="GDP per capita $US", main= "Life Expectancy versus GDP per capita - 2017")

Hypthesis Testing.

• The Appropriate Hypothesss tests are:

Null Hypothesis: The data do not fit the linear regression model Alternative Hypothesis: The data fit the linear regression model

F-test …

leogdpmodel2017 <- lm(Life ~ GDP, data = Life_GDP)
leogdpmodel2017 %>% summary()

## 
## Call:
## lm(formula = Life ~ GDP, data = Life_GDP)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -16.309  -3.771   1.325   4.303   9.237 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 6.839e+01  4.565e-01   149.8   <2e-16 ***
## GDP         2.724e-04  2.033e-05    13.4   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.576 on 227 degrees of freedom
## Multiple R-squared:  0.4416, Adjusted R-squared:  0.4392 
## F-statistic: 179.5 on 1 and 227 DF,  p-value: < 2.2e-16

F-test results…

F-statistic: 179.5 on 1 and 227 DF, p-value: < 2.2e-16

Yields a p-value below that is less than 0.001

RESULT: Reject Null Hypothesis. Hece support for a linear relationshp existing between GDP per capita and Life Expectancy.

Pearson test

r = 0.665, p < 0.001, 95% CI [0.5911188 0.7270721] The positive crrelation was statistically significant.

Result: Fail to reject Null Hypothesis

r <- cor(Life_GDP$Life, Life_GDP$GDP)
r

## [1] 0.6645596

library(psychometric)
CIr(r, n = 263, level = .95)

## [1] 0.5911188 0.7270721

Plot the regression Line

• correlation of 0.66 was found in the pearson test. Again in plot below

ggscatter(Life_GDP, y = "Life", x = "GDP", 
          add = "reg.line", conf.int = TRUE, 
          cor.coef = TRUE, cor.method = "pearson",
          xlab = "x", ylab = "y")

#Results The F-test yield a sufficiently low p-value that we can reject the null hypothesis.

Hence there is support for a linear relationship existing between GDP per capita and Life Expectancy.
The positive crrelation was statistically significant. r = 0.665, p < 0.001, 95% CI [0.5911188 0.7270721] Result: Fail to reject Null Hypothesis

Discussion

Linearity has been established in this analysis.
A moderate, positve correlation of 0.66 with statistical sugnificance was shown.

Wealth is a statistically likely predictor of greater life expectancy.

References

• GDP per capita by country, World Bank, viewed 2nd of June 2019, https://data.worldbank.org/indicator/NY.GDP.MKTP.CD

• Life Expectancy by country, World Bank, viewed 2nd of June 2019, https://data.worldbank.org/indicator/SP.DYN.LE00.IN