RPubs link information

• Rpubs link comes here: http://rpubs.com/jing086/542160

Introduction

• The happiness is the most important thing in the world.
• The World Happiness ranking was made among top 100 countries.
• Six different variables were used for calculation of Happiness score of each country, which are Generosity, Trust, Freedom, Economic GDP, Family and Health.
• In this report, the health and wealth of countries were mainly studied and compared.

Introduction Cont.

• The relationship between wealth and health are studied.
• ‘T.test()’ function R is used to calculate the pair sample t-test.
• The paired sample t-test visulation is used as well.
• The null hypothesis will be used to analyse the result.

Problem Statement

• The main focus of this study will be on analysing the relationship between Health and Wealth of each country.
• Different tests will be carried out on the data to get the outcome.

Data

• The dataset is from : https://www.kaggle.com/unsdsn/world-happiness.
• The data consists 2015, 2016, 2017 report and 2017 will be used to the main study focus in this report.
• The dataframe is mainly constructed by following variables.
  • Happiness Rank
  • Happiness Score
  • Whisker.high
  • Whisker.low
  • Economy (GDP per Capital)
  • Family
  • Health..Life.Expectancy.
  • Freedom
  • Generosity
  • Trust (Government Corruption)
  • Dystopia Residual
• The main focus of this study will study between health and economy.

X2017 <- read.csv("world-happiness/2017.csv")

Descriptive Statistics and Visualisation

• Economy (GDP per capita) and Health (life Expectancy) will be studied.
• First of all, minimum, Q1, median, Q3, maximum, mean, standard deviation for Economy ( GDP per capita) have been figured out.

Wealth_summary <- X2017%>% 
            summarise(
             Min = min(Economy..GDP.per.Capita.,na.rm = TRUE),
             Q1 = quantile(Economy..GDP.per.Capita.,probs = .25,na.rm = TRUE),
             Median = median(Economy..GDP.per.Capita., na.rm = TRUE),
             Q3 = quantile(Economy..GDP.per.Capita.,probs = .75,na.rm = TRUE),
             Max = max(Economy..GDP.per.Capita.,na.rm = TRUE), 
             Mean = mean(Economy..GDP.per.Capita., na.rm = TRUE),
             SD = sd(Economy..GDP.per.Capita., na.rm = TRUE),
             n = n()
             )
knitr::kable(Wealth_summary)

Decsriptive Statistics Cont.

• Secondly, the minimum, Q1, median, Q3, maximum, mean, standard deviation for Health (life expectancy) will be figured out.

Health_summary<- X2017%>% 
            summarise(
             Min = min(Health..Life.Expectancy.,na.rm = TRUE),
             Q1 = quantile(Health..Life.Expectancy.,probs = .25,na.rm = TRUE),
             Median = median(Health..Life.Expectancy., na.rm = TRUE),
             Q3 = quantile(Health..Life.Expectancy.,probs = .75,na.rm = TRUE),
             Max = max(Health..Life.Expectancy.,na.rm = TRUE), 
             Mean = mean(Health..Life.Expectancy., na.rm = TRUE),
             SD = sd(Health..Life.Expectancy., na.rm = TRUE),
             n = n())


knitr::kable(Health_summary)

Decsriptive Statistics Cont.

Boxplot

boxplot(
  X2017$Health..Life.Expectancy.,
  X2017$Economy..GDP.per.Capita.,
  ylab = "Scores Ratings",
  xlab = "Health and Happiness"
  )
axis(1, at = 1:2, labels = c("Health", "Wealth"))

Decsriptive Statistics Cont. (qqplot for Health)

X2017$Health..Life.Expectancy.  %>% qqPlot(dist="norm")

## [1] 139 106

qq plot for wealth

X2017$Economy..GDP.per.Capita.  %>% qqPlot(dist="norm")

## [1] 155  93

Matplot

matplot(t(data.frame(X2017$Health..Life.Expectancy.,X2017$Economy..GDP.per.Capita.)),
type = "b",
  pch = 19,
  col = 1,
  lty = 1,
  xlab = "Comparison",
  ylab = "Score rating",
  xaxt = "n"
  )
axis(1, at = 1:2, labels = c("Health Score", "Wealth Score"))

From the plot above, it can be concluded that the health score is directly proportional to the wealth score.

T-test

t.test(X2017$Health..Life.Expectancy., X2017$Economy..GDP.per.Capita.,
       paired = TRUE,
       alternative = "two.sided")

## 
##  Paired t-test
## 
## data:  X2017$Health..Life.Expectancy. and X2017$Economy..GDP.per.Capita.
## t = -21.153, df = 154, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.4738510 -0.3929038
## sample estimates:
## mean of the differences 
##              -0.4333774

From t-test above, it can be concluded that the mean of the difference between health and wealth variable is -0.43.

Linear regression model

Derive a linear regression model to fit the available data as shown below:

b2 <- X2017$Economy..GDP.per.Capita.^2
a2 <- X2017$Health..Life.Expectancy.^2
ab <- X2017$Economy..GDP.per.Capita.*X2017$Health..Life.Expectancy.
sum_a <- sum(X2017$Economy..GDP.per.Capita.)
sum_b <- sum(X2017$Health..Life.Expectancy.)
sum_a_sq <- sum(X2017$Economy..GDP.per.Capita.^2)
sum_b_sq <- sum(X2017$Health..Life.Expectancy.^2)
sum_ab <- sum(X2017$Economy..GDP.per.Capita.*X2017$Health..Life.Expectancy.)
n <- length(X2017$Economy..GDP.per.Capita.) #Sample size

Laa <- sum_a_sq-((sum_a^2)/n)
Lbb <- sum_b_sq-((sum_b^2)/n)
Lab = sum_ab - (((sum_a)*(sum_b))/n)
y = Lab/Laa
x = mean(X2017$Economy..GDP.per.Capita. - y*mean(X2017$Health..Life.Expectancy.))

plot(X2017$Economy..GDP.per.Capita. ~ X2017$Health..Life.Expectancy., 
     data = X2017, alab = "Happiness Score", blab = "Economy Score")

abline(x = x, y = y, col= "Red")
abline(lm(X2017$Economy..GDP.per.Capita. ~ X2017$Health..Life.Expectancy.))

# Linear regression model

model <- lm( X2017$Economy..GDP.per.Capita. ~ X2017$Health..Life.Expectancy., data = X2017)
model %>% summary()

## 
## Call:
## lm(formula = X2017$Economy..GDP.per.Capita. ~ X2017$Health..Life.Expectancy., 
##     data = X2017)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.43425 -0.13199 -0.01460  0.09913  0.64848 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     0.15968    0.04629   3.449 0.000726 ***
## X2017$Health..Life.Expectancy.  1.49642    0.07717  19.391  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.227 on 153 degrees of freedom
## Multiple R-squared:  0.7108, Adjusted R-squared:  0.7089 
## F-statistic:   376 on 1 and 153 DF,  p-value: < 2.2e-16

Hypothesis Testing

• Apply an appropriate hypothesis test for your investigation.
• Ensure you state and check any assumptions.
• Report the appropriate values and interpret the results.
• Here is an example:

pf(q = 376,1,153,lower.tail = FALSE)

## [1] 4.638967e-43

P is less than 0.05, so that the H0 can be rejected and state that this data fits into the linear regression model statistically.

model %>% summary() %>% coef()

##                                 Estimate Std. Error   t value     Pr(>|t|)
## (Intercept)                    0.1596804 0.04629111  3.449484 7.258877e-04
## X2017$Health..Life.Expectancy. 1.4964207 0.07717141 19.390869 4.635065e-43

• The value of intercept was obtained as 0.160. What does it mean? It means that the wealth score is 0.16 when health score is 0. Other than that, the factor of wealth of a country dependent on health is 1.5. It means that whenever a unit change in wealth, there is a increase in health in 1.5 units.

Hypthesis Testing Cont.

plot(model)

\[H_0: \mu_1 = \mu_2 \]

\[H_A: \mu_1 \ne \mu_2\]

\[S = \sum^n_{i = 1}d^2_i\]

• You can also place equations inline: \(z = \frac{x - \mu}{\sigma}\)

Discussion

• The analysis above showed that between wealth and health is existing strong colleration.
• However, the test carried out and outcome were only valid and cover 65% of the data.
• Propose directions for future investigations.
• The actual increasing situation of health after wealth was increased needed to be following studied.
• A further and deeper analysis would be neccessary.

References

• https://www.kaggle.com/unsdsn/world-happiness