RPubs link information

RPubs link: http://rpubs.com/Dhachu18/d543369

Introduction

• According to (McKenzie, 2014),Dalai Lama has stated, happiness is the highest form of health.
• In 2012, United Nation adapoted the resolution of Bhutan in perceiving pursuit of happiness instead of Gross Domestic Product as a goal in attaining Millennium Development (UNRIC, 2019).
• A total of 156 countries were examined in this survey, quantifying variables such as generousity, freedom, social support, healthy life expectancy and many more.
• Health life expectancy is chosen to correlate with happiness score to analyse whether happiness link to longer life using linear regression.

10 Happiest Countries in the World

Problem Statement

• The aim of this statistical study is to investigate the relationship between happiness and healthy life expectancy.
• Happiness Score and healthy life expectancy are the variables that utilized in this survey.
• Plots such a scatter plot and box plot are used to effectively visualize the data.
• Regression analysis is used to analyze the correlation between happiness and healthy life expectancy.

Data

• The dataset is obtained from World Happiness Report 2019 which can access via https://worldhappiness.report/ed/2019/
• This dataset contains large sample size of 156 countries and 10 variables.
• The data is sourced from Gallup World Poll which consists of above 100 questions and approximately 1000 people (per country) from 160 countries participate in this poll on yearly basis.

happy <- read_csv("happy.csv")

names(happy)[names(happy) == "Happiness score"] <- "HappinessScore"
names(happy)[names(happy) == "Explained by: Healthy life expectancy"] <- "HealthyLifeExpectancy"
head(happy)

Data Cont.

• The important variables of the dataset is outlined below:
  • Country=name of the participated countries
  • Happiness score= A metric measured using the scale of 0 to 10 where 10 indicates the happiest
  • Explained by: Healthy life expectancy= measure life expectancy based on WHO data
• In this analysis, we focus on the correlation between happiness and healthy life expectancy.Hence, I renamed variable Happiness score into HappinessScore and Explained by: Healthy life expectancy into HealthyLifeExpectancy for better readability.

Descriptive Statistics and Visualisation

• The table below shows there are three missing values in HealthyLifeExpectancy.Thus, the mean value of HealthyLifeExpectancy is used to replace the missing values.

x<-happy %>% summarise(MissingValuesInHealthyLifeStyle=sum(is.na(happy$HealthyLifeExpectancy)))
y<-happy %>% summarise(MissingValuesInHappinessScore=sum(is.na(happy$HappinessScore)))
data.frame(y,x)

happy<-happy %>%mutate(HappinessScore = ifelse (is.na(HappinessScore), mean(HappinessScore, na.rm = TRUE), HappinessScore))
happy<-happy %>%mutate(HealthyLifeExpectancy = ifelse (is.na(HealthyLifeExpectancy), mean(HealthyLifeExpectancy, na.rm = TRUE), HealthyLifeExpectancy))

x<-happy %>% summarise(MissingValuesInHealthyLifeStyle=sum(is.na(happy$HealthyLifeExpectancy)))
y<-happy %>% summarise(MissingValuesInHappinessScore=sum(is.na(happy$HappinessScore)))
data.frame(y,x)

Descriptive Statistics cont.

• Boxplot is used to visualize how the values in the dataset have been spread out.
• The outliers in HealthyLifeExpectancy were removed by utilising the imputation method.Since the outliers are small in number, they are replaced by the mean of the non-missing variable.
• There is an obvious difference in the boxplot which is worth for further investigation.
  • the boxplot for happiness score is comparatively tall indicating the countries hold different range of happiness score
  • the healthy life expectancy is comparatively short indicating the countries have similar life expectancy with each other

Descriptive Statistics cont.

#boxplot
happy %>% boxplot(happy$HappinessScore, happy$HealthyLifeExpectancy, names=c("HappinessScore"
, "HealthyLifeExpectancy"), data = .,
main="Boxplot of Happines sScore and Life Expectancy",
xlab="happy", ylab="Range", col=c("yellow", "green"))

Descriptive Statistics cont.

HappinessScore <- happy$HappinessScore[!is.na(happy$HappinessScore)]
z_score<-HappinessScore %>% scores(type = "z")
HappinessScore[ which( abs(z_score) >3 )]

## numeric(0)

HappinessScore[ which( abs(z_score) >3 )]<-mean(HappinessScore,na.rm=TRUE)

boxplot(HappinessScore, main = "Box Plot of Happiness Score",ylab="Happiness Score",verticle
=TRUE, col = "green")

Decsriptive Statistics Cont.

• Table below shows the summary of Happiness Score and Healthy Life Expectancy

HealthyLifeExpectancy <- happy%>% summarise(Min = min(HealthyLifeExpectancy,na.rm = TRUE),
Q1 = quantile(HealthyLifeExpectancy,probs = .25,na.rm=TRUE),
Median = median(HealthyLifeExpectancy, na.rm = TRUE),
Q3 = quantile(HealthyLifeExpectancy,probs = .75,na.rm=TRUE),
Max = max(HealthyLifeExpectancy,na.rm = TRUE),
Mean = mean(HealthyLifeExpectancy, na.rm = TRUE),
SD = sd(HealthyLifeExpectancy, na.rm = TRUE)
)

HappinessScore <- happy%>% summarise(Min = min(HappinessScore,na.rm = TRUE),
Q1 = quantile(HappinessScore,probs = .25,na.rm=TRUE),
Median = median(HappinessScore, na.rm = TRUE),
Q3 = quantile(HappinessScore,probs = .75,na.rm=TRUE),
Max = max(HappinessScore,na.rm = TRUE),
Mean = mean(HappinessScore, na.rm = TRUE),
SD = sd(HappinessScore, na.rm = TRUE)
)

combination <- rbind(HappinessScore, HealthyLifeExpectancy)
rownames(combination) <- c("HappinessScore", "HealthyLifeExpectancy")
kable(round(combination,2), caption = "Summary table of Happiness Score and Healthy Life Expectancy", row.names = TRUE)

Decsriptive Statistics Cont.

• The matplot clearly shows there is a positive increase relationship between Happiness and Healthy Life Expectancy. When the happiness score increases, Healthy Life Expectancy also increases.

matplot(t(data.frame(happy$HealthyLifeExpectancy,happy$HappinessScore)),
type="b",
pch = 19,
col = 1,
lty = 1,
xlab = "Comparison",
ylab = "Happiness Score",
xaxt = "n")
axis(1, at=1:2,labels = c("HappinessScore","HealthyLifeExpectancy") )

Decsriptive Statistics Cont.

• The scatter plot shows an uphill pattern which indicates a positive relationship between the happiness score and Healthy Life Expectancy.With the regression line, the happiness score and Healthy Life Expectancy are well aligned

#scatterplot

x <- happy$HappinessScore
y <- happy$HealthyLifeExpectancy
plot(x, y, main = "Happiness Score Price VS Healthy Life Expectancy ",
     xlab = "Happiness", ylab = " HealthyLifeExpectancy",
     pch = 19, frame = FALSE)
abline(lm(y ~ x, data = happy), col="red", lty=6)

Hypothesis Testing

• The linear regression is used to examine the association between the Happiness Score and Healthy Life Expectancy
• The normality of the variables are not examine since the sample size n=156
• According to the Central Limit Theorem if the size of the sample is greater than 30 then the mean of sampling distribution is approximately normal.
• The hypotheses of the linear regression is as below :
  • H0: There is no association between the Happiness Score and Healthy Life Expectancy
  • HA: There is an association between the Happiness Score and Healthy Life Expectancy

Assumptions:

Independence: Happiness Score and Healthy Life Expectancy are independent Linearity: as shown in scatter plot, there is a possitive relationship between Happiness Score and Healthy Life Expectancy

• Normality of residuals and Homoscedasticity will be checked after model is fitted

Testing the Overall Model

score <- lm(HappinessScore ~ HealthyLifeExpectancy, data = happy)
summary(score)

## 
## Call:
## lm(formula = HappinessScore ~ HealthyLifeExpectancy, data = happy)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.6831 -0.4604  0.0743  0.5230  1.5904 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             2.7832     0.1771   15.72   <2e-16 ***
## HealthyLifeExpectancy   3.6382     0.2331   15.61   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6949 on 154 degrees of freedom
## Multiple R-squared:  0.6127, Adjusted R-squared:  0.6102 
## F-statistic: 243.7 on 1 and 154 DF,  p-value: < 2.2e-16

The p-value for the F-test is very small, F(1,154) = 243.7, p<.001. Since the p value is less than the 0.05 level of significance, H0 is rejected. Hence, there was statistically significant evidence that there is an association between the Happiness Score and Healthy Life Expectancy

Linear Regression - R-squared

• The value of R-square is 0.6127 which means the total of 61.27% of the variability in the Healthy Life Expectancy can be explained by a linear relationship with happiness score.
• This denotes a poor fitting model (R-squared=0).
• Thus, F statistic which is used to test the overall regression model.
• The F-test for the linear regression has the following statistical hypotheses:
  • H0:The data do not fit the linear regression model
  • HA:The data fit the linear regression model

pf(q = 239.1,1,154,lower.tail = FALSE)

## [1] 3.767232e-33

The p value is less than 0.001. Since, the p is less than the 0.05 level of significance, we reject H0. There was statistically significant evidence that the data fit a linear regression model.

Testing Model Parameters

score %>% summary() %>% coef()

##                       Estimate Std. Error  t value     Pr(>|t|)
## (Intercept)           2.783194  0.1770647 15.71852 7.979033e-34
## HealthyLifeExpectancy 3.638231  0.2330765 15.60960 1.544574e-33

score %>% confint()

##                          2.5 %   97.5 %
## (Intercept)           2.433405 3.132984
## HealthyLifeExpectancy 3.177791 4.098671

The intercept/constant is reported as a=2.783194. The 95% CI for a to be [2.433405, 3.132984]. H0:α=0 is clearly not captured by this interval. Thus, H0 is rejected.

Testing assumption

score <- lm(HappinessScore ~ HealthyLifeExpectancy, data = happy)
par(mfrow=c(2,2))
plot(score)

• In the Residual vs. Fitted plot the points seems to be randomly spread out about the line and the red line is quite flat and fits to the data.
• The Q-Q plot shows the residuals are approximately normally distributed.
• The Scale-Location plot shows the residuals appear randomly spread and the red line is close to flat.
• The Residual vs Leverage plot shows the relationship between fitted values and residuals is quite flat
• Hence, it is safe to assume the homoscedasticity of data.

Discussion

Findings:

• The investigation shows there is statistically significant positive correlation between Healthy Life Expectancy and Happiness Score.
• Based on the study, the linear regression model was fitted to predict the Healthy Life Expectancy using Happiness Score.
• A scatter plot shows the bivariate relationship between Healthy Life Expectancy and Happiness Score demonstrated evidence of a positive linear relationship.

Strengths:

• The dataset is highly reliable as it has global recognition.
• Hypothesis testing knowledge is applied effectively using different methodologies

Limitations:

• More elements needs to be considered while analyzing the correlation between happiness and life expectancy.

The directions for future research:

• Whether the happiness in the society leads people to consious on health which leads to longer life.
• Does the happiness leads to healthy life with less diseases?

Conclusion:

• There is a statistically significant difference in the Happiness Score and Healthy Life Expectancy. The happiness positively correlates with improving life expectancy.
• Positive emotions contribute to better physical health. Hence, happiness leads to longer life (MacMillan, 2018).

Happy humans

References

1. kaggle, 2019. World Happiness Report 2019. [Online] Available at: https://www.kaggle.com/PromptCloudHQ/world-happiness-report-2019 [Accessed 8 October 2019].

2. MacMillan, A., 2018. Happiness linked to longer life. [Online] Available at: https://edition.cnn.com/2011/10/31/health/happiness-linked-longer-life/index.html [Accessed 20 October 2019].

3. McKenzie, D. J., 2014. Happiness - The Highest Form of Health. [Online] Available at: https://www.naturopathiccurrents.com/articles/happiness-highest-form-health [Accessed 10 October 2019].

4. UNRIC, 2019. The UN and happiness. [Online] Available at: https://www.unric.org/en/happiness/27709-the-un-and-happiness [Accessed 10 October 2019].

5. World Happiness Report , 2019. World Happiness Report 2019. [Online] Available at: https://worldhappiness.report/ed/2019/ [Accessed 10 October 2019].