rm(list=ls())

##Life Expectancy (WHO)
##https://www.kaggle.com/datasets/kumarajarshi/life-expectancy-who?ref=hackernoon.com

## Linear and Loess estimation for
## Life Expct. vs %Expenditure on Health (PE)

D = read.csv("WHO_Life_expectancy.csv",header=TRUE)

D = D[D$Year == 2007,]
D = D[,c(1,4,7,8,17,22)]
D = na.omit(D)

Country = D[,1]
D = D[,-1]
attach(D)
n = nrow(D)

pdf("WHOLinear1.pdf")

lifeExp = Life.expectancy
PE = percentage.expenditure
plot(PE,lifeExp,xlab="",ylab="", pch=21,cex=2.2,bg="pink",cex.axis=1.5)
out = lm(lifeExp ~ PE)
abline(out,col="purple",lwd=4)

LL1 = loess(lifeExp ~ PE)

o=order(PE)
lines(PE[o],LL1$fitted[o],col="red",lwd=4)
title(ylab="Life Expectancy",line=2, cex.lab=2)
title(xlab="Percent. Health Expend. (PE)",line=2.6, cex.lab=2)
dev.off()

logPE = log(PE)

pdf("WHOLinear2.pdf")

plot(logPE,lifeExp,xlab="",ylab="", pch=21,cex=2.2,bg="pink",cex.axis=1.5)
out = lm(lifeExp ~ logPE)
abline(out,col="purple",lwd=4)

LL2 = loess(lifeExp ~ logPE)

o=order(logPE)
lines(logPE[o],LL2$fitted[o],col="red",lwd=4)
title(ylab="Life Expectancy",line=2, cex.lab=2)
title(xlab="log(PE)",line=2.6, cex.lab=2)
dev.off()

#### Estimates and confidence intervals for the four covariates

logSchooling = log(Schooling)
logGDP = log(GDP)
outout = lm(lifeExp ~ Alcohol + logPE + logSchooling + logGDP)
summary(outout)

## Call:
## 
## outout = lm(lifeExp~Alcohol+logPE+logSchooling+logGDP)
## summary(outout)
## 
## Call:
## lm(formula = lifeExp ~ Alcohol + logPE + logGDP + logSchooling)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.6711  -2.1579   0.2749   3.8964  15.1584 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    9.9925     4.9812   2.006   0.0466 *  
## Alcohol       -0.2968     0.1512  -1.963   0.0515 .  
## logPE          1.1062     0.6699   1.651   0.1008    
## logGDP        -0.1052     0.7724  -0.136   0.8919    
## logSchooling  22.8483     2.3185   9.855   <2e-16 ***
## ---
## Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
## 
## Residual standard error: 6.119 on 151 degrees of freedom
## Multiple R-squared:  0.6141,	Adjusted R-squared:  0.6039 
## F-statistic: 60.07 on 4 and 151 DF,  p-value: < 2.2e-16


print(confint(outout))

##                   2.5 %       97.5 %
## (Intercept)   0.1505836 19.834316992
## Alcohol      -0.5955614  0.001956565
## logPE        -0.2173624  2.429732098
## logGDP       -1.6312304  1.420914581
## logSchooling 18.2673598 27.429274189


#######
#######   WHO ANOVA with 4 covariates
#######

TableAOV = aov(Life.expectancy ~ Alcohol + logPE +  logGDP +
               logSchooling)

summary(TableAOV)

##               Df Sum Sq Mean Sq F value   Pr(>F)    
## Alcohol        1   2317    2317   61.89 6.47e-13 ***
## logPE          1   2825    2825   75.45 5.72e-15 ***
## logGDP         1    218     218    5.82    0.017 *  
## logSchooling   1   3636    3636   97.11  < 2e-16 ***
## Residuals    151   5654      37                     
## ---
## Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


## SS_regr = 2317+2825+218+3636 = 8966
## SS_tot  = 8966+5654 = 14620