library(gapminder)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

# Extract life expectancy data
life_data <- gapminder$lifeExp

# Generate 1000 sample means
sample_means <- replicate(1000, mean(sample(life_data, size = 30, replace = TRUE)))

# Visualise
hist(sample_means, main = "Sampling Distribution of Sample Mean", xlab = "Mean Life Expectancy")

# Try with n = 10 and n = 100
means_10 <- replicate(1000, mean(sample(life_data, 10, replace = TRUE)))
means_100 <- replicate(1000, mean(sample(life_data, 100, replace = TRUE)))


hist(means_10, main="n = 10")

hist(means_100, main="n = 100")

simulate_means <- function(n, reps = 1000) {
  replicate(reps, mean(sample(life_data, size = n, replace = TRUE)))
}

sample_sizes <- c(10, 30, 50, 100)
par(mfrow = c(1,1))
for (n in sample_sizes) {
  hist(simulate_means(n), main = paste("n =10", n))}

library(gapminder)  
head(gapminder) 

## # A tibble: 6 × 6
##   country     continent  year lifeExp      pop gdpPercap
##   <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
## 1 Afghanistan Asia       1952    28.8  8425333      779.
## 2 Afghanistan Asia       1957    30.3  9240934      821.
## 3 Afghanistan Asia       1962    32.0 10267083      853.
## 4 Afghanistan Asia       1967    34.0 11537966      836.
## 5 Afghanistan Asia       1972    36.1 13079460      740.
## 6 Afghanistan Asia       1977    38.4 14880372      786.

#install.packages("ggplot2")   # only once
library(ggplot2)              # every session

summary(gapminder)  

##         country        continent        year         lifeExp     
##  Afghanistan:  12   Africa  :624   Min.   :1952   Min.   :23.60  
##  Albania    :  12   Americas:300   1st Qu.:1966   1st Qu.:48.20  
##  Algeria    :  12   Asia    :396   Median :1980   Median :60.71  
##  Angola     :  12   Europe  :360   Mean   :1980   Mean   :59.47  
##  Argentina  :  12   Oceania : 24   3rd Qu.:1993   3rd Qu.:70.85  
##  Australia  :  12                  Max.   :2007   Max.   :82.60  
##  (Other)    :1632                                                
##       pop              gdpPercap       
##  Min.   :6.001e+04   Min.   :   241.2  
##  1st Qu.:2.794e+06   1st Qu.:  1202.1  
##  Median :7.024e+06   Median :  3531.8  
##  Mean   :2.960e+07   Mean   :  7215.3  
##  3rd Qu.:1.959e+07   3rd Qu.:  9325.5  
##  Max.   :1.319e+09   Max.   :113523.1  
## 

ggplot(gapminder, aes(x = gdpPercap, y = lifeExp)) + geom_point() 

# R Code
cor(gapminder$lifeExp, gapminder$gdpPercap, method = "pearson")

## [1] 0.5837062

# Visualise# install.packages("ggpubr")library(ggpubr)  ggscatter(gapminder, x = "gdpPercap", y = "lifeExp", add = "reg.line") 

# R Code for correlation
cor(gapminder$lifeExp, gapminder$gdpPercap, method = "spearman") 

## [1] 0.8264712

europe <- gapminder %>% filter(continent == "Europe") %>% pull(lifeExp) 
africa <- gapminder %>% filter(continent == "Africa") %>% pull(lifeExp) 
t.test(europe, africa) 

## 
##  Welch Two Sample t-test
## 
## data:  europe and africa
## t = 49.551, df = 981.2, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  22.12595 23.95076
## sample estimates:
## mean of x mean of y 
##  71.90369  48.86533

model <- lm(lifeExp ~ gdpPercap, data = gapminder) 
summary(model) 

## 
## Call:
## lm(formula = lifeExp ~ gdpPercap, data = gapminder)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -82.754  -7.758   2.176   8.225  18.426 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.396e+01  3.150e-01  171.29   <2e-16 ***
## gdpPercap   7.649e-04  2.579e-05   29.66   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.49 on 1702 degrees of freedom
## Multiple R-squared:  0.3407, Adjusted R-squared:  0.3403 
## F-statistic: 879.6 on 1 and 1702 DF,  p-value: < 2.2e-16

model_multi <- lm(lifeExp ~ gdpPercap + year + continent, data = gapminder)
summary(model_multi)

## 
## Call:
## lm(formula = lifeExp ~ gdpPercap + year + continent, data = gapminder)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -28.4264  -4.0725   0.2154   4.4853  19.9977 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       -5.207e+02  1.979e+01  -26.31   <2e-16 ***
## gdpPercap          2.967e-04  1.996e-05   14.87   <2e-16 ***
## year               2.874e-01  1.000e-02   28.73   <2e-16 ***
## continentAmericas  1.433e+01  4.936e-01   29.03   <2e-16 ***
## continentAsia      9.506e+00  4.567e-01   20.81   <2e-16 ***
## continentEurope    1.940e+01  5.173e-01   37.49   <2e-16 ***
## continentOceania   2.059e+01  1.469e+00   14.01   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.884 on 1697 degrees of freedom
## Multiple R-squared:  0.717,  Adjusted R-squared:  0.716 
## F-statistic: 716.6 on 6 and 1697 DF,  p-value: < 2.2e-16