#this is my first code
1+1
x<-3
x^2
income<-c(873,1050,2765,3423,4536)
mean(income)
age<-c(21,22,NA,51)
mean(age)
  mean(age,na.rm=TRUE)      

#part 1----
  
setwd("C:/Users/harari/Desktop/econometrics")
  OLS_EPOG_2016_population <-
    read.csv("OLS_EPOG_2016_population.csv", sep=";")
  
population<-OLS_EPOG_2016_population

N<-nrow(population);N
index<-sample(1:N,1)  
index
population[index,]

head(population)
names(population)

library(tidyverse)#install.package("tidyverse")

ggplot(population)+
  geom_histogram(aes(Income),color="black",
                 fill="white",bins=40)

q<-quantile(population$Income,c(.25,.5,.75))
quarts<-as_tibble(q) %>% mutate(y=0)

#sampling
n<- 50
indexes<-sample(1:N,n,replace=T);
sample_n<-population[indexes,]
#head(sample_n)
m_hat<-mean(sample_n$Income);m_hat
var_hat<-var(sample_n$Income)
means<-tibble(x=c(mean(population$Income),mean(sample_n$Income)), y=0)

ggplot(population,aes(y=..density..))+
  geom_histogram(aes(Income),color="black",fill="white",bins = 40)+
  geom_histogram(data=sample_n,aes(Income),fill="blue",alpha=0.3,bins = 20)+
  geom_point(data=means,aes(x=x,y=y),col=c("red","blue"),pch='x', cex=8)


#Confidence Interval ------------
n<- 50
indexes<-sample(1:N,n,replace=T);
sample_n<-population[indexes,]
#head(sample_n)
m_hat<-mean(sample_n$Income);m_hat
var_hat<-var(sample_n$Income)
means<-tibble(x=c(mean(population$Income),mean(sample_n$Income)), y=0)
l_b<-m_hat-sqrt(var_hat/n)*qt(.995, df=n-1);l_b # formula for the lower bound
u_b<-m_hat+sqrt(var_hat/n)*qt(.995, df=n-1);u_b # formula for the upper bound
IC<-tibble(x=c(l_b,u_b), y=0)

ggplot(population,aes(y=..density..))+
  geom_histogram(aes(Income),color="black",fill="white",bins = 40)+
  geom_histogram(data=sample_n,aes(Income),fill="blue",alpha=0.3,bins = 20)+
  geom_point(data=means,aes(x=x,y=y),col=c("red","blue"),pch='x', cex=8)+
  geom_point(data=IC,aes(x=x,y=y),col="blue",pch='I', cex=8)


# Linear model
ggplot(population,aes(x=Experience,y=Income))+
  geom_point()

ggplot(sample_n,aes(x=Experience,y=Income))+
  geom_point()+
  geom_line()

lm1<-lm(data=sample_n,Income~Experience)
summary(lm1)
plot(lm1)

lm2<-lm(sample_n$Income ~ sample_n$Experience-1)
ggplot(sample_n,aes(x=Experience,y=Income))+
  geom_point()+
  geom_line(aes(x=Experience,y=lm1$fitted.values),col='blue')+
  geom_line(aes(x=Experience,y=lm2$fitted.values),col='red')