print("******Simulation_Experiment_I******")

###Random_Variables###
x1 <- runif(100,min=0,max=5)
x2 <- rnorm(100,mean=5,sd=sqrt(2))+0.5*x1
u <- rnorm(100,mean=0,sd=1)
y <- 5+x1+0.5*x2+u
 
#Regression1: estimate_beta0_and_beta1
lm1.yx <- lm(y~1+x1+x2)
coe <- coefficients(lm1.yx)
coe0 <- coe[1]
coe1 <- coe[2]
print("---Regression1: estimate beta0 and beta1---")
print(paste("beta0:",coe0))
print(paste("beta1:",coe1))
 
#Regression2：estimate_alpha0_and_alpha1
lm2.yx <- lm(y~1+x1)
coe <- coefficients(lm2.yx)
coe0 <- coe[1]
coe1 <- coe[2]
print("---Regression2: estimate alpha0 and alpha1---")
print(paste("alpha0:",coe0))
print(paste("alpha1:",coe1))

#1000_mean
print("---1000 mean---")
###Regression1_1000###
sum1=0
for (i in 1:1000){
x1 <- runif(100,min=0,max=5)
x2 <- rnorm(100,mean=5,sd=sqrt(2))+0.5*x1
u <- rnorm(100,mean=0,sd=1)
y <- 5+x1+0.5*x2+u
lm1.yx <- lm(y~1+x1+x2)
coe=lm1.yx$coefficients
coe1 <- coe[2]
sum1 <- sum1+coe1
}
coe1 <- sum1/1000
print(paste("beta1:",coe1))
###Regression2_1000###
sum2=0
for (i in 1:1000){
x1 <- runif(100,min=0,max=5)
x2 <- rnorm(100,mean=5,sd=sqrt(2))+0.5*x1
u <- rnorm(100,mean=0,sd=1)
y <- 5+x1+0.5*x2+u
lm2.yx <- lm(y~1+x1)
coe=lm2.yx$coefficients
coe1 <- coe[2]
sum2 <- sum2+coe1
}
coe1 <- sum2/1000
print(paste("alpha1:",coe1))