diff --git a/.RData b/.RData
index f9c4142..0d1a132 100644
Binary files a/.RData and b/.RData differ
diff --git a/.Rhistory b/.Rhistory
index 6ab6247..2c5941f 100644
--- a/.Rhistory
+++ b/.Rhistory
@@ -1,493 +1,512 @@
-# definegrid
-p_grid <-seq(from=0,to=1,length.out=20)
-# defineprior
-#prior <-rep(1,20)
-prior <-ifelse(p_grid<0.5,0,1)
-# computelikelihoodateachvalueingrid
-likelihood <-dbinom(6,size=9,prob=p_grid)
-# computeproductoflikelihoodandprior
-unstd.posterior <-likelihood*prior
-# standardizetheposterior,soitsumsto1
-posterior <-unstd.posterior/sum(unstd.posterior)
-# definegrid
-p_grid <-seq(from=0,to=1,length.out=20)
-# defineprior
-#prior <-rep(1,20)
-prior <-ifelse(p_grid<0.5,0,1)
-# computelikelihoodateachvalueingrid
-likelihood <-dbinom(6,size=9,prob=p_grid)
-# computeproductoflikelihoodandprior
-unstd.posterior <-likelihood*prior
-# standardizetheposterior,soitsumsto1
-posterior <-unstd.posterior/sum(unstd.posterior)
-plot( p_grid,posterior,type="b",
-xlab="probability ofwater",ylab="posteriorprobability")
-mtext( "20points")
-# 2.7 analyticalcalculation
-W <-6
-L <-3
-curve( dbeta(x,W+1,L+1),from=0,to=1)
-# quadraticapproximation
-curve( dnorm(x,0.67,0.16),lty=2,add=TRUE)
+#dev.off()
+var = (1/20)*(theta_hat^2*(1+theta_hat)^2)/(theta_hat^2+(theta_hat+1)^2)
+post_approx = dnorm(theta_vec, theta_hat,sqrt(var))
+#pdf(file = "~/Dropbox/pubh8442/2015/Asymptotic_Posterior_Approximation_NormApp##.pdf", width = 7, height=4)
+plot(theta_vec,post_approx,xlim = c(0,6),  ylab = "Density", xlab = "theta", type = 'l', lwd = 2, main = "")
+abline(v=theta_hat, col = 'red')
+#dev.off()
 library(rethinking)
-f <- alist(
-y ~ dnorm( mu , sigma ),
-mu ~ dnorm( 0 , 10 ),
-sigma ~ dexp( 1 )
-)
-fit <- quap(
-f ,
-data=list(y=c(-1,1)) ,
-start=list(mu=0,sigma=1)
-)
-# definegrid
-p_grid <-seq(from=0,to=1,length.out=20)
-# defineprior
-#prior <-rep(1,20)
-prior <-ifelse(p_grid<0.5,0,1)
-# computelikelihoodateachvalueingrid
-likelihood <-dbinom(6,size=9,prob=p_grid)
-# computeproductoflikelihoodandprior
-unstd.posterior <-likelihood*prior
-# standardizetheposterior,soitsumsto1
-posterior <-unstd.posterior/sum(unstd.posterior)
-plot( p_grid,posterior,type="b",
-xlab="probability ofwater",ylab="posteriorprobability")
-mtext( "20points")
-# 2.7 analyticalcalculation
-W <-6
-L <-3
-curve( dbeta(x,W+1,L+1),from=0,to=1)
-# quadraticapproximation
-curve( dnorm(x,0.67,0.16),lty=2,add=TRUE)
-p <- c(0, .25, .5, .75, 1)
-model <- sapply(p, function (p, W, L) return (4*p)^W*(4-4*p)^L)
-print(model)
-n_samples <-1000
-p <-rep(NA,n_samples)
-p[1] <-0.5
-W <-6
-L <-3
-for (i in 2:n_samples){
-p_new <-rnorm(1,p[i-1],0.1)
-if (p_new < 0) p_new <- abs(p_new)
-if (p_new > 1) p_new <- 2-p_new
-q0 <-dbinom(W,W+L,p[i-1])
-q1 <-dbinom(W,W+L,p_new)
-p[i] <-ifelse(runif(1)<q1/q0,p_new,p[i-1])
-}
-plot(density(p),xlim=c(0,1))
-curve( dbeta(x, W+1, L+1 ),lty=2,add=TRUE)
-sample <- c('W','L','W','W','W','L','W','L','W')
-W <- sum(sample=='W') # No. of W observed
-L <- sum(sample=='L') # No. of L observed
-p <- c(0,.25,.5,.75,1) # Proportions W
-ways <- sapply(p, function (q) (q*4)^W*((1-q)*4)^L)
-prob <- ways/sum(ways)
-cbind(p, ways, prob)
-sim_globe <- function (p=.7, N = 9) {
-sample(c('W','L'), size = N, prob = c(p, 1-p), replace=TRUE)
-}
-sim_globe()
-replicate(sim_globe(p = .5, N = 9), n = 10)
-# definegrid
-p_grid <-seq(from=0,to=1,length.out=20)
-# defineprior
-#prior <-rep(1,20)
-prior <-ifelse(p_grid<0.5,0,1)
-# computelikelihoodateachvalueingrid
-likelihood <-dbinom(6,size=9,prob=p_grid)
-# computeproductoflikelihoodandprior
-unstd.posterior <-likelihood*prior
-# standardizetheposterior,soitsumsto1
-posterior <-unstd.posterior/sum(unstd.posterior)
-plot( p_grid,posterior,type="b",
-xlab="probability ofwater",ylab="posteriorprobability")
-mtext( "20points")
-# 2.7 analyticalcalculation
-W <-6
-L <-3
-curve( dbeta(x,W+1,L+1),from=0,to=1)
-# quadraticapproximation
-curve( dnorm(x,0.67,0.16),lty=2,add=TRUE)
-# definegrid
-p_grid <-seq(from=0,to=1,length.out=20)
-# defineprior
-#prior <-rep(1,20)
-prior <-ifelse(p_grid<0.5,0,1)
-# computelikelihoodateachvalueingrid
-likelihood <-dbinom(6,size=9,prob=p_grid)
-# computeproductoflikelihoodandprior
-unstd.posterior <-likelihood*prior
-# standardizetheposterior,soitsumsto1
-posterior <-unstd.posterior/sum(unstd.posterior)
-plot( p_grid,posterior,type="b",
-xlab="probability ofwater",ylab="posteriorprobability")
-mtext( "20points")
-# 2.7 analyticalcalculation
-W <-6
-L <-3
-curve( dbeta(x,W+1,L+1),from=0,to=1)
-# quadraticapproximation
-curve( dnorm(x,0.67,0.16),lty=2,add=TRUE)
-p <- c(0, .25, .5, .75, 1)
-model <- sapply(p, function (p, W, L) return (4*p)^W*(4-4*p)^L)
-print(model)
-n_samples <-1000
-p <-rep(NA,n_samples)
-p[1] <-0.5
-W <-6
-L <-3
-for (i in 2:n_samples){
-p_new <-rnorm(1,p[i-1],0.1)
-if (p_new < 0) p_new <- abs(p_new)
-if (p_new > 1) p_new <- 2-p_new
-q0 <-dbinom(W,W+L,p[i-1])
-q1 <-dbinom(W,W+L,p_new)
-p[i] <-ifelse(runif(1)<q1/q0,p_new,p[i-1])
-}
-plot(density(p),xlim=c(0,1))
-curve( dbeta(x, W+1, L+1 ),lty=2,add=TRUE)
-sample <- c('W','L','W','W','W','L','W','L','W')
-W <- sum(sample=='W') # No. of W observed
-L <- sum(sample=='L') # No. of L observed
-p <- c(0,.25,.5,.75,1) # Proportions W
-ways <- sapply(p, function (q) (q*4)^W*((1-q)*4)^L)
-prob <- ways/sum(ways)
-cbind(p, ways, prob)
-sim_globe <- function (p=.7, N = 9) {
-sample(c('W','L'), size = N, prob = c(p, 1-p), replace=TRUE)
-}
-sim_globe()
-replicate(sim_globe(p = .5, N = 9), n = 10)
-sum(sim_globe(p = .5, N = 1e4 )=='W')/1e4
-library(ggplot2)
-compute_posterior <- function (the_sample, poss = c(0,.25,.5,.75,1)) {
-W <- sum(the_sample=='W')  # No. of 'W'
-L <- sum(the_sample=='L')  # No. of 'L'
-ways <- sapply(p, function (q) (q*4)^W*((1-q)*4)^L)
-post <- ways/sum(ways)
-# bars <- sapply(post, function (q) make_bar(q))
-# data.frame(poss, ways, post=round(post,3), bars)
-df <- data.frame(poss, ways, post=round(post,3))
-ggplot(aes(x=poss, y=post), data=df)+
-geom_bar(stat="identity")
-}
-the_sample <- sim_globe()
-print(the_sample)
-compute_posterior(the_sample)
-post_samples <- rbeta(1e3, 6+1, 3+1)
-dens(post_samples, lwd=4, col=2, xlab="proportion water", adj=.1)
-curve(dbeta(x, 6+1, 3+1), add=TRUE, lty=2, lwd=3)
-w <-6;n<-9;
-p_grid <-seq(from=0,to=1,length.out=100)
-posterior <-dbinom(w,n,p_grid)*dunif(p_grid,0,1)
-posterior <-posterior/sum(posterior)
-plot(posterior,col=2, type="l")
-library(rethinking)
-sim_weight <- function (H, b, sd) {
-U <-  rnorm(length(H),0,sd)
-W <- b*H + U
-return(W)
-}
-H <-  runif(200, min=130, max=170)
-W <- sim_weight(H, b=.5, sd=5)
-plot(W ~ H, col=2, lwd=3)
+data(Howell1)
+d <-Howell1[Howell1$age>=18,]
 library(rethinking)
+library(tidyverse)
+library(dplyr)
 data(Howell1)
 d <-Howell1[Howell1$age>=18,]
-#Similate a sample of 10 people
-set.seed(93)
-H <- runif(10,130,170)
-W <- sim_weight(H,b=0.5, sd=5)
-#Run Model
-m3.1 <- quap(
+Howell |>
+plot(H, W)
+Howell1 |>
+ggplot(aes(x=height, y=weight))+
+geom_point()
+Howell1 |>
+ggplot(aes(x=height, y=weight))+
+geom_point(color=sex)+
+plot(H, W)
+Howell1 |>
+ggplot(aes(x=height, y=weight))+
+geom_point(color=sex)
+Howell1 |>
+ggplot(aes(x=height, y=weight))+
+geom_point(color=sex)
+View(Howell1)
+Howell1 |>
+ggplot(aes(x=height, y=weight))+
+geom_point(color=male)
+Howell1 |>
+ggplot(aes(x=height, y=weight, color=male))+
+geom_point()
+Howell1 |>
+ggplot(aes(x=weight, y=height, color=male))+
+geom_point()
+Howell1 |>
+ggplot(aes(x=weight, y=height, color=factor(male)))+
+geom_point()
+Howell1 |>
+ggplot(aes(x=hight, y=weight, color=factor(male)))+
+geom_point()
+Howell1 |>
+ggplot(aes(x=height, y=weight, color=factor(male)))+
+geom_point()
+d |>
+ggplot(aes(x=height, y=weight, color=factor(male)))+
+geom_point()
+plot(H, W)
+5/24
+d |>
+ggplot(aes(x=height, y=weight, color=factor(male)))+
+geom_point()
+d |>
+ggplot(aes(x=height, y=weight, color=factor(male)))+
+geom_point()
+d |>
+ggplot(aes(x=height, y=weight, color=factor(male)))+
+geom_density()
+d |>
+ggplot(aes(x=height, color=factor(male)))+
+geom_density(aes(y=weight))
+d |>
+ggplot(aes(x=weight))+
+geom_density(aes(color=factor(male)))
+d |>
+ggplot(aes(x=height, y=weight, color=factor(male)))+
+geom_point()+
+theme_bw()
+d |>
+ggplot(aes(x=weight))+
+geom_density(aes(color=factor(male)))+
+theme_bw()
+d |>
+ggplot(aes(x=height, y=weight, color=factor(male)))+
+geom_point()+
+theme_bw()
+d |>
+ggplot(aes(x=weight))+
+geom_density(aes(color=factor(male)))+
+theme_bw()
+d |>
+ggplot(aes(x=hight))+
+geom_density(aes(color=factor(male)))+
+theme_bw()
+d |>
+ggplot(aes(x=height, y=weight, color=factor(male)))+
+geom_point()+
+theme_bw()
+d |>
+ggplot(aes(x=weight))+
+geom_density(aes(color=factor(male)))+
+theme_bw()
+d |>
+ggplot(aes(x=height))+
+geom_density(aes(color=factor(male)))+
+theme_bw()
+# S = 1: female, S=2: male
+sim_HW <- function(S, b, a) {
+N <- length(S)
+H <- ifelse(S==1,150,160)+rnorm(N,0,5)
+data.frame(S,H,W)
+}
+W <- a[S] + b[S]*H + rnorm(N, 0, 5)
+# S = 1: female, S=2: male
+sim_HW <- function(S, b, a) {
+N <- length(S)
+H <- ifelse(S==1,150,160)+rnorm(N,0,5)
+W <- a[S] + b[S]*H + rnorm(N, 0, 5)
+data.frame(S,H,W)
+}
+S <- rbern(100)+1
+dat <- sim_HW(S, b=c(.5,.6), a=c(0,0))
+head(dat)
+dat |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+theme_bw()
+# female sample
+S <- rep(1,100)
+simF <- sim_HW(S, b=c(.5,.6), a=c(0,0))
+# male sample
+S <- rep(2,100)
+simM <- sim_HW(S, b=c(.5,.6), a=c(0,0))
+# effect of sex (male-female)
+mean(simM$W-simF$W)
+S <- rbern(100)+1
+dat <- sim_HW(S, b=c(.5,.6), a=c(0,0))
+# estimate posterior
+m_SW <- quap(
+alist(
+W~dnorm(mu,sigma),
+mu <- a[S],
+a[S] ~ dnorm(60,10),
+sigma ~ dunif(0,10)
+), data=dat
+)
+precis(m_SW,depth=2)
+# recoding
+dat <- list(
+W = d$weight,
+S = d$male+1
+)
+# estimate posterior
+m_SW <- quap(
+alist(
+W~dnorm(mu,sigma),
+mu <- a[S],
+a[S] ~ dnorm(60,10),
+sigma ~ dunif(0,10)
+), data=dat
+)
+precis(m_SW,depth=2)
+View(dat)
+post <- extract.samples(m_SW)
+dens(post$a[,1],xlim=c(35, 55),lwd=3,col=2,xlab="posterior mean weight(kg")
+dens(post$a[,2], lwd=3,col=4,add=TRUE)
+W1 <- rnorm(1000,post$a[,1], post$sigma)
+W2 <- rnorm(1000,post$a[,2], post$sigma)
+dens(W1,xlim=c(20,70),ylim(0,.085),lwd=3, col=2)
+W1 <- rnorm(1000,post$a[,1], post$sigma)
+W2 <- rnorm(1000,post$a[,2], post$sigma)
+dens(W1,xlim=c(20,70),ylim=c(0,.085),lwd=3, col=2)
+dens(W2,lwd=3, col=4, add=TRUE)
+W1
+post
+mu_contrast <- post$a[,2]-post$a[,1]
+dens(mu_contrast,xlim=c(3,10),lwd=3, col=1,xlab="posterior mean weight contrast(kg)")
+W1 <- rnorm(1000,post$a[,1], post$sigma)
+W2 <- rnorm(1000,post$a[,2], post$sigma)
+# conntrast
+W_contrast <- W2 - W1
+dens(W_contrast,xlim=c(-25,35),lwd=3, col=1,
+xlab="posterior weight contrast (kg)")
+W1 <- rnorm(1000,post$a[,1], post$sigma)
+W2 <- rnorm(1000,post$a[,2], post$sigma)
+# conntrast
+W_contrast <- W2 - W1
+dens(W_contrast,xlim=c(-25,35),lwd=3, col=1,
+xlab="posterior weight contrast (kg)")
+sum(W_contrast>0)/1000
+sum(W_contrast<0)/1000
+df <- data.frame (
+W1 = W1,
+W2 = W2,
+W_contrast = W_contrast
+)
+View(df)
+ggplot(df, aes(x=W_contrast, fill=W_contrast))
+ggplot(df, aes(x=W_contrast))
+ggplot(df, aes(x=W_contrast))+
+geom_area()
+ggplot(df, aes(x=W_contrast,fill=W_contrast))+
+geom_area()
+df <- data.frame (
+W1 = W1,
+W2 = W2,
+W_contrast = W_contrast,
+W_up = (W_contrast>0),
+W_down = !(W_up)
+)
+df <- data.frame (
+W1 = W1,
+W2 = W2,
+W_contrast = W_contrast,
+W_up = (W_contrast>0),
+W_down = (W_contrast<0)
+)
+ggplot(df, aes(x=W_contrast,fill=W_up))+
+geom_area()
+View(df)
+df <- data.frame (
+W1 = W1,
+W2 = W2,
+W_contrast = W_contrast,
+W_up = factor(W_contrast>0),
+W_down = factor(W_contrast<0)
+)
+View(df)
+ggplot(df, aes(x=W_contrast,fill=W_up))+
+geom_area()
+ggplot(df, aes(y=W_contrast,fill=W_up))+
+geom_area()
+ggplot(df, aes(y=W_contrast))+
+geom_area()
+View(post)
+df <- data.frame (
+W1 = W1,
+W2 = W2,
+W_contrast = W_contrast,
+W_up = factor(W_contrast>0),
+W_down = factor(W_contrast<0)
+)
+ggplot(df, aes(y=W_contrast))+
+geom_density()
+ggplot(df, aes(x=W_contrast))+
+geom_density()
+ggplot(df, aes(x=W_contrast))+
+geom_density()+
+theme_bw()
+ggplot(df, aes(x=W_contrast, fill=W_up))+
+geom_density()+
+theme_bw()
+ggplot(df, aes(x=W_contrast, fill=W_up))+
+geom_area()+
+theme_bw()
+ggplot(df, aes(x=W_contrast), fill=W_up))+
+ggplot(df, aes(x=W_contrast), fill=W_up))+
+ggplot(df, aes(x=W_contrast), fill=W_up)+
+geom_area()+
+theme_bw()
+ggplot(df, aes(x=W_contrast, y=W_contrastfill=W_up))+
+ggplot(df, aes(x=W_contrast, y=W_contrast,fill=W_up))+
+geom_area()+
+theme_bw()
+ggplot(df, aes(x=W_contrast, y=W1,fill=W_up))+
+geom_area()+
+theme_bw()
+df <- data.frame (
+W1 = W1,
+W2 = W2,
+W_contrast = W_contrast,
+W_flag = factor(W_contrast>W_up)
+)
+W_up <- sum(W_contrast>0)/1000
+W_down <- sum(W_contrast<0)/1000
+df <- data.frame (
+W1 = W1,
+W2 = W2,
+W_contrast = W_contrast,
+W_flag = factor(W_contrast>W_up)
+)
+View(df)
+ggplot(df, aes(x=W_contrast,fill=W_flag))+
+geom_area()+
+theme_bw()
+ggplot(df, aes(x=W_contrast,fill=W_flag))+
+geom_areadensity()+
+theme_bw()
+ggplot(df, aes(x=W_contrast,fill=W_flag))+
+geom_density()+
+theme_bw()
+W1 <- rnorm(1000,post$a[,1], post$sigma)
+W2 <- rnorm(1000,post$a[,2], post$sigma)
+# conntrast
+W_contrast <- W2 - W1
+dens(W_contrast,xlim=c(-25,35),lwd=3, col=1,
+xlab="posterior weight contrast (kg)")
+W_up <- sum(W_contrast>0)/1000
+W_down <- sum(W_contrast<0)/1000
+cat("W_up:",W_up," and W_down:",W_down)
+df <- data.frame (
+W1 = W1,
+W2 = W2,
+W_contrast = W_contrast,
+W_flag = factor(W_contrast>W_up)
+)
+ggplot(df, aes(x=W_contrast,fill=W_flag))+
+geom_density()+
+theme_bw()
+S <- rbern(100)+1
+dat <- sim_HW(S, b=c(.5,.5), a=c(0,10))
+# Indirect effect (b) is the same for men and women
+# Indirect effect (b) is the same for men and women
+dat |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+theme_bw()
+# Indirect effect (b) is the same for men and women
+dat |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+geom_smooth(method = lm)+
+theme_bw()
+# Indirect effect (b) is the same for men and women
+dat |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+geom_smooth(method = lm)+
+facet_wrap(~S)+
+theme_bw()
+```{r, warning=FALSE}
+S <- rbern(100)+1
+dat <- sim_HW(S, b=c(.5,.5), a=c(0,10))
+# Indirect effect (b) is the same for men and women
+dat |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+geom_smooth(method = lm)+
+facet_wrap(~S)+
+theme_bw()
+S <- rbern(100)+1
+dat <- sim_HW(S, b=c(.5,.5), a=c(0,10))
+# Indirect effect (b) is the same for men and women
+dat |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+geom_smooth(method = lm)+
+facet_wrap(~S)+
+theme_bw()
+S <- rbern(100)+1
+dat <- sim_HW(S, b=c(.5,.5), a=c(0,10))
+# Indirect effect (b) is the same for men and women
+dat |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+geom_smooth(method = lm)+
+# facet_wrap(~S)+
+theme_bw()
+dat <- list(
+W = d$weight,
+H = d$height,
+Hbar = mean(d$height),
+S = d$male+1 )
+m_SHW <- quap(
 alist(
 W ~ dnorm(mu,sigma),
-mu <- a + b*H,
-a ~ dnorm(0,10),
-b ~ dunif(0,1),
-sigma~dunif(0,10)
-),data=list(W=W, H=H))
-#Summary
-precis(m3.1)
-n <- 1e3
-a <- rnorm(n,0,10)
-b <- runif(n,0,1)
-plot(NULL,xlim=c(130,170),ylim=c(50,90),
-xlab="height(cm)", ylab="weight(kg)",)
-for (j in 1:50 ) abline(a=a[j], b=b[j], lwd=2, col=2)
-dat <- list(W=d$weight, H=d$height)
-#k <- 10
-#dat <- list(W=d$weight[1:k], H=d$height[1:k])
-#Run Model
-m3.2 <- quap(
+mu <- a[S]+b[S]*(H-Hbar),
+a[S] ~ dnorm(60,10),
+b[S] ~ dunif(0,1),
+sigma ~ dunif(0,10)
+), data=dat
+)
+dat <- list(
+W = d$weight,
+H = d$height,
+Hbar = mean(d$height),
+S = d$male+1 )
+m_SHW <- quap(
 alist(
 W ~ dnorm(mu,sigma),
-mu <- a + b*H,
-a ~ dnorm(0,10),
-b ~ dunif(0,1),
-sigma~dunif(0,10)
-),data=dat)
-precis(m3.2)
-post <- extract.samples(m3.2)
-plot(dat$H,dat$W,col=2,lwd=3,
-xlim=c(min(dat$H),max(dat$H)), ylim=c(min(30,dat$w),max(dat$W)),
-xlab="height(cm)", ylab="weight(kg)")
-for (j in 1:20)
-abline(a=post$a[j],b=post$b[j], lty=1)
-post <- extract.samples(m3.2)
-pairs(post)
-head(post)
-plot(d$height,d$weight,col=2,lwd=3,
-xlab="height(cm)", ylab="weight(kg)")
-for (j in 1:20)
-abline(a=post$a[j],b=post$b[j], lty=1)
-height_seq <- seq(130,190,len=20)
-W_postpred <- sim(m3.2,data=list(H=height_seq))
-W_PI <- apply(W_postpred,2,PI)
-lines(height_seq,W_PI[1,],lty=2,lwd=2)
-lines(height_seq,W_PI[2,],lty=2,lwd=2)
-# definegrid
-p_grid <-seq(from=0,to=1,length.out=20)
-# defineprior
-#prior <-rep(1,20)
-prior <-ifelse(p_grid<0.5,0,1)
-# computelikelihoodateachvalueingrid
-likelihood <-dbinom(6,size=9,prob=p_grid)
-# computeproductoflikelihoodandprior
-unstd.posterior <-likelihood*prior
-# standardizetheposterior,soitsumsto1
-posterior <-unstd.posterior/sum(unstd.posterior)
-plot( p_grid,posterior,type="b",
-xlab="probability ofwater",ylab="posteriorprobability")
-mtext( "20points")
-# 2.7 analyticalcalculation
-W <-6
-L <-3
-curve( dbeta(x,W+1,L+1),from=0,to=1)
-# quadraticapproximation
-curve( dnorm(x,0.67,0.16),lty=2,add=TRUE)
-# definegrid
-p_grid <-seq(from=0,to=1,length.out=20)
-# defineprior
-#prior <-rep(1,20)
-prior <-ifelse(p_grid<0.5,0,1)
-# computelikelihoodateachvalueingrid
-likelihood <-dbinom(6,size=9,prob=p_grid)
-# computeproductoflikelihoodandprior
-unstd.posterior <-likelihood*prior
-# standardizetheposterior,soitsumsto1
-posterior <-unstd.posterior/sum(unstd.posterior)
-plot( p_grid,posterior,type="b",
-xlab="probability ofwater",ylab="posteriorprobability")
-mtext( "20points")
-# 2.7 analyticalcalculation
-W <-6
-L <-3
-curve( dbeta(x,W+1,L+1),from=0,to=1)
-# quadraticapproximation
-curve( dnorm(x,0.67,0.16),lty=2,add=TRUE)
-p <- c(0, .25, .5, .75, 1)
-model <- sapply(p, function (p, W, L) return (4*p)^W*(4-4*p)^L)
-print(model)
-n_samples <-1000
-p <-rep(NA,n_samples)
-p[1] <-0.5
-W <-6
-L <-3
-for (i in 2:n_samples){
-p_new <-rnorm(1,p[i-1],0.1)
-if (p_new < 0) p_new <- abs(p_new)
-if (p_new > 1) p_new <- 2-p_new
-q0 <-dbinom(W,W+L,p[i-1])
-q1 <-dbinom(W,W+L,p_new)
-p[i] <-ifelse(runif(1)<q1/q0,p_new,p[i-1])
-}
-plot(density(p),xlim=c(0,1))
-curve( dbeta(x, W+1, L+1 ),lty=2,add=TRUE)
-sample <- c('W','L','W','W','W','L','W','L','W')
-W <- sum(sample=='W') # No. of W observed
-L <- sum(sample=='L') # No. of L observed
-p <- c(0,.25,.5,.75,1) # Proportions W
-ways <- sapply(p, function (q) (q*4)^W*((1-q)*4)^L)
-prob <- ways/sum(ways)
-cbind(p, ways, prob)
-sim_globe <- function (p=.7, N = 9) {
-sample(c('W','L'), size = N, prob = c(p, 1-p), replace=TRUE)
-}
-sim_globe()
-replicate(sim_globe(p = .5, N = 9), n = 10)
-sum(sim_globe(p = .5, N = 1e4 )=='W')/1e4
-library(ggplot2)
-compute_posterior <- function (the_sample, poss = c(0,.25,.5,.75,1)) {
-W <- sum(the_sample=='W')  # No. of 'W'
-L <- sum(the_sample=='L')  # No. of 'L'
-ways <- sapply(p, function (q) (q*4)^W*((1-q)*4)^L)
-post <- ways/sum(ways)
-# bars <- sapply(post, function (q) make_bar(q))
-# data.frame(poss, ways, post=round(post,3), bars)
-df <- data.frame(poss, ways, post=round(post,3))
-ggplot(aes(x=poss, y=post), data=df)+
-geom_bar(stat="identity")
-}
-the_sample <- sim_globe()
-print(the_sample)
-compute_posterior(the_sample)
-library(rethinking)
-post_samples <- rbeta(1e3, 6+1, 3+1)
-dens(post_samples, lwd=4, col=2, xlab="proportion water", adj=.1)
-curve(dbeta(x, 6+1, 3+1), add=TRUE, lty=2, lwd=3)
-w <-6;n<-9;
-p_grid <-seq(from=0,to=1,length.out=100)
-posterior <-dbinom(w,n,p_grid)*dunif(p_grid,0,1)
-posterior <-posterior/sum(posterior)
-plot(posterior,col=2, type="l")
-library(rethinking)
-sim_weight <- function (H, b, sd) {
-U <-  rnorm(length(H),0,sd)
-W <- b*H + U
-return(W)
-}
-H <-  runif(200, min=130, max=170)
-W <- sim_weight(H, b=.5, sd=5)
-plot(W ~ H, col=2, lwd=3)
-library(rethinking)
-data(Howell1)
-d <-Howell1[Howell1$age>=18,]
-#Similate a sample of 10 people
-set.seed(93)
-H <- runif(10,130,170)
-W <- sim_weight(H,b=0.5, sd=5)
-#Run Model
-m3.1 <- quap(
+mu <- a[S]+b[S]*(H-Hbar),
+a[S] ~ dnorm(60,10),
+b[S] ~ dunif(0,1),
+sigma ~ dunif(0,10)
+), data=dat
+)
+precis(m_SHW,depth=2)
+post <- extract.samples(m_SHW)
+dens(post$a[,1],xlim=c(35, 55),lwd=3,col=2,xlab="posterior mean weight(kg")
+dens(post$a[,2], lwd=3,col=4,add=TRUE)
+post <- extract.samples(m_SHW)
+dens(post$b[,1],xlim=c(35, 55),lwd=3,col=2,xlab="posterior mean weight(kg")
+dens(post$b[,2], lwd=3,col=4,add=TRUE)
+post <- extract.samples(m_SHW)
+dens(post$b[,1],lwd=3,col=2,xlab="posterior mean weight(kg")
+dens(post$b[,2],lwd=3,col=4,add=TRUE)
+post <- extract.samples(m_SHW)
+dens(post$b[,1],xlim=c(.3, .9),lwd=3,col=2,xlab="posterior mean weight(kg")
+dens(post$b[,2],lwd=3,col=4,add=TRUE)
+post <- extract.samples(m_SHW)
+dens(post$b[,1],xlim=c(.3, .9),ylim=c(0,8),
+lwd=3,col=2,xlab="posterior mean weight(kg")
+dens(post$b[,2],lwd=3,col=4,add=TRUE)
+dat <- list(
+W = d$weight,
+H = d$height,
+Hbar = mean(d$height),
+S = d$male+1 )
+m_SHW <- quap(
 alist(
 W ~ dnorm(mu,sigma),
-mu <- a + b*H,
-a ~ dnorm(0,10),
-b ~ dunif(0,1),
-sigma~dunif(0,10)
-),data=list(W=W, H=H))
-#Summary
-precis(m3.1)
-n <- 1e3
-a <- rnorm(n,0,10)
-b <- runif(n,0,1)
-plot(NULL,xlim=c(130,170),ylim=c(50,90),
-xlab="height(cm)", ylab="weight(kg)",)
-for (j in 1:50 ) abline(a=a[j], b=b[j], lwd=2, col=2)
-dat <- list(W=d$weight, H=d$height)
-#k <- 10
-#dat <- list(W=d$weight[1:k], H=d$height[1:k])
-#Run Model
-m3.2 <- quap(
+mu <- a[S]+b[S]*(H-Hbar),
+a[S] ~ dnorm(60,10),
+b[S] ~ dunif(0,1),
+sigma ~ dunif(0,10)
+), data=dat
+)
+dat |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+geom_smooth(method = lm)+
+# facet_wrap(~S)+
+theme_bw()
+data.frame(dat) |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+geom_smooth(method = lm)+
+# facet_wrap(~S)+
+theme_bw()
+```{r, message=FALSE}
+dat <- list(
+W = d$weight,
+H = d$height,
+Hbar = mean(d$height),
+S = d$male+1 )
+m_SHW <- quap(
 alist(
 W ~ dnorm(mu,sigma),
-mu <- a + b*H,
-a ~ dnorm(0,10),
-b ~ dunif(0,1),
-sigma~dunif(0,10)
-),data=dat)
-precis(m3.2)
-post <- extract.samples(m3.2)
-plot(dat$H,dat$W,col=2,lwd=3,
-xlim=c(min(dat$H),max(dat$H)), ylim=c(min(30,dat$w),max(dat$W)),
-xlab="height(cm)", ylab="weight(kg)")
-for (j in 1:20)
-abline(a=post$a[j],b=post$b[j], lty=1)
-post <- extract.samples(m3.2)
-pairs(post)
-head(post)
-plot(d$height,d$weight,col=2,lwd=3,
-xlab="height(cm)", ylab="weight(kg)")
-for (j in 1:20)
-abline(a=post$a[j],b=post$b[j], lty=1)
-height_seq <- seq(130,190,len=20)
-W_postpred <- sim(m3.2,data=list(H=height_seq))
-W_PI <- apply(W_postpred,2,PI)
-lines(height_seq,W_PI[1,],lty=2,lwd=2)
-lines(height_seq,W_PI[2,],lty=2,lwd=2)
-pos_true <- .95
-pos <- .01
-true_pos <- (pos_true*pos)/(pos_true*pos+(1-pos_true)*(1-pos))
-true_pos
-true_pos <- sapply(seq(from=.01, to=.95, by=0.01), function (pos) return (pos_true*pos)/(pos_true*pos+(1-pos_true)*(1-pos)))
-plot(true_pos, col=2, lwd=2)
-true_pos <- sapply(pos=seq(from=.01, to=.95, by=0.01), function (pos) return (pos_true*pos)/(pos_true*pos+(1-pos_true)*(1-pos)))
-true_pos <- sapply(c(.01), function (pos) return (pos_true*pos)/(pos_true*pos+(1-pos_true)*(1-pos)))
-plot(true_pos, col=2, lwd=2)
-true_pos <- sapply(c(.01), function (p) return (pos_true*p)/(pos_true*p+(1-pos_true)*(1-p)))
-true_pos <- sapply(c(.01), function (p, pt) return (pt*p)/(pt*p+(1-pt)*(1-p)))
-pt <- pos_true
-true_pos <- sapply(c(.01), function (p, pt) return (pt*p)/(pt*p+(1-pt)*(1-p)))
-pt <- pos_true
-true_pos <- sapply(c(.01), function (p, pt) return (pt*p)/(pt*p+(1-pt)*(1-p)))
-seq(from=.01, to=.95, by=0.01)
-seq(from=.01, to=1, by=0.01)
-x <- list(p = seq(from=.01, to=1, by=0.01), pt=rep(.95, 100))
-x <- list(p = seq(from=.01, to=1, by=0.01), pt=rep(.95, 100))
-View(x)
-true_pos <- sapply(x, function (p, pt) return (pt*p)/(pt*p+(1-pt)*(1-p)))
-true_pos <- sapply(x, function (p) return (pt*p)/(pt*p+(1-pt)*(1-p)))
-true_pos <- sapply(x, function (p) return (pt*p)/(pt*p+(1-pt)*(1-p)))
-plot(true_pos, col=2, lwd=2)
-pos_true <- .95 # likelihood
-pos <- .01 # prior
-true_pos <- (pos_true*pos)/(pos_true*pos+(1-pos_true)*(1-pos))
-true_pos  # posterior
-x[1]
-x[,1]
-x[1]
-x[2]
-p <- c(0, .25, .5, .75, 1)
-model <- sapply(p, function (p, W, L) return (4*p)^W*(4-4*p)^L)
-print(model)
-x <- list(p = seq(from=.01, to=1, by=0.01), pt=rep(.95, 100))
-true_pos <- sapply(x, function (p=p, pt=pt) return (pt*p)/(pt*p+(1-pt)*(1-p)))
-x <- list(p = seq(from=.01, to=1, by=0.01), ptr=rep(.95, 100))
-true_pos <- sapply(x, function (p,ptr) return (ptr*p)/(ptr*p+(1-ptr)*(1-p)))
-View(x)
-true_pos <- sapply(x$p, x$ptr, function (p,ptr) return (ptr*p)/(ptr*p+(1-ptr)*(1-p)))
-ptr <- .95
-true_pos <- sapply(x$p, function (p,ptr) return (ptr*p)/(ptr*p+(1-ptr)*(1-p)))
-p <- seq(from=.01, to=1, by=0.01)
-true_pos <- sapply(p, function (p) return (ptr*p)/(ptr*p+(1-ptr)*(1-p)))
-plot(true_pos, col=2, lwd=2)
-(ptr*p)/(ptr*p+(1-ptr)*(1-p))
-true_pos <- apply(p, function (p) return (ptr*p)/(ptr*p+(1-ptr)*(1-p)))
-plot(true_pos, col=2, lwd=2)
-true_pos <- lapply(p, function (p) return (ptr*p)/(ptr*p+(1-ptr)*(1-p)))
-plot(true_pos, col=2, lwd=2)
-View(true_pos)
-true_pos <- sapply(p, function (p) return (ptr*p)/(ptr*p+(1-ptr)*(1-p)))
-(ptr*p[1])/(ptr*p[1]+(1-ptr)*(1-p[1]))
-sample <- c('W','L','W','W','W','L','W','L','W')
-W <- sum(sample=='W') # No. of W observed
-L <- sum(sample=='L') # No. of L observed
-p <- c(0,.25,.5,.75,1) # Proportions W
-ways <- sapply(p, function (q) (q*4)^W*((1-q)*4)^L)
-prob <- ways/sum(ways)
-cbind(p, ways, prob)
-(q*4)^W*((1-q)*4)^L
-true_pos <- sapply(p, function (q) return (ptr*q)/(ptr*q+(1-ptr)*(1-q)))
-p <- seq(from=.01, to=1, by=0.01)
-ptr <- .95
-true_pos <- sapply(p, function (q) return (ptr*q)/(ptr*q+(1-ptr)*(1-q)))
-sapply(p, function (q) return (ptr*q)/(ptr*q+(1-ptr)*(1-q)))
-sapply(p, function (q) (q*4)^W*((1-q)*4)^L)
-ways <- sapply(p, function (q) (q*4)^W*((1-q)*4)^L)
-p <- c(0,.25,.5,.75,1) # Proportions W
-ways <- sapply(p, function (q) (q*4)^W*((1-q)*4)^L)
-p <- seq(from=.01, to=1, by=0.01)
-ptr <- .95
-true_pos <- sapply(p, function (q) (ptr*q)/(ptr*q+(1-ptr)*(1-q)))
-plot(true_pos, col=2, lwd=2)
-plot(true_pos, p, col=2, lwd=2)
-plot(true_pos, p, col=2, lwd=3, lty="l")
-plot(true_pos, p, col=2, lwd=3, lty=3)
-p <- seq(from=.01, to=1, by=0.01); ptr <- .95
-true_pos <- sapply(p, function (q) (ptr*q)/(ptr*q+(1-ptr)*(1-q)))
-plot(true_pos, p, col=2, lwd=3, lty=3)
-p <- seq(from=.01, to=1, by=0.01); ptr <- .95
-true_pos <- sapply(p, function (q) (ptr*q)/(ptr*q+(1-ptr)*(1-q)))
-plot(true_pos, p, col=2, lwd=3)
+mu <- a[S]+b[S]*(H-Hbar),
+a[S] ~ dnorm(60,10),
+b[S] ~ dunif(0,1),
+sigma ~ dunif(0,10)
+), data=dat
+)
+dat <- list(
+W = d$weight,
+H = d$height,
+Hbar = mean(d$height),
+S = d$male+1 )
+m_SHW <- quap(
+alist(
+W ~ dnorm(mu,sigma),
+mu <- a[S]+b[S]*(H-Hbar),
+a[S] ~ dnorm(60,10),
+b[S] ~ dunif(0,1),
+sigma ~ dunif(0,10)
+), data=dat
+)
+dat <- list(
+W = d$weight,
+H = d$height,
+Hbar = mean(d$height),
+S = d$male+1 )
+m_SHW <- quap(
+alist(
+W ~ dnorm(mu,sigma),
+mu <- a[S]+b[S]*(H-Hbar),
+a[S] ~ dnorm(60,10),
+b[S] ~ dunif(0,1),
+sigma ~ dunif(0,10)
+), data=dat
+)
+data.frame(dat) |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+geom_smooth(method = lm)+
+# facet_wrap(~S)+
+theme_bw()
+precis(m_SHW,depth=2)
+dat <- list(
+W = d$weight,
+H = d$height,
+Hbar = mean(d$height),
+S = d$male+1 )
+m_SHW <- quap(
+alist(
+W ~ dnorm(mu,sigma),
+mu <- a[S]+b[S]*(H-Hbar),
+a[S] ~ dnorm(60,10),
+b[S] ~ dunif(0,1),
+sigma ~ dunif(0,10)
+), data=dat
+)
+dat <- list(
+W = d$weight,
+H = d$height,
+Hbar = mean(d$height),
+S = d$male+1 )
+m_SHW <- quap(
+alist(
+W ~ dnorm(mu,sigma),
+mu <- a[S]+b[S]*(H-Hbar),
+a[S] ~ dnorm(60,10),
+b[S] ~ dunif(0,1),
+sigma ~ dunif(0,10)
+), data=dat
+)
+data.frame(dat) |>
+ggplot(aes(x=H, y=W, color=factor(S)))+
+geom_point()+
+geom_smooth(method = lm)+
+# facet_wrap(~S)+
+theme_bw()
+precis(m_SHW,depth=2)
+xseq <- seq(from=130,to=190, len=50)
+muF <-
+link(m_adults2, data=list(S=rep(1,50),H=xseq,Hbar=mean(d$height)))
diff --git a/.Rproj.user/B584AE7E/pcs/windowlayoutstate.pper b/.Rproj.user/B584AE7E/pcs/windowlayoutstate.pper
index abd43e2..6065b0a 100644
--- a/.Rproj.user/B584AE7E/pcs/windowlayoutstate.pper
+++ b/.Rproj.user/B584AE7E/pcs/windowlayoutstate.pper
@@ -1,6 +1,6 @@
 {
     "left": {
-        "splitterpos": 401,
+        "splitterpos": 155,
         "topwindowstate": "NORMAL",
         "panelheight": 959,
         "windowheight": 997
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/77F68D30 b/.Rproj.user/B584AE7E/sources/per/t/77F68D30
similarity index 80%
rename from .Rproj.user/B584AE7E/sources/session-605e3cd7/77F68D30
rename to .Rproj.user/B584AE7E/sources/per/t/77F68D30
index 1f97a83..f1f442a 100644
--- a/.Rproj.user/B584AE7E/sources/session-605e3cd7/77F68D30
+++ b/.Rproj.user/B584AE7E/sources/per/t/77F68D30
@@ -3,7 +3,7 @@
     "path": "C:/Users/lacor/OneDrive/100. Personal/SelfDevelopment/25. Project 2022/Statistical-Thinking-2023/Statistical Thinking 2023_v2.qmd",
     "project_path": "Statistical Thinking 2023_v2.qmd",
     "type": "quarto_markdown",
-    "hash": "1895704522",
+    "hash": "799310168",
     "contents": "",
     "dirty": false,
     "created": 1673908998203.0,
@@ -16,16 +16,16 @@
         "Source": "Source",
         "docOutlineVisible": "1",
         "rmdVisualCollapsedChunks": "",
-        "rmdVisualModeLocation": "10046:19198",
-        "cursorPosition": "527,0",
+        "rmdVisualModeLocation": "11232:22202",
+        "cursorPosition": "602,0",
         "scrollLine": "0"
     },
     "folds": "",
-    "lastKnownWriteTime": 1674170667,
+    "lastKnownWriteTime": 1674187233,
     "encoding": "UTF-8",
     "collab_server": "",
     "source_window": "",
-    "last_content_update": 1674170667303,
+    "last_content_update": 1674187233984,
     "read_only": false,
     "read_only_alternatives": []
 }
\ No newline at end of file
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/77F68D30-contents b/.Rproj.user/B584AE7E/sources/per/t/77F68D30-contents
similarity index 91%
rename from .Rproj.user/B584AE7E/sources/session-605e3cd7/77F68D30-contents
rename to .Rproj.user/B584AE7E/sources/per/t/77F68D30-contents
index 70a56f8..e67ef4b 100644
--- a/.Rproj.user/B584AE7E/sources/session-605e3cd7/77F68D30-contents
+++ b/.Rproj.user/B584AE7E/sources/per/t/77F68D30-contents
@@ -549,3 +549,57 @@ ggplot(df, aes(x=W_contrast,fill=W_flag))+
   geom_density()+
   theme_bw()
 ```
+
+Now, what is the direct effect of sex over weight?
+
+```{r, message=FALSE}
+S <- rbern(100)+1
+dat <- sim_HW(S, b=c(.5,.5), a=c(0,10))
+
+# Indirect effect (b) is the same for men and women
+dat |> 
+  ggplot(aes(x=H, y=W, color=factor(S)))+
+  geom_point()+
+  geom_smooth(method = lm)+
+  # facet_wrap(~S)+
+  theme_bw()
+```
+
+```{r, message=FALSE}
+dat <- list(
+  W = d$weight,
+  H = d$height,
+  Hbar = mean(d$height),
+  S = d$male+1 )
+
+m_SHW <- quap(
+  alist(
+    W ~ dnorm(mu,sigma),
+    mu <- a[S]+b[S]*(H-Hbar),
+    a[S] ~ dnorm(60,10),
+    b[S] ~ dunif(0,1),
+    sigma ~ dunif(0,10)
+  ), data=dat
+)
+data.frame(dat) |> 
+  ggplot(aes(x=H, y=W, color=factor(S)))+
+  geom_point()+
+  geom_smooth(method = lm)+
+  # facet_wrap(~S)+
+  theme_bw()
+
+precis(m_SHW,depth=2)
+```
+
+Note that regression line's slopes are almost the same for both male and female.
+
+```{r}
+post <- extract.samples(m_SHW)
+dens(post$b[,1],xlim=c(.3, .9),ylim=c(0,8),
+     lwd=3,col=2,xlab="posterior mean weight(kg)")
+dens(post$b[,2],lwd=3,col=4,add=TRUE)
+```
+
+```{r}
+
+```
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/884F836F b/.Rproj.user/B584AE7E/sources/per/t/884F836F
similarity index 100%
rename from .Rproj.user/B584AE7E/sources/session-605e3cd7/884F836F
rename to .Rproj.user/B584AE7E/sources/per/t/884F836F
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/884F836F-contents b/.Rproj.user/B584AE7E/sources/per/t/884F836F-contents
similarity index 100%
rename from .Rproj.user/B584AE7E/sources/session-605e3cd7/884F836F-contents
rename to .Rproj.user/B584AE7E/sources/per/t/884F836F-contents
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/9F66EA64 b/.Rproj.user/B584AE7E/sources/per/t/9F66EA64
similarity index 100%
rename from .Rproj.user/B584AE7E/sources/session-605e3cd7/9F66EA64
rename to .Rproj.user/B584AE7E/sources/per/t/9F66EA64
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/9F66EA64-contents b/.Rproj.user/B584AE7E/sources/per/t/9F66EA64-contents
similarity index 100%
rename from .Rproj.user/B584AE7E/sources/session-605e3cd7/9F66EA64-contents
rename to .Rproj.user/B584AE7E/sources/per/t/9F66EA64-contents
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/E0A14F48 b/.Rproj.user/B584AE7E/sources/per/t/E0A14F48
similarity index 96%
rename from .Rproj.user/B584AE7E/sources/session-605e3cd7/E0A14F48
rename to .Rproj.user/B584AE7E/sources/per/t/E0A14F48
index e870a96..7983484 100644
--- a/.Rproj.user/B584AE7E/sources/session-605e3cd7/E0A14F48
+++ b/.Rproj.user/B584AE7E/sources/per/t/E0A14F48
@@ -3,7 +3,7 @@
     "path": "C:/Users/lacor/OneDrive/100. Personal/SelfDevelopment/20. Project 2019/StockMarket/Asset_Analysis_v23.Rmd",
     "project_path": null,
     "type": "r_markdown",
-    "hash": "0",
+    "hash": "1870848255",
     "contents": "",
     "dirty": false,
     "created": 1674164268355.0,
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/E0A14F48-contents b/.Rproj.user/B584AE7E/sources/per/t/E0A14F48-contents
similarity index 100%
rename from .Rproj.user/B584AE7E/sources/session-605e3cd7/E0A14F48-contents
rename to .Rproj.user/B584AE7E/sources/per/t/E0A14F48-contents
diff --git a/.Rproj.user/B584AE7E/sources/prop/EA93BB00 b/.Rproj.user/B584AE7E/sources/prop/EA93BB00
index a71d353..f21c38d 100644
--- a/.Rproj.user/B584AE7E/sources/prop/EA93BB00
+++ b/.Rproj.user/B584AE7E/sources/prop/EA93BB00
@@ -5,7 +5,7 @@
     "Source": "Source",
     "docOutlineVisible": "1",
     "rmdVisualCollapsedChunks": "",
-    "rmdVisualModeLocation": "10046:19198",
-    "cursorPosition": "527,0",
+    "rmdVisualModeLocation": "11232:22202",
+    "cursorPosition": "602,0",
     "scrollLine": "0"
 }
\ No newline at end of file
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/231C5E6B-contents b/.Rproj.user/B584AE7E/sources/session-605e3cd7/231C5E6B-contents
deleted file mode 100644
index e69de29..0000000
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/388DADFE-contents b/.Rproj.user/B584AE7E/sources/session-605e3cd7/388DADFE-contents
deleted file mode 100644
index e69de29..0000000
diff --git a/.Rproj.user/B584AE7E/sources/session-605e3cd7/lock_file b/.Rproj.user/B584AE7E/sources/session-605e3cd7/lock_file
deleted file mode 100644
index e69de29..0000000
diff --git a/.Rproj.user/B584AE7E/viewer-cache/993CD89E.Rdata b/.Rproj.user/B584AE7E/viewer-cache/993CD89E.Rdata
new file mode 100644
index 0000000..3d0653e
Binary files /dev/null and b/.Rproj.user/B584AE7E/viewer-cache/993CD89E.Rdata differ
diff --git a/.Rproj.user/B584AE7E/viewer-cache/FBB44727.Rdata b/.Rproj.user/B584AE7E/viewer-cache/FBB44727.Rdata
new file mode 100644
index 0000000..109d1f0
Binary files /dev/null and b/.Rproj.user/B584AE7E/viewer-cache/FBB44727.Rdata differ
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/B584AE7E605e3cd7/chunks.json b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/B584AE7E605e3cd7/chunks.json
index 6ebb033..eefcdce 100644
--- a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/B584AE7E605e3cd7/chunks.json	
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/B584AE7E605e3cd7/chunks.json	
@@ -1 +1 @@
-{"chunk_definitions":[{"row":47,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-40"},"document_id":"77F68D30","chunk_id":"c0jrftmj331il","chunk_label":"unnamed-chunk-1"},{"row":53,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-41"},"document_id":"77F68D30","chunk_id":"cnq8c446n0wtz","chunk_label":"unnamed-chunk-2"},{"row":67,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-42"},"document_id":"77F68D30","chunk_id":"c3qooae84c4xs","chunk_label":"unnamed-chunk-3"},{"row":87,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-43"},"document_id":"77F68D30","chunk_id":"c8k36ylh3ik2z","chunk_label":"unnamed-chunk-4"},{"row":93,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-44"},"document_id":"77F68D30","chunk_id":"cff5zae4b4ix2","chunk_label":"unnamed-chunk-5"},{"row":107,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-45"},"document_id":"77F68D30","chunk_id":"cuj4f1k7oy0f9","chunk_label":"unnamed-chunk-6"},{"row":113,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-25"},"document_id":"77F68D30","chunk_id":"c3b4hkzi6i1gq","chunk_label":"unnamed-chunk-7"},{"row":129,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-47"},"document_id":"77F68D30","chunk_id":"cryc9nwjktom8","chunk_label":"unnamed-chunk-8"},{"row":134,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-48"},"document_id":"77F68D30","chunk_id":"c11kjcel8rada","chunk_label":"unnamed-chunk-9"},{"row":144,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-52"},"document_id":"77F68D30","chunk_id":"cu5f4f0k460vm","chunk_label":"unnamed-chunk-10"},{"row":151,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-50"},"document_id":"77F68D30","chunk_id":"cr9sbhfkl0l7m","chunk_label":"unnamed-chunk-11"},{"row":155,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-51"},"document_id":"77F68D30","chunk_id":"c67fek8fh1vdj","chunk_label":"unnamed-chunk-12"},{"row":159,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-52"},"document_id":"77F68D30","chunk_id":"c0qzt99s3uz17","chunk_label":"unnamed-chunk-13"},{"row":175,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-53"},"document_id":"77F68D30","chunk_id":"cf9t8qccs9es8","chunk_label":"unnamed-chunk-14"},{"row":203,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-57"},"document_id":"77F68D30","chunk_id":"cy1yzqk9v6smc","chunk_label":"unnamed-chunk-18"},{"row":237,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-59"},"document_id":"77F68D30","chunk_id":"c85mkxl3u2xgh","chunk_label":"unnamed-chunk-20"},{"row":231,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-58"},"document_id":"77F68D30","chunk_id":"c2fn3g4qdmzyy","chunk_label":"unnamed-chunk-19"},{"row":279,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-60"},"document_id":"77F68D30","chunk_id":"c2jly3c97ig8i","chunk_label":"unnamed-chunk-21"},{"row":299,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-61"},"document_id":"77F68D30","chunk_id":"cefh5ihzkcqbl","chunk_label":"unnamed-chunk-22"},{"row":308,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-62"},"document_id":"77F68D30","chunk_id":"cilpuhvqdmpej","chunk_label":"unnamed-chunk-23"},{"row":356,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-20"},"document_id":"77F68D30","chunk_id":"c1tfzdz2b80hy","chunk_label":"unnamed-chunk-26"},{"row":347,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-64"},"document_id":"77F68D30","chunk_id":"c63m2qhze3u2y","chunk_label":"unnamed-chunk-25"},{"row":331,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-63"},"document_id":"77F68D30","chunk_id":"czxt33feq8xzf","chunk_label":"unnamed-chunk-24"},{"row":363,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-61"},"document_id":"77F68D30","chunk_id":"c211ibf7ouri8","chunk_label":"unnamed-chunk-27"},{"row":195,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-56"},"document_id":"77F68D30","chunk_id":"cuafhnftbidp9","chunk_label":"unnamed-chunk-17"},{"row":190,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-55"},"document_id":"77F68D30","chunk_id":"cra8e128kr9o9","chunk_label":"unnamed-chunk-16"},{"row":183,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-54"},"document_id":"77F68D30","chunk_id":"c9ajju6cf9cv8","chunk_label":"unnamed-chunk-15"},{"row":393,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-2"},"document_id":"77F68D30","chunk_id":"cwqxet0zexx43","chunk_label":"unnamed-chunk-28"},{"row":406,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-4"},"document_id":"77F68D30","chunk_id":"cp6949hwjcirq","chunk_label":"unnamed-chunk-29"},{"row":423,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-23"},"document_id":"77F68D30","chunk_id":"c52kj3limvhya","chunk_label":"unnamed-chunk-30"},{"row":433,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-26"},"document_id":"77F68D30","chunk_id":"c4d2y4qjjl0e3","chunk_label":"unnamed-chunk-31"},{"row":446,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-28"},"document_id":"77F68D30","chunk_id":"cfk35uawz2hsn","chunk_label":"unnamed-chunk-32"},{"row":462,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-29"},"document_id":"77F68D30","chunk_id":"czw0rd1u0m33e","chunk_label":"unnamed-chunk-33"},{"row":480,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-30"},"document_id":"77F68D30","chunk_id":"cowzykbnv5xxz","chunk_label":"unnamed-chunk-34"},{"row":500,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-31"},"document_id":"77F68D30","chunk_id":"cct9s4x1m0a0t","chunk_label":"unnamed-chunk-35"},{"row":506,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-32"},"document_id":"77F68D30","chunk_id":"cozvs9s6hxsfi","chunk_label":"unnamed-chunk-36"},{"row":516,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-34"},"document_id":"77F68D30","chunk_id":"cwztp6gqf9w0s","chunk_label":"unnamed-chunk-37"},{"row":525,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-35"},"document_id":"77F68D30","chunk_id":"csmeeql20tusx","chunk_label":"unnamed-chunk-38"},{"row":550,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-68"},"document_id":"77F68D30","chunk_id":"cqa1e485jcrzr","chunk_label":"unnamed-chunk-39"}],"doc_write_time":1674158939,"chunk_rendered_width":661}
\ No newline at end of file
+{"chunk_definitions":[{"row":47,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-40"},"document_id":"77F68D30","chunk_id":"c0jrftmj331il","chunk_label":"unnamed-chunk-1"},{"row":53,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-41"},"document_id":"77F68D30","chunk_id":"cnq8c446n0wtz","chunk_label":"unnamed-chunk-2"},{"row":67,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-42"},"document_id":"77F68D30","chunk_id":"c3qooae84c4xs","chunk_label":"unnamed-chunk-3"},{"row":87,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-43"},"document_id":"77F68D30","chunk_id":"c8k36ylh3ik2z","chunk_label":"unnamed-chunk-4"},{"row":93,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-44"},"document_id":"77F68D30","chunk_id":"cff5zae4b4ix2","chunk_label":"unnamed-chunk-5"},{"row":107,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-45"},"document_id":"77F68D30","chunk_id":"cuj4f1k7oy0f9","chunk_label":"unnamed-chunk-6"},{"row":113,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-25"},"document_id":"77F68D30","chunk_id":"c3b4hkzi6i1gq","chunk_label":"unnamed-chunk-7"},{"row":129,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-47"},"document_id":"77F68D30","chunk_id":"cryc9nwjktom8","chunk_label":"unnamed-chunk-8"},{"row":134,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-48"},"document_id":"77F68D30","chunk_id":"c11kjcel8rada","chunk_label":"unnamed-chunk-9"},{"row":144,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-52"},"document_id":"77F68D30","chunk_id":"cu5f4f0k460vm","chunk_label":"unnamed-chunk-10"},{"row":151,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-50"},"document_id":"77F68D30","chunk_id":"cr9sbhfkl0l7m","chunk_label":"unnamed-chunk-11"},{"row":155,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-51"},"document_id":"77F68D30","chunk_id":"c67fek8fh1vdj","chunk_label":"unnamed-chunk-12"},{"row":159,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-52"},"document_id":"77F68D30","chunk_id":"c0qzt99s3uz17","chunk_label":"unnamed-chunk-13"},{"row":175,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-53"},"document_id":"77F68D30","chunk_id":"cf9t8qccs9es8","chunk_label":"unnamed-chunk-14"},{"row":203,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-57"},"document_id":"77F68D30","chunk_id":"cy1yzqk9v6smc","chunk_label":"unnamed-chunk-18"},{"row":237,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-59"},"document_id":"77F68D30","chunk_id":"c85mkxl3u2xgh","chunk_label":"unnamed-chunk-20"},{"row":231,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-58"},"document_id":"77F68D30","chunk_id":"c2fn3g4qdmzyy","chunk_label":"unnamed-chunk-19"},{"row":279,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-60"},"document_id":"77F68D30","chunk_id":"c2jly3c97ig8i","chunk_label":"unnamed-chunk-21"},{"row":299,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-61"},"document_id":"77F68D30","chunk_id":"cefh5ihzkcqbl","chunk_label":"unnamed-chunk-22"},{"row":308,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-62"},"document_id":"77F68D30","chunk_id":"cilpuhvqdmpej","chunk_label":"unnamed-chunk-23"},{"row":356,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-20"},"document_id":"77F68D30","chunk_id":"c1tfzdz2b80hy","chunk_label":"unnamed-chunk-26"},{"row":347,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-64"},"document_id":"77F68D30","chunk_id":"c63m2qhze3u2y","chunk_label":"unnamed-chunk-25"},{"row":331,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-63"},"document_id":"77F68D30","chunk_id":"czxt33feq8xzf","chunk_label":"unnamed-chunk-24"},{"row":363,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-61"},"document_id":"77F68D30","chunk_id":"c211ibf7ouri8","chunk_label":"unnamed-chunk-27"},{"row":195,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-56"},"document_id":"77F68D30","chunk_id":"cuafhnftbidp9","chunk_label":"unnamed-chunk-17"},{"row":190,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-55"},"document_id":"77F68D30","chunk_id":"cra8e128kr9o9","chunk_label":"unnamed-chunk-16"},{"row":183,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-54"},"document_id":"77F68D30","chunk_id":"c9ajju6cf9cv8","chunk_label":"unnamed-chunk-15"},{"row":393,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-2"},"document_id":"77F68D30","chunk_id":"cwqxet0zexx43","chunk_label":"unnamed-chunk-28"},{"row":406,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-4"},"document_id":"77F68D30","chunk_id":"cp6949hwjcirq","chunk_label":"unnamed-chunk-29"},{"row":423,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-23"},"document_id":"77F68D30","chunk_id":"c52kj3limvhya","chunk_label":"unnamed-chunk-30"},{"row":433,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-26"},"document_id":"77F68D30","chunk_id":"c4d2y4qjjl0e3","chunk_label":"unnamed-chunk-31"},{"row":446,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-28"},"document_id":"77F68D30","chunk_id":"cfk35uawz2hsn","chunk_label":"unnamed-chunk-32"},{"row":462,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-29"},"document_id":"77F68D30","chunk_id":"czw0rd1u0m33e","chunk_label":"unnamed-chunk-33"},{"row":480,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-30"},"document_id":"77F68D30","chunk_id":"cowzykbnv5xxz","chunk_label":"unnamed-chunk-34"},{"row":500,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-31"},"document_id":"77F68D30","chunk_id":"cct9s4x1m0a0t","chunk_label":"unnamed-chunk-35"},{"row":506,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-32"},"document_id":"77F68D30","chunk_id":"cozvs9s6hxsfi","chunk_label":"unnamed-chunk-36"},{"row":516,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-34"},"document_id":"77F68D30","chunk_id":"cwztp6gqf9w0s","chunk_label":"unnamed-chunk-37"},{"row":525,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-35"},"document_id":"77F68D30","chunk_id":"csmeeql20tusx","chunk_label":"unnamed-chunk-38"},{"row":550,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-68"},"document_id":"77F68D30","chunk_id":"cqa1e485jcrzr","chunk_label":"unnamed-chunk-39"},{"row":565,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","message":false,"label":"unnamed-chunk-76"},"document_id":"77F68D30","chunk_id":"c6t5kj9r0xqzx","chunk_label":"unnamed-chunk-40"},{"row":591,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","message":false,"label":"unnamed-chunk-94"},"document_id":"77F68D30","chunk_id":"cgq5kq1n6i5pg","chunk_label":"unnamed-chunk-41"},{"row":600,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-83"},"document_id":"77F68D30","chunk_id":"cuugb0843jsqr","chunk_label":"unnamed-chunk-42"},{"row":604,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-95"},"document_id":"77F68D30","chunk_id":"cnh2brq8uipgl","chunk_label":"unnamed-chunk-43"}],"doc_write_time":1674186864,"chunk_rendered_width":661}
\ No newline at end of file
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/000019.csv b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/000019.csv
new file mode 100644
index 0000000..8f91174
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/000019.csv	
@@ -0,0 +1,10 @@
+"0","S <- rbern(100)+1"
+"0","dat <- sim_HW(S, b=c(.5,.5), a=c(0,10))"
+"0",""
+"0","# Indirect effect (b) is the same for men and women"
+"0","dat |> "
+"0","  ggplot(aes(x=H, y=W, color=factor(S)))+"
+"0","  geom_point()+"
+"0","  geom_smooth(method = lm)+"
+"0","  # facet_wrap(~S)+"
+"0","  theme_bw()"
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/00001a.metadata b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/00001a.metadata
new file mode 100644
index 0000000..6399179
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/00001a.metadata	
@@ -0,0 +1 @@
+{"height":408.5290482076638,"width":661.0,"size_behavior":0,"conditions":[]}
\ No newline at end of file
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/00001a.png b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/00001a.png
new file mode 100644
index 0000000..c9d9347
Binary files /dev/null and b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/00001a.png differ
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/00001a.snapshot b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/00001a.snapshot
new file mode 100644
index 0000000..802e2e4
Binary files /dev/null and b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/c6t5kj9r0xqzx/00001a.snapshot differ
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001e.csv b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001e.csv
new file mode 100644
index 0000000..43c755f
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001e.csv	
@@ -0,0 +1,21 @@
+"0","dat <- list("
+"0","  W = d$weight,"
+"0","  H = d$height,"
+"0","  Hbar = mean(d$height),"
+"0","  S = d$male+1 )"
+"0",""
+"0","m_SHW <- quap("
+"0","  alist("
+"0","    W ~ dnorm(mu,sigma),"
+"0","    mu <- a[S]+b[S]*(H-Hbar),"
+"0","    a[S] ~ dnorm(60,10),"
+"0","    b[S] ~ dunif(0,1),"
+"0","    sigma ~ dunif(0,10)"
+"0","  ), data=dat"
+"0",")"
+"0","data.frame(dat) |> "
+"0","  ggplot(aes(x=H, y=W, color=factor(S)))+"
+"0","  geom_point()+"
+"0","  geom_smooth(method = lm)+"
+"0","  # facet_wrap(~S)+"
+"0","  theme_bw()"
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001f.metadata b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001f.metadata
new file mode 100644
index 0000000..6399179
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001f.metadata	
@@ -0,0 +1 @@
+{"height":408.5290482076638,"width":661.0,"size_behavior":0,"conditions":[]}
\ No newline at end of file
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001f.png b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001f.png
new file mode 100644
index 0000000..bfd6775
Binary files /dev/null and b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001f.png differ
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001f.snapshot b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001f.snapshot
new file mode 100644
index 0000000..4bd6fe9
Binary files /dev/null and b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/00001f.snapshot differ
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/000020.csv b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/000020.csv
new file mode 100644
index 0000000..73066c3
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/000020.csv	
@@ -0,0 +1,2 @@
+"0",""
+"0","precis(m_SHW,depth=2)"
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/000021.metadata b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/000021.metadata
new file mode 100644
index 0000000..723792d
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/000021.metadata	
@@ -0,0 +1 @@
+{"classes":["data.frame"],"nrow":5,"ncol":4,"summary":{"Description":["df [5 × 4]"]}}
\ No newline at end of file
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/000021.rdf b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/000021.rdf
new file mode 100644
index 0000000..986ebb1
Binary files /dev/null and b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cgq5kq1n6i5pg/000021.rdf differ
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/chunks.json b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/chunks.json
index 6ebb033..eefcdce 100644
--- a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/chunks.json	
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/chunks.json	
@@ -1 +1 @@
-{"chunk_definitions":[{"row":47,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-40"},"document_id":"77F68D30","chunk_id":"c0jrftmj331il","chunk_label":"unnamed-chunk-1"},{"row":53,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-41"},"document_id":"77F68D30","chunk_id":"cnq8c446n0wtz","chunk_label":"unnamed-chunk-2"},{"row":67,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-42"},"document_id":"77F68D30","chunk_id":"c3qooae84c4xs","chunk_label":"unnamed-chunk-3"},{"row":87,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-43"},"document_id":"77F68D30","chunk_id":"c8k36ylh3ik2z","chunk_label":"unnamed-chunk-4"},{"row":93,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-44"},"document_id":"77F68D30","chunk_id":"cff5zae4b4ix2","chunk_label":"unnamed-chunk-5"},{"row":107,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-45"},"document_id":"77F68D30","chunk_id":"cuj4f1k7oy0f9","chunk_label":"unnamed-chunk-6"},{"row":113,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-25"},"document_id":"77F68D30","chunk_id":"c3b4hkzi6i1gq","chunk_label":"unnamed-chunk-7"},{"row":129,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-47"},"document_id":"77F68D30","chunk_id":"cryc9nwjktom8","chunk_label":"unnamed-chunk-8"},{"row":134,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-48"},"document_id":"77F68D30","chunk_id":"c11kjcel8rada","chunk_label":"unnamed-chunk-9"},{"row":144,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-52"},"document_id":"77F68D30","chunk_id":"cu5f4f0k460vm","chunk_label":"unnamed-chunk-10"},{"row":151,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-50"},"document_id":"77F68D30","chunk_id":"cr9sbhfkl0l7m","chunk_label":"unnamed-chunk-11"},{"row":155,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-51"},"document_id":"77F68D30","chunk_id":"c67fek8fh1vdj","chunk_label":"unnamed-chunk-12"},{"row":159,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-52"},"document_id":"77F68D30","chunk_id":"c0qzt99s3uz17","chunk_label":"unnamed-chunk-13"},{"row":175,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-53"},"document_id":"77F68D30","chunk_id":"cf9t8qccs9es8","chunk_label":"unnamed-chunk-14"},{"row":203,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-57"},"document_id":"77F68D30","chunk_id":"cy1yzqk9v6smc","chunk_label":"unnamed-chunk-18"},{"row":237,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-59"},"document_id":"77F68D30","chunk_id":"c85mkxl3u2xgh","chunk_label":"unnamed-chunk-20"},{"row":231,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-58"},"document_id":"77F68D30","chunk_id":"c2fn3g4qdmzyy","chunk_label":"unnamed-chunk-19"},{"row":279,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-60"},"document_id":"77F68D30","chunk_id":"c2jly3c97ig8i","chunk_label":"unnamed-chunk-21"},{"row":299,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-61"},"document_id":"77F68D30","chunk_id":"cefh5ihzkcqbl","chunk_label":"unnamed-chunk-22"},{"row":308,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-62"},"document_id":"77F68D30","chunk_id":"cilpuhvqdmpej","chunk_label":"unnamed-chunk-23"},{"row":356,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-20"},"document_id":"77F68D30","chunk_id":"c1tfzdz2b80hy","chunk_label":"unnamed-chunk-26"},{"row":347,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-64"},"document_id":"77F68D30","chunk_id":"c63m2qhze3u2y","chunk_label":"unnamed-chunk-25"},{"row":331,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-63"},"document_id":"77F68D30","chunk_id":"czxt33feq8xzf","chunk_label":"unnamed-chunk-24"},{"row":363,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-61"},"document_id":"77F68D30","chunk_id":"c211ibf7ouri8","chunk_label":"unnamed-chunk-27"},{"row":195,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-56"},"document_id":"77F68D30","chunk_id":"cuafhnftbidp9","chunk_label":"unnamed-chunk-17"},{"row":190,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-55"},"document_id":"77F68D30","chunk_id":"cra8e128kr9o9","chunk_label":"unnamed-chunk-16"},{"row":183,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-54"},"document_id":"77F68D30","chunk_id":"c9ajju6cf9cv8","chunk_label":"unnamed-chunk-15"},{"row":393,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-2"},"document_id":"77F68D30","chunk_id":"cwqxet0zexx43","chunk_label":"unnamed-chunk-28"},{"row":406,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-4"},"document_id":"77F68D30","chunk_id":"cp6949hwjcirq","chunk_label":"unnamed-chunk-29"},{"row":423,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-23"},"document_id":"77F68D30","chunk_id":"c52kj3limvhya","chunk_label":"unnamed-chunk-30"},{"row":433,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-26"},"document_id":"77F68D30","chunk_id":"c4d2y4qjjl0e3","chunk_label":"unnamed-chunk-31"},{"row":446,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-28"},"document_id":"77F68D30","chunk_id":"cfk35uawz2hsn","chunk_label":"unnamed-chunk-32"},{"row":462,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-29"},"document_id":"77F68D30","chunk_id":"czw0rd1u0m33e","chunk_label":"unnamed-chunk-33"},{"row":480,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-30"},"document_id":"77F68D30","chunk_id":"cowzykbnv5xxz","chunk_label":"unnamed-chunk-34"},{"row":500,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-31"},"document_id":"77F68D30","chunk_id":"cct9s4x1m0a0t","chunk_label":"unnamed-chunk-35"},{"row":506,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-32"},"document_id":"77F68D30","chunk_id":"cozvs9s6hxsfi","chunk_label":"unnamed-chunk-36"},{"row":516,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-34"},"document_id":"77F68D30","chunk_id":"cwztp6gqf9w0s","chunk_label":"unnamed-chunk-37"},{"row":525,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-35"},"document_id":"77F68D30","chunk_id":"csmeeql20tusx","chunk_label":"unnamed-chunk-38"},{"row":550,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-68"},"document_id":"77F68D30","chunk_id":"cqa1e485jcrzr","chunk_label":"unnamed-chunk-39"}],"doc_write_time":1674158939,"chunk_rendered_width":661}
\ No newline at end of file
+{"chunk_definitions":[{"row":47,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-40"},"document_id":"77F68D30","chunk_id":"c0jrftmj331il","chunk_label":"unnamed-chunk-1"},{"row":53,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-41"},"document_id":"77F68D30","chunk_id":"cnq8c446n0wtz","chunk_label":"unnamed-chunk-2"},{"row":67,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-42"},"document_id":"77F68D30","chunk_id":"c3qooae84c4xs","chunk_label":"unnamed-chunk-3"},{"row":87,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-43"},"document_id":"77F68D30","chunk_id":"c8k36ylh3ik2z","chunk_label":"unnamed-chunk-4"},{"row":93,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-44"},"document_id":"77F68D30","chunk_id":"cff5zae4b4ix2","chunk_label":"unnamed-chunk-5"},{"row":107,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-45"},"document_id":"77F68D30","chunk_id":"cuj4f1k7oy0f9","chunk_label":"unnamed-chunk-6"},{"row":113,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-25"},"document_id":"77F68D30","chunk_id":"c3b4hkzi6i1gq","chunk_label":"unnamed-chunk-7"},{"row":129,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-47"},"document_id":"77F68D30","chunk_id":"cryc9nwjktom8","chunk_label":"unnamed-chunk-8"},{"row":134,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-48"},"document_id":"77F68D30","chunk_id":"c11kjcel8rada","chunk_label":"unnamed-chunk-9"},{"row":144,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-52"},"document_id":"77F68D30","chunk_id":"cu5f4f0k460vm","chunk_label":"unnamed-chunk-10"},{"row":151,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-50"},"document_id":"77F68D30","chunk_id":"cr9sbhfkl0l7m","chunk_label":"unnamed-chunk-11"},{"row":155,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-51"},"document_id":"77F68D30","chunk_id":"c67fek8fh1vdj","chunk_label":"unnamed-chunk-12"},{"row":159,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-52"},"document_id":"77F68D30","chunk_id":"c0qzt99s3uz17","chunk_label":"unnamed-chunk-13"},{"row":175,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-53"},"document_id":"77F68D30","chunk_id":"cf9t8qccs9es8","chunk_label":"unnamed-chunk-14"},{"row":203,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-57"},"document_id":"77F68D30","chunk_id":"cy1yzqk9v6smc","chunk_label":"unnamed-chunk-18"},{"row":237,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-59"},"document_id":"77F68D30","chunk_id":"c85mkxl3u2xgh","chunk_label":"unnamed-chunk-20"},{"row":231,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-58"},"document_id":"77F68D30","chunk_id":"c2fn3g4qdmzyy","chunk_label":"unnamed-chunk-19"},{"row":279,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-60"},"document_id":"77F68D30","chunk_id":"c2jly3c97ig8i","chunk_label":"unnamed-chunk-21"},{"row":299,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-61"},"document_id":"77F68D30","chunk_id":"cefh5ihzkcqbl","chunk_label":"unnamed-chunk-22"},{"row":308,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-62"},"document_id":"77F68D30","chunk_id":"cilpuhvqdmpej","chunk_label":"unnamed-chunk-23"},{"row":356,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-20"},"document_id":"77F68D30","chunk_id":"c1tfzdz2b80hy","chunk_label":"unnamed-chunk-26"},{"row":347,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-64"},"document_id":"77F68D30","chunk_id":"c63m2qhze3u2y","chunk_label":"unnamed-chunk-25"},{"row":331,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-63"},"document_id":"77F68D30","chunk_id":"czxt33feq8xzf","chunk_label":"unnamed-chunk-24"},{"row":363,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-61"},"document_id":"77F68D30","chunk_id":"c211ibf7ouri8","chunk_label":"unnamed-chunk-27"},{"row":195,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-56"},"document_id":"77F68D30","chunk_id":"cuafhnftbidp9","chunk_label":"unnamed-chunk-17"},{"row":190,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-55"},"document_id":"77F68D30","chunk_id":"cra8e128kr9o9","chunk_label":"unnamed-chunk-16"},{"row":183,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-54"},"document_id":"77F68D30","chunk_id":"c9ajju6cf9cv8","chunk_label":"unnamed-chunk-15"},{"row":393,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-2"},"document_id":"77F68D30","chunk_id":"cwqxet0zexx43","chunk_label":"unnamed-chunk-28"},{"row":406,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-4"},"document_id":"77F68D30","chunk_id":"cp6949hwjcirq","chunk_label":"unnamed-chunk-29"},{"row":423,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-23"},"document_id":"77F68D30","chunk_id":"c52kj3limvhya","chunk_label":"unnamed-chunk-30"},{"row":433,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-26"},"document_id":"77F68D30","chunk_id":"c4d2y4qjjl0e3","chunk_label":"unnamed-chunk-31"},{"row":446,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-28"},"document_id":"77F68D30","chunk_id":"cfk35uawz2hsn","chunk_label":"unnamed-chunk-32"},{"row":462,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-29"},"document_id":"77F68D30","chunk_id":"czw0rd1u0m33e","chunk_label":"unnamed-chunk-33"},{"row":480,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-30"},"document_id":"77F68D30","chunk_id":"cowzykbnv5xxz","chunk_label":"unnamed-chunk-34"},{"row":500,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-31"},"document_id":"77F68D30","chunk_id":"cct9s4x1m0a0t","chunk_label":"unnamed-chunk-35"},{"row":506,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-32"},"document_id":"77F68D30","chunk_id":"cozvs9s6hxsfi","chunk_label":"unnamed-chunk-36"},{"row":516,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-34"},"document_id":"77F68D30","chunk_id":"cwztp6gqf9w0s","chunk_label":"unnamed-chunk-37"},{"row":525,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-35"},"document_id":"77F68D30","chunk_id":"csmeeql20tusx","chunk_label":"unnamed-chunk-38"},{"row":550,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-68"},"document_id":"77F68D30","chunk_id":"cqa1e485jcrzr","chunk_label":"unnamed-chunk-39"},{"row":565,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","message":false,"label":"unnamed-chunk-76"},"document_id":"77F68D30","chunk_id":"c6t5kj9r0xqzx","chunk_label":"unnamed-chunk-40"},{"row":591,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","message":false,"label":"unnamed-chunk-94"},"document_id":"77F68D30","chunk_id":"cgq5kq1n6i5pg","chunk_label":"unnamed-chunk-41"},{"row":600,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-83"},"document_id":"77F68D30","chunk_id":"cuugb0843jsqr","chunk_label":"unnamed-chunk-42"},{"row":604,"row_count":1,"visible":true,"expansion_state":0,"options":{"engine":"r","label":"unnamed-chunk-95"},"document_id":"77F68D30","chunk_id":"cnh2brq8uipgl","chunk_label":"unnamed-chunk-43"}],"doc_write_time":1674186864,"chunk_rendered_width":661}
\ No newline at end of file
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cnh2brq8uipgl/00000f.csv b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cnh2brq8uipgl/00000f.csv
new file mode 100644
index 0000000..9eddef6
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cnh2brq8uipgl/00000f.csv	
@@ -0,0 +1,6 @@
+"0","xseq <- seq(from=130,to=190, len=50)"
+"0","muF <- "
+"0","  link(m_adults2, data=list(S=rep(1,50),H=xseq,Hbar=mean(d$height)))"
+"2","Error in h(simpleError(msg, call)) : 
+  error in evaluating the argument 'fit' in selecting a method for function 'link': object 'm_adults2' not found
+"
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cnh2brq8uipgl/000010.error b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cnh2brq8uipgl/000010.error
new file mode 100644
index 0000000..bee1728
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cnh2brq8uipgl/000010.error	
@@ -0,0 +1 @@
+{"frames":[{"func":"link(m_adults2, data = list(S = rep(1, 50), H = xseq, Hbar = mean(d$height)))","file":"","line_number":0,"end_line_number":0,"character_number":0,"end_character_number":0},{"func":".handleSimpleError(function (cond) \n.Internal(C_tryCatchHelper(addr, 1L, cond)), \"object 'm_adults2' not found\", \n    base::quote(link(m_adults2, data = list(S = rep(1, 50), H = xseq, \n        Hbar = mean(d$height)))))","file":"","line_number":0,"end_line_number":0,"character_number":0,"end_character_number":0},{"func":"h(simpleError(msg, call))","file":"","line_number":0,"end_line_number":0,"character_number":0,"end_character_number":0}],"message":"Error in h(simpleError(msg, call)) : \n  error in evaluating the argument 'fit' in selecting a method for function 'link': object 'm_adults2' not found\n"}
\ No newline at end of file
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/00001f.csv b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/00001f.csv
new file mode 100644
index 0000000..8510ab8
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/00001f.csv	
@@ -0,0 +1,3 @@
+"0","post <- extract.samples(m_SHW)"
+"0","dens(post$b[,1],xlim=c(.3, .9),ylim=c(0,8),"
+"0","     lwd=3,col=2,xlab=""posterior mean weight(kg"")"
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000021.csv b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000021.csv
new file mode 100644
index 0000000..26bdb3c
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000021.csv	
@@ -0,0 +1 @@
+"0","dens(post$b[,2],lwd=3,col=4,add=TRUE)"
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000022.metadata b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000022.metadata
new file mode 100644
index 0000000..6399179
--- /dev/null
+++ b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000022.metadata	
@@ -0,0 +1 @@
+{"height":408.5290482076638,"width":661.0,"size_behavior":0,"conditions":[]}
\ No newline at end of file
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000022.png b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000022.png
new file mode 100644
index 0000000..571f620
Binary files /dev/null and b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000022.png differ
diff --git a/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000022.snapshot b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000022.snapshot
new file mode 100644
index 0000000..5c15f70
Binary files /dev/null and b/.Rproj.user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cuugb0843jsqr/000022.snapshot differ
diff --git a/Articles/Quadractic Approximation (1988).pdf b/Articles/Quadractic Approximation (1988).pdf
new file mode 100644
index 0000000..a3dfa5e
Binary files /dev/null and b/Articles/Quadractic Approximation (1988).pdf differ
diff --git a/Statistical Thinking 2023_v2.qmd b/Statistical Thinking 2023_v2.qmd
index 70a56f8..e67ef4b 100644
--- a/Statistical Thinking 2023_v2.qmd	
+++ b/Statistical Thinking 2023_v2.qmd	
@@ -549,3 +549,57 @@ ggplot(df, aes(x=W_contrast,fill=W_flag))+
   geom_density()+
   theme_bw()
 ```
+
+Now, what is the direct effect of sex over weight?
+
+```{r, message=FALSE}
+S <- rbern(100)+1
+dat <- sim_HW(S, b=c(.5,.5), a=c(0,10))
+
+# Indirect effect (b) is the same for men and women
+dat |> 
+  ggplot(aes(x=H, y=W, color=factor(S)))+
+  geom_point()+
+  geom_smooth(method = lm)+
+  # facet_wrap(~S)+
+  theme_bw()
+```
+
+```{r, message=FALSE}
+dat <- list(
+  W = d$weight,
+  H = d$height,
+  Hbar = mean(d$height),
+  S = d$male+1 )
+
+m_SHW <- quap(
+  alist(
+    W ~ dnorm(mu,sigma),
+    mu <- a[S]+b[S]*(H-Hbar),
+    a[S] ~ dnorm(60,10),
+    b[S] ~ dunif(0,1),
+    sigma ~ dunif(0,10)
+  ), data=dat
+)
+data.frame(dat) |> 
+  ggplot(aes(x=H, y=W, color=factor(S)))+
+  geom_point()+
+  geom_smooth(method = lm)+
+  # facet_wrap(~S)+
+  theme_bw()
+
+precis(m_SHW,depth=2)
+```
+
+Note that regression line's slopes are almost the same for both male and female.
+
+```{r}
+post <- extract.samples(m_SHW)
+dens(post$b[,1],xlim=c(.3, .9),ylim=c(0,8),
+     lwd=3,col=2,xlab="posterior mean weight(kg)")
+dens(post$b[,2],lwd=3,col=4,add=TRUE)
+```
+
+```{r}
+
+```