# 複因子直線迴歸模型 (two factor General linear model)
###### tags: `R教學` `基礎統計`
參考資料：
1. [Linear Models with R](http://www.utstat.toronto.edu/~brunner/books/LinearModelsWithR.pdf)
2. [Regression With Factor Variables](http://courses.atlas.illinois.edu/spring2016/STAT/STAT200/RProgramming/RegressionFactors.html)
3. [迴歸分析筆記 之 虛擬變數 Dummy Variable](https://belleaya.pixnet.net/blog/post/30877354)

rm(list=ls())

# model simulation: y = 5x + 10
x1 <- rnorm(50, 10, 4)
y1 <- x1*5 + 10 + rnorm(50, 0, 5)
x2 <- rnorm(50, 30, 4)
y2 <- x2*5 + 10 + rnorm(50, 0, 5)
x3 <- rnorm(50, 10, 4)
y3 <- x3*5 + 10 + rnorm(50, 0, 5)

sd(y1); sd(y2); sd(y3)

dat <- c(y1, y2, y3)
x <- c(x1, x2, x3)
trt <- rep(c("A", "B", "C"), each = 50)

hist(dat, breaks = 30)
hist(y1, breaks = 20, add = T, col = 2)
hist(y2, breaks = 20, add = T, col = 3)


plot(y1 ~ x1, xlim = c(0,50), ylim = c(0,250), col = 1, pch = 19)
points(y2 ~ x2, col = 2, pch = 19)
points(y3 ~ x3, col = 3, pch = 19)

abline (10,5)
t.test(y1,y2)

summary(model <- (lm (dat ~ x + trt)))
summary(lm (dat ~ trt))

mean(y2) - mean(y1)
sqrt(sum((y1-mean(y1))^2)/50)/sqrt(50)