stats.md

• ANOVA
• Line and curve fitting

ANOVA

video source

Group1 <- c(2,3,7,2,6)
Group2 <- c(10,8,7,5,10)
Group3 <- c(10,13,14,13,15)

Combined_Groups <- data.frame(cbind(Group1, Group2, Group3))
Stacked_Groups <- stack(Combined_Groups)
Anova_Results <- aov(values ~ ind, data = Stacked_Groups)
summary(Anova_Results)

Line and curve fitting

Fit a line to series of points

#data
m <- 5
n <- 2
input <- matrix(c(1, 6, 2, 5, 3, 7, 4, 10, 5, 14), ncol = n, byrow = T)
k <- rep(1,m)
X <- cbind(k, input[,1])
y <- input[,2]

X.T <- t(X)
betaHat <- solve(X.T%*%X) %*% X.T %*%y
print(betaHat)
plot(input)
abline(betaHat[1], betaHat[2])

Fit a 2nd degree polynomial to series of points

X <- cbind(rep(1,m), input[,1], (input[,1])^2)
y <- input[,2]
X.T <- t(X)
betaHat <- solve(X.T%*%X) %*% X.T %*%y
print(betaHat)
plot(input)

#plot curve beyond original data
num_points <- 10
new_X <- c(1:num_points)
new_poly <- cbind(rep(1,num_points),new_X,new_X^2)
plot(x = new_X, y = new_poly%*%betaHat,col='red')
lines(input)