amv29 - Tests on a Mean Vector with Known Covariance Matrix

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[BenBenford-xi]

The following line of code does not appear to get used in the script and causes and error m<-vec[2, 2]/vec[1, 2] ??

[statisticsmatt]

begin video 1

x<-c(69, 74, 68, 70, 72, 67, 66, 70, 76, 68, 72, 79, 74, 67, 66, 71, 74, 75, 75, 76)
y<-c(153, 175, 155, 135, 172, 150, 115, 137, 200, 130, 140, 265, 185, 112, 140, 150, 165, 185, 210, 220)
mu<-c(70, 170)
Sig<-matrix(c(20, 100, 100, 1000), ncol=2)
mahalanobis(c(mean(x), mean(y)), mu, Sig/length(x))
qchisq(.95, 2)

## Simple function to draw ellipes
draw.ellipse <- function(mu, cov.mat, c2, jmp=.1) {
vec<- eigen(cov.mat)$vectors
val<- eigen(cov.mat)$values
len.x <- sqrt(c2*val[1])
len.y <- sqrt(c2*val[2])
angle <- atan(vec[2, 1]/vec[1, 1])
rotate <- matrix(c(cos(angle), sin(angle), -sin(angle), cos(angle)), ncol=2)
x.ellip <- seq(-len.x, len.x, jmp)
y1 <- sqrt(len.y^2 - (len.y*x.ellip/len.x)^2)
y2 <- -y1
angle <- atan(vec[2, 1]/vec[1, 1])
rotate <- matrix(c(cos(angle), sin(angle), -sin(angle), cos(angle)), ncol=2)
ellip1 <- rotate %*% rbind(x.ellip, y1)
ellip2 <- rotate %*% rbind(x.ellip, y2)
list("x"=ellip1[1, ]+mu[1], "x.e"=ellip1[2, ]+mu[2], "y"=ellip2[1, ]+mu[1], "y.e"=ellip2[2, ]+mu[2])
}

x<-c(69, 74, 68, 70, 72, 67, 66, 70, 76, 68, 72, 79, 74, 67, 66, 71, 74, 75, 75, 76)
y<-c(153, 175, 155, 135, 172, 150, 115, 137, 200, 130, 140, 265, 185, 112, 140, 150, 165, 185, 210, 220)
mu<-c(70, 170)
Sig<-matrix(c(20, 100, 100, 1000), ncol=2)/length(x)
m<-vec[2, 2]/vec[1, 2]
alpha <- 0.05
plot(x, y, ylab="Weight (lbs)", xlab="Height (inches)", main="20 College-age Males")
points(mu[1], mu[2], pch=18, col='red', cex=2)
points(mean(x), mean(y), pch=18, col='blue', cex=1)
elli <- draw.ellipse(mu, Sig, qchisq(1-alpha, 2), .001)
lines(elli$x, elli$x.e, col='red')
lines(elli$y, elli$y.e, col='red')
legend("topleft", c("95% Conf Ellipse", "95% Univariate CI's", "Null Hypothesis", "Sample Mean"),
lty=c(1, 1, NA, NA), pch=c(NA, NA, 18, 18), col=c('red', 'black', 'red', 'blue'))
x1<-mu[1]+qnorm(alpha/2)*sqrt(Sig[1, 1])
x2<-mu[1]+qnorm(1-alpha/2)*sqrt(Sig[1, 1])
y1<-mu[2]+qnorm(alpha/2)*sqrt(Sig[2, 2])
y2<-mu[2]+qnorm(1-alpha/2)*sqrt(Sig[2, 2])
polygon(c(x1, x2, x2, x1), c(y1, y1, y2, y2))

plot(x, y, ylab="Weight (lbs)", xlab="Height (inches)", main="20 College-age Males",
xlim=c(67, 73), ylim=c(150, 190), type = 'n')
mtext("Zoomed In")
points(mu[1], mu[2], pch=18, col='red', cex=2)
points(mean(x), mean(y), pch=18, col='blue', cex=1)
lines(elli$x, elli$x.e, col='red')
lines(elli$y, elli$y.e, col='red')
polygon(c(x1, x2, x2, x1), c(y1, y1, y2, y2))

end video 1