reghojas

Regresión hojas de mango

x=c(5.6,4.7,5.1,5.8,5.3)
y=c(28.5,23,25,29,26.9)
plot(x,y,xlab="Ancho Maximo cms",ylab="Longitud cms",main="Gráfico de Dispersión",col=c("black","red", "blue","green", "purple"))

mu_x=5.2
yrbar=sum(y)/sum(x)*mu_x; yrbar

## [1] 25.98038

A=3.14159/4*mean(x)*mean(y);A

## [1] 110.2258

ygor1=sum(y)/sum(x)*4.8
ygor2=sum(y)/sum(x)*4.9
ygor3=sum(y)/sum(x)*5.3
c(ygor1,ygor2,ygor3)

## [1] 23.98189 24.48151 26.48000

r=(sum(x*y)-sum(x)*sum(y)/5)/sqrt((sum(x^2)-(sum(x)^2/5))*(sum(y^2)-(sum(y)^2/5)));r

## [1] 0.9899281

b=(sum(x*y)-sum(x)*sum(y)/5)/(sum(x^2)-(sum(x)^2/5));b

## [1] 5.743243

a=(sum(y)-b*sum(x))/5;a

## [1] -3.959189

ygorlr1=a+b*4.8
ygorlr2=a+b*4.9
ygorlr3=a+b*5.3
c(ygorlr1,ygorlr2,ygorlr3)

## [1] 23.60838 24.18270 26.48000

vrgor=1/(5*mean(x)^2)*(var(y)-2*sum(y)/sum(x)*cov(x,y)+(sum(y)/sum(x))^2*var(x));vrgor

## [1] 0.001623641

vygor1=vrgor*4.8^2
vygor2=vrgor*4.9^2
vygor3=vrgor*5.3^2
ee1=sqrt(vygor1)
ee2=sqrt(vygor2)
ee3=sqrt(vygor3)
ea1=2.38*ee1
ea2=2.38*ee2
ea3=2.38*ee3
rbind(c(vygor1,vygor2,vygor3),c(ee1,ee2,ee3),c(ea1,ea2,ea3))

##            [,1]       [,2]       [,3]
## [1,] 0.03740869 0.03898362 0.04560807
## [2,] 0.19341326 0.19744270 0.21356047
## [3,] 0.46032355 0.46991362 0.50827392