Please answer this question in both mathematically and with R. I need R code also.. Its urgent...
(a) R code:
y1=c(35,35,40,10,6,20,35,35,35,30)
y2=c(3.5,4.9,30,2.8,2.7,2.8,4.6,10.9,8,1.6)
y3=c(2.80,2.70,4.38,3.21,2.73,2.81,2.88,2.90,3.28,3.20)
z=3*y1-y2+2*y3
mean(z)
sum(z^2)
s=(sum(z^2)-10*mean(z)^2)/9
s
Output:
> mean(z)
[1] 83.298
> sum(z^2)
[1] 78823.5
> s=(sum(z^2)-10*mean(z)^2)/9
> s
[1] 1048.659
(b)
R code:
y1=c(35,35,40,10,6,20,35,35,35,30)
y2=c(3.5,4.9,30,2.8,2.7,2.8,4.6,10.9,8,1.6)
y3=c(2.80,2.70,4.38,3.21,2.73,2.81,2.88,2.90,3.28,3.20)
s11=(sum(y1^2)-10*mean(y1)^2)/9
s22=(sum(y2^2)-10*mean(y2)^2)/9
s33=(sum(y3^2)-10*mean(y3)^2)/9
s12=(sum(y1*y2)-10*mean(y1)*mean(y2))/9
s13=(sum(y1*y3)-10*mean(y1)*mean(y3))/9
s23=(sum(y2*y3)-10*mean(y2)*mean(y3))/9
M=matrix(c(s11,s12,s13,s12,s22,s23,s13,s23,s33),nrow=3,ncol=3)
Mean_z=c(3,-1,2)%*%c(mean(y1),mean(y2),mean(y3))
var_z=c(3,-1,2)%*%M%*%c(3,-1,2)
Mean_z
var_z
Output:
> Mean_z
[,1]
[1,] 83.298
> var_z
[,1]
[1,] 1048.659
Please answer this question in both mathematically and with R. I need R code also.. Its...
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