Nobel Prize Winners

An example on Nobel prize winners by G8 countries from 1901 to
2015 from a Youtube video by Francois Husson,
\url{www.youtube.com/watch?v=Z5Lo1hvZ9fA}


\textbf{Code is incomplete or wrong.} I just liked the data.



rm(list = ls())
nobel = matrix(c(
 4,  3,  2,  4,  1,  4,
 8,  3, 11, 12, 10,  9,
24,  1,  8, 18,  5, 24,
 1,  1,  6,  5,  1,  5,
 6,  0,  2,  3,  1, 11,
 4,  3,  5,  2,  3, 10,
23,  6,  7, 26, 11, 20,
51, 43,  8, 70, 19, 66),6,8)
nobel=t(nobel)
nobel
rowSums(nobel)
colSums(nobel)
# rownames Canada France Germany Italy Japan Russia UK USA
# colnames Chem Econ Lit Med Peace Physics

# fit indep/homogen model to table
fit <- chisq.test(nobel,correct=FALSE)
fit
fit$expected
fit$residual

# Singular Value Decomp of residual matrix
ca=svd(fit$residual)
L=diag(ca$d)
L
U=ca$u %*% sqrt(L)
U
V=ca$v %*% sqrt(L)
V
#This should reproduce fit$residual
PR=U%*%L%*%t(V)
PR

# Pearson Chi-square
X2=PR%*%t(PR)
sum(diag(X2))

#SVD Plot
plot(U[,1],U[,2],
    xlim=c(-1,1),ylim=c(-1,1),
     ,xlab="Factor 1",ylab="Factor 2")
text(U[,1],U[,2]-.075,labels=
    c("Canada","France","Germany",
    "Italy","Japan","USSR","UK","USA"))
lines(V[,1],V[,2],pch=15,type="p")
text(V[,1]+.075,V[,2],labels=
    c("Chem","Econ","Lit","Med","Peace","Phys"))