KSo<-c(0.90,0.95,1.00,1.05,1.10)
T<-c(1/12,3/12,6/12,1,2,5)
mapping<-c(14.2, 13.0, 12.0, 13.1, 14.5,
           14.0, 13.0, 12.0, 13.1, 14.2,
           14.1, 13.3, 12.5, 13.4, 14.3,
           14.7, 14.0, 13.5, 14.0, 14.8,
           15.0, 14.4, 14.0, 14.5, 15.1,
           14.8, 14.6, 14.4, 14.7, 15.0)
mapped<-matrix(mapping, ncol=5, byrow=TRUE)

#predict
x<-0.98
y<-11/12

#Perform 2D interpolation
#find index
ki<-as.integer(cut(x, KSo, right=FALSE))
Ti<-as.integer(cut(y, T, right=FALSE))
dx<-(x-KSo[ki])/(KSo[ki+1]-KSo[ki])
dy<-(y-T[Ti])/(T[Ti+1]-T[Ti])

#find values and weighed sums of neighboring points
f00<-mapped[Ti, ki]*(1-dx)*(1-dy)
f01<-mapped[Ti+1, ki]*(1-dx)*dy
f10<-mapped[Ti, ki+1]*dx*(1-dy)
f11<-mapped[Ti+1, ki+1]*dx*dy
sum(f00, f10, f01, f11)

#estaablish data frame with raw data
df<-data.frame(expand.grid(KSo, T), mapping)
names(df)<-c("KSo", "T", "z")

#Perform regression
model<-lm(z~I(KSo^2)+I(T^2)+KSo*T, data=df)

#Predict results at desired coordinates
dfnew<-data.frame(KSo=c(1, 0.98), T=c(0.5, 0.9166667))
predict(model, dfnew)