dat = read.table('fat.txt')
X1 = dat[,1]
X2 = dat[,2]
X3 = dat[,3]
Y = dat[,4]


fit1 = lm(Y~X1)

fit2 = lm(Y~X2)


fit12 = lm(Y~X1+X2)
fit21 = lm(Y~X2+X1)


fit = lm(Y~X1+X2+X3)

SSE1 = deviance(fit1)   
SSE2 = deviance(fit2)
SSE12 = deviance(fit12)
SSE123 = deviance(fit)

####Coefficient of partial determination
SSR1.2 = deviance(fit2)-deviance(fit12)

SSE2 = deviance(fit2)

RY1.2 = SSR1.2/SSE2

###another way of calculating
e1 = residuals(lm(Y~X2))
e2 = residuals(lm(X1~X2))

cor(e1,e2)^2