Heterogeneity

data=read.csv("karpur.csv")
head(data)

##    depth caliper ind.deep ind.med  gamma phi.N R.deep  R.med      SP
## 1 5667.0   8.685  618.005 569.781 98.823 0.410  1.618  1.755 -56.587
## 2 5667.5   8.686  497.547 419.494 90.640 0.307  2.010  2.384 -61.916
## 3 5668.0   8.686  384.935 300.155 78.087 0.203  2.598  3.332 -55.861
## 4 5668.5   8.686  278.324 205.224 66.232 0.119  3.593  4.873 -41.860
## 5 5669.0   8.686  183.743 131.155 59.807 0.069  5.442  7.625 -34.934
## 6 5669.5   8.686  109.512  75.633 57.109 0.048  9.131 13.222 -39.769
##   density.corr density phi.core   k.core Facies phi.core.frac
## 1       -0.033   2.205  33.9000 2442.590     F1      0.339000
## 2       -0.067   2.040  33.4131 3006.989     F1      0.334131
## 3       -0.064   1.888  33.1000 3370.000     F1      0.331000
## 4       -0.053   1.794  34.9000 2270.000     F1      0.349000
## 5       -0.054   1.758  35.0644 2530.758     F1      0.350644
## 6       -0.058   1.759  35.3152 2928.314     F1      0.353152

data = data[order(data$k.core, decreasing=TRUE), ]
k = data$k.core
sample = c(1: length(k))
k_percent = (sample * 100 / length(k))
xlab = "Portion of Total Samples Having Larger or Equal K"
ylab = "Permeability k (md)"
plot(k_percent, k, log =  'y', xlab = xlab, ylab = ylab, pch = 10, cex = 0.5, col = "#16423C")

log.k = log(k)
model = lm(log.k ~ k_percent)
plot(k_percent, log.k, xlab = xlab , ylab = ylab, pch = 10, cex = 0.5, col = "#16423C")
abline(model, col = "red", lwd = 2)

N_data = data.frame(k_percent = c(50, 84.1))
predict_values    = predict(model, N_data)
HI = (predict_values[1] - predict_values[2]) / predict_values[1]
HI

##         1 
## 0.2035464