import data

karpur <- read.csv("C:/Users/hp ZBook/OneDrive/Desktop/karpur.csv")
View(karpur)
summary(karpur)
##      depth         caliper         ind.deep          ind.med       
##  Min.   :5667   Min.   :8.487   Min.   :  6.532   Min.   :  9.386  
##  1st Qu.:5769   1st Qu.:8.556   1st Qu.: 28.799   1st Qu.: 27.892  
##  Median :5872   Median :8.588   Median :217.849   Median :254.383  
##  Mean   :5873   Mean   :8.622   Mean   :275.357   Mean   :273.357  
##  3rd Qu.:5977   3rd Qu.:8.686   3rd Qu.:566.793   3rd Qu.:544.232  
##  Max.   :6083   Max.   :8.886   Max.   :769.484   Max.   :746.028  
##      gamma            phi.N            R.deep            R.med        
##  Min.   : 16.74   Min.   :0.0150   Min.   :  1.300   Min.   :  1.340  
##  1st Qu.: 40.89   1st Qu.:0.2030   1st Qu.:  1.764   1st Qu.:  1.837  
##  Median : 51.37   Median :0.2450   Median :  4.590   Median :  3.931  
##  Mean   : 53.42   Mean   :0.2213   Mean   : 24.501   Mean   : 21.196  
##  3rd Qu.: 62.37   3rd Qu.:0.2640   3rd Qu.: 34.724   3rd Qu.: 35.853  
##  Max.   :112.40   Max.   :0.4100   Max.   :153.085   Max.   :106.542  
##        SP          density.corr          density         phi.core     
##  Min.   :-73.95   Min.   :-0.067000   Min.   :1.758   Min.   :0.1570  
##  1st Qu.:-42.01   1st Qu.:-0.016000   1st Qu.:2.023   1st Qu.:0.2390  
##  Median :-32.25   Median :-0.007000   Median :2.099   Median :0.2760  
##  Mean   :-30.98   Mean   :-0.008883   Mean   :2.102   Mean   :0.2693  
##  3rd Qu.:-19.48   3rd Qu.: 0.002000   3rd Qu.:2.181   3rd Qu.:0.3070  
##  Max.   : 25.13   Max.   : 0.089000   Max.   :2.387   Max.   :0.3630  
##      k.core            Facies         
##  Min.   :    0.42   Length:819        
##  1st Qu.:  657.33   Class :character  
##  Median : 1591.22   Mode  :character  
##  Mean   : 2251.91                     
##  3rd Qu.: 3046.82                     
##  Max.   :15600.00
par(mfrow=c(1,1))
plot(karpur$phi.N,karpur$phi.core, xlab = 'Log Porosity',ylab='Core Porosity')

model1 <- lm(karpur$phi.core ~ karpur$phi.N)
summary(model1)
## 
## Call:
## lm(formula = karpur$phi.core ~ karpur$phi.N)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.135237 -0.030779  0.009432  0.033563  0.104025 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.30962    0.00485  63.846   <2e-16 ***
## karpur$phi.N -0.18207    0.02080  -8.753   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04368 on 817 degrees of freedom
## Multiple R-squared:  0.08573,    Adjusted R-squared:  0.08462 
## F-statistic: 76.61 on 1 and 817 DF,  p-value: < 2.2e-16
model1 <- lm((karpur$phi.core/100) ~., data = karpur)
summary(model1)
## 
## Call:
## lm(formula = (karpur$phi.core/100) ~ ., data = karpur)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -9.907e-04 -8.962e-05  7.960e-06  8.740e-05  9.077e-04 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.613e-02  2.577e-03   6.261 6.24e-10 ***
## depth        -3.948e-07  2.686e-07  -1.470 0.142023    
## caliper      -8.627e-04  1.484e-04  -5.812 8.90e-09 ***
## ind.deep      5.081e-07  3.492e-07   1.455 0.146104    
## ind.med      -3.357e-07  3.839e-07  -0.874 0.382160    
## gamma         3.993e-07  9.246e-07   0.432 0.665963    
## phi.N         1.368e-03  2.141e-04   6.392 2.78e-10 ***
## R.deep       -1.528e-06  9.406e-07  -1.624 0.104683    
## R.med         1.954e-06  1.377e-06   1.419 0.156296    
## SP           -4.974e-08  4.686e-07  -0.106 0.915504    
## density.corr -1.546e-03  7.125e-04  -2.170 0.030298 *  
## density      -1.865e-03  1.618e-04 -11.531  < 2e-16 ***
## k.core        4.240e-08  5.037e-09   8.418  < 2e-16 ***
## FaciesF10    -4.419e-04  5.120e-05  -8.631  < 2e-16 ***
## FaciesF2     -7.517e-04  8.238e-05  -9.126  < 2e-16 ***
## FaciesF3     -2.873e-04  4.868e-05  -5.900 5.35e-09 ***
## FaciesF5     -3.388e-04  4.964e-05  -6.824 1.75e-11 ***
## FaciesF7     -5.684e-04  8.290e-05  -6.857 1.41e-11 ***
## FaciesF8     -1.282e-04  5.849e-05  -2.193 0.028630 *  
## FaciesF9     -2.453e-04  6.515e-05  -3.765 0.000179 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0001874 on 799 degrees of freedom
## Multiple R-squared:  0.8354, Adjusted R-squared:  0.8315 
## F-statistic: 213.4 on 19 and 799 DF,  p-value: < 2.2e-16
model1 <- lm((karpur$phi.core/100) ~caliper+phi.N+density.corr+density+k.core+Facies, data = karpur)

coef(model1)
##   (Intercept)       caliper         phi.N  density.corr       density 
##  1.230508e-02 -6.539734e-04  1.578649e-03 -1.666614e-03 -1.974317e-03 
##        k.core     FaciesF10      FaciesF2      FaciesF3      FaciesF5 
##  3.995669e-08 -4.516805e-04 -7.913582e-04 -2.999990e-04 -3.794323e-04 
##      FaciesF7      FaciesF8      FaciesF9 
## -6.198164e-04 -1.863043e-04 -2.692968e-04
summary(model1)
## 
## Call:
## lm(formula = (karpur$phi.core/100) ~ caliper + phi.N + density.corr + 
##     density + k.core + Facies, data = karpur)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -9.995e-04 -9.649e-05 -1.340e-06  9.053e-05  9.038e-04 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.231e-02  8.952e-04  13.746  < 2e-16 ***
## caliper      -6.540e-04  9.916e-05  -6.595 7.68e-11 ***
## phi.N         1.579e-03  1.770e-04   8.918  < 2e-16 ***
## density.corr -1.667e-03  7.013e-04  -2.376   0.0177 *  
## density      -1.974e-03  1.540e-04 -12.819  < 2e-16 ***
## k.core        3.996e-08  4.363e-09   9.158  < 2e-16 ***
## FaciesF10    -4.517e-04  5.037e-05  -8.967  < 2e-16 ***
## FaciesF2     -7.914e-04  8.051e-05  -9.829  < 2e-16 ***
## FaciesF3     -3.000e-04  4.684e-05  -6.404 2.57e-10 ***
## FaciesF5     -3.794e-04  3.788e-05 -10.018  < 2e-16 ***
## FaciesF7     -6.198e-04  7.222e-05  -8.582  < 2e-16 ***
## FaciesF8     -1.863e-04  3.765e-05  -4.948 9.11e-07 ***
## FaciesF9     -2.693e-04  3.821e-05  -7.047 3.92e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000189 on 806 degrees of freedom
## Multiple R-squared:  0.8312, Adjusted R-squared:  0.8287 
## F-statistic: 330.7 on 12 and 806 DF,  p-value: < 2.2e-16
par(mfrow=c(2,2))

plot(model1,lwd=3)

CphiL <- predict(model1,karpur)
plot(CphiL,karpur$k.core)

model2 <- lm(karpur$k.core ~., data = karpur)
summary(model2)
## 
## Call:
## lm(formula = karpur$k.core ~ ., data = karpur)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5585.6  -568.9    49.2   476.5  8928.4 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -6.783e+04  1.760e+04  -3.853 0.000126 ***
## depth         8.544e+00  1.785e+00   4.786 2.02e-06 ***
## caliper       1.413e+03  1.019e+03   1.387 0.165789    
## ind.deep     -2.418e-01  2.354e+00  -0.103 0.918220    
## ind.med       1.224e+00  2.585e+00   0.473 0.636062    
## gamma        -4.583e+01  6.010e+00  -7.626 6.88e-14 ***
## phi.N        -2.010e+03  1.476e+03  -1.362 0.173540    
## R.deep       -2.344e+01  6.288e+00  -3.727 0.000207 ***
## R.med         5.643e+01  9.065e+00   6.225 7.76e-10 ***
## SP           -7.125e+00  3.145e+00  -2.266 0.023736 *  
## density.corr -2.567e+03  4.809e+03  -0.534 0.593602    
## density       2.319e+03  1.173e+03   1.976 0.048458 *  
## phi.core      1.921e+04  2.282e+03   8.418  < 2e-16 ***
## FaciesF10     8.921e+02  3.590e+02   2.485 0.013157 *  
## FaciesF2      9.243e+02  5.818e+02   1.589 0.112514    
## FaciesF3      4.393e+02  3.344e+02   1.313 0.189394    
## FaciesF5      7.411e+02  3.428e+02   2.162 0.030908 *  
## FaciesF7     -4.152e+01  5.742e+02  -0.072 0.942377    
## FaciesF8     -1.179e+03  3.927e+02  -3.002 0.002770 ** 
## FaciesF9     -2.969e+03  4.298e+02  -6.908 1.00e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1262 on 799 degrees of freedom
## Multiple R-squared:  0.6889, Adjusted R-squared:  0.6815 
## F-statistic: 93.12 on 19 and 799 DF,  p-value: < 2.2e-16
model2.red <- lm(karpur$k.core~CphiL+depth+gamma+R.deep+R.med+SP+density+phi.core+Facies, data =karpur)

summary(model2.red)
## 
## Call:
## lm(formula = karpur$k.core ~ CphiL + depth + gamma + R.deep + 
##     R.med + SP + density + phi.core + Facies, data = karpur)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4135.7  -472.0    23.3   527.5  5188.7 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.176e+04  4.382e+03  -9.532  < 2e-16 ***
## CphiL        1.165e+07  4.682e+05  24.873  < 2e-16 ***
## depth       -5.431e+00  9.641e-01  -5.634 2.44e-08 ***
## gamma       -7.751e+01  3.556e+00 -21.799  < 2e-16 ***
## R.deep      -1.685e+01  4.714e+00  -3.574 0.000373 ***
## R.med        1.904e+01  6.673e+00   2.854 0.004433 ** 
## SP          -2.610e+00  2.350e+00  -1.111 0.267025    
## density      2.203e+04  1.126e+03  19.568  < 2e-16 ***
## phi.core     1.319e+03  1.783e+03   0.740 0.459517    
## FaciesF10    5.237e+03  3.206e+02  16.337  < 2e-16 ***
## FaciesF2     8.244e+03  5.183e+02  15.906  < 2e-16 ***
## FaciesF3     3.420e+03  2.725e+02  12.552  < 2e-16 ***
## FaciesF5     3.648e+03  2.723e+02  13.397  < 2e-16 ***
## FaciesF7     4.753e+03  4.538e+02  10.474  < 2e-16 ***
## FaciesF8    -7.758e+02  2.309e+02  -3.359 0.000819 ***
## FaciesF9     8.768e+02  3.251e+02   2.697 0.007143 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 952.1 on 803 degrees of freedom
## Multiple R-squared:  0.8219, Adjusted R-squared:  0.8186 
## F-statistic: 247.1 on 15 and 803 DF,  p-value: < 2.2e-16
coef(model2.red)
##   (Intercept)         CphiL         depth         gamma        R.deep 
## -4.176340e+04  1.164644e+07 -5.431412e+00 -7.751049e+01 -1.684708e+01 
##         R.med            SP       density      phi.core     FaciesF10 
##  1.904341e+01 -2.609740e+00  2.203356e+04  1.319447e+03  5.237387e+03 
##      FaciesF2      FaciesF3      FaciesF5      FaciesF7      FaciesF8 
##  8.244242e+03  3.419732e+03  3.647958e+03  4.752532e+03 -7.757516e+02 
##      FaciesF9 
##  8.768178e+02
par(mfrow=c(2,2))
plot(model2.red,lwd=3)

C_PERM_L <- predict(model2.red,karpur)
AdjR.sq2 <- 1-sum((C_PERM_L - karpur$k.core)^2)/sum((karpur$k.core-mean(karpur$k.core))^2)
AdjR.sq2
## [1] 0.8219384
rmse.model2 <- sqrt(sum((C_PERM_L - karpur$k.core)^2)/nrow(karpur))
rmse.model2
## [1] 942.7917

let’s plot parameters after and before correction

par(mfrow=c(1,3))

plot(y=y<-(karpur$depth),ylim=rev(range(karpur$depth)),x=x<-(karpur$phi.N), type="l", col="506", lwd = 5, pch=17, xlab='Log Porosity', ylab='Depth, m', xlim=c(0,0.5), cex=1.5, cex.lab=1.5, cex.axis=1.2,col.axis="637",col.lab="506")

grid(nx= NULL, ny= NULL, lty=2,col="red",lwd=1)

plot(y=y<-(karpur$depth),ylim=rev(range(karpur$depth)),x=x<-(karpur$phi.core/100), type="l", col="375", lwd = 5, pch=17, xlab='Core Porosity and Corrected core porosity', ylab='Depth, m', xlim=c(0.15,0.4), cex=1.5, cex.lab=1.5, cex.axis=1.2,col.axis="637",col.lab="375")

lines(CphiL,karpur$depth, type="l", col="617",lwd=5)

grid(nx= NULL, ny= NULL, lty=2,col="red",lwd=1)

plot(y=y<-(karpur$depth),ylim=rev(range(karpur$depth)),x=x<-(karpur$k.core), type="l", col="gray", lwd = 5, pch=17, xlab='core k and corrected core k ', ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2,col.axis="200",col.lab="gray" , main = 'Adjusted R-squared=0.8255 & RMSE= 924.827 ')

lines(C_PERM_L,karpur$depth, type="l", col="92",lwd=5)

grid(nx= NULL, ny= NULL, lty=2,col="blue",lwd=1)

par(mfrow=c(1,1))

boxplot(karpur$depth~karpur$Facies,col="375" ,xlab='Core Porosity and Corrected core porosity', ylab='Depth, m',cex=1.5, cex.lab=1.5, cex.axis=1.2,col.axis="100",col.lab="gray")

grid(nx= NULL, ny= NULL, lty=2,col="red",lwd=1)

model2.redS <- lm(log10(karpur$k.core)~ . , data = karpur )
summary(model2.redS)
## 
## Call:
## lm(formula = log10(karpur$k.core) ~ ., data = karpur)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.5804 -0.1138  0.0322  0.1529  0.7384 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -2.3461877  4.6532000  -0.504  0.61425    
## depth         0.0007425  0.0004718   1.574  0.11596    
## caliper      -0.4605945  0.2693103  -1.710  0.08760 .  
## ind.deep     -0.0007951  0.0006222  -1.278  0.20168    
## ind.med       0.0007137  0.0006833   1.044  0.29659    
## gamma        -0.0091269  0.0015885  -5.746 1.30e-08 ***
## phi.N        -1.7628155  0.3901024  -4.519 7.16e-06 ***
## R.deep       -0.0025878  0.0016620  -1.557  0.11987    
## R.med         0.0044073  0.0023960   1.839  0.06622 .  
## SP           -0.0016935  0.0008312  -2.037  0.04194 *  
## density.corr  1.4462633  1.2712045   1.138  0.25558    
## density       1.6148374  0.3100921   5.208 2.44e-07 ***
## phi.core      9.4863406  0.6032903  15.724  < 2e-16 ***
## FaciesF10     0.0786460  0.0948909   0.829  0.40746    
## FaciesF2     -0.0184334  0.1537793  -0.120  0.90462    
## FaciesF3     -0.0307548  0.0883957  -0.348  0.72799    
## FaciesF5      0.1094193  0.0906034   1.208  0.22753    
## FaciesF7      0.2811620  0.1517797   1.852  0.06433 .  
## FaciesF8     -0.0976234  0.1038054  -0.940  0.34727    
## FaciesF9     -0.3562116  0.1135966  -3.136  0.00178 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3335 on 799 degrees of freedom
## Multiple R-squared:  0.6806, Adjusted R-squared:  0.673 
## F-statistic:  89.6 on 19 and 799 DF,  p-value: < 2.2e-16
model2.red2 <- lm(log10(karpur$k.core)~CphiL+SP+gamma+density+phi.core+Facies , data = karpur )

summary(model2.red2)
## 
## Call:
## lm(formula = log10(karpur$k.core) ~ CphiL + SP + gamma + density + 
##     phi.core + Facies, data = karpur)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.88465 -0.11551  0.02528  0.14484  0.71677 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -6.364e+00  8.589e-01  -7.409 3.21e-13 ***
## CphiL        1.005e+03  1.310e+02   7.668 5.05e-14 ***
## SP          -1.130e-03  7.866e-04  -1.436 0.151272    
## gamma       -1.317e-02  1.151e-03 -11.439  < 2e-16 ***
## density      2.597e+00  3.091e-01   8.400  < 2e-16 ***
## phi.core     7.214e+00  6.175e-01  11.683  < 2e-16 ***
## FaciesF10    4.019e-01  1.012e-01   3.972 7.77e-05 ***
## FaciesF2     4.903e-01  1.698e-01   2.887 0.003999 ** 
## FaciesF3     1.484e-01  9.055e-02   1.639 0.101607    
## FaciesF5     2.518e-01  7.018e-02   3.587 0.000355 ***
## FaciesF7     6.107e-01  1.418e-01   4.306 1.87e-05 ***
## FaciesF8    -2.647e-01  6.204e-02  -4.266 2.22e-05 ***
## FaciesF9    -2.730e-01  6.846e-02  -3.988 7.27e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3309 on 806 degrees of freedom
## Multiple R-squared:  0.6828, Adjusted R-squared:  0.6781 
## F-statistic: 144.6 on 12 and 806 DF,  p-value: < 2.2e-16
par(mfrow=c(2,2))
plot(model2.red2)

C_PERM_L2 <- predict(model2.red2, karpur)
C_PERM_L2<-10^C_PERM_L2 
AdjR.sq2 <- 1-sum((C_PERM_L2 - karpur$k.core)^2)/sum((karpur$k.core-mean(karpur$k.core))^2)
AdjR.sq2
## [1] 0.7185139
rmse.model2 <- sqrt(sum((C_PERM_L2 - karpur$k.core)^2)/nrow(karpur))
rmse.model2
## [1] 1185.384
require(MASS)
## Loading required package: MASS
library(MASS)
par(mfrow=c(1,1))
bc = boxcox(model2.red)

best.lam = bc$x[which(bc$y== max(bc$y))]
model2.red3 <- lm(((karpur$k.core^best.lam-1)/best.lam)~., karpur)
summary(model2.red3)
## 
## Call:
## lm(formula = ((karpur$k.core^best.lam - 1)/best.lam) ~ ., data = karpur)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -53.701  -6.334   0.602   6.741  47.178 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -4.270e+02  1.697e+02  -2.516 0.012075 *  
## depth         6.092e-02  1.721e-02   3.540 0.000424 ***
## caliper      -2.072e+00  9.823e+00  -0.211 0.833027    
## ind.deep     -9.159e-03  2.269e-02  -0.404 0.686652    
## ind.med       1.192e-02  2.492e-02   0.478 0.632687    
## gamma        -5.075e-01  5.794e-02  -8.759  < 2e-16 ***
## phi.N        -4.703e+01  1.423e+01  -3.305 0.000991 ***
## R.deep       -1.858e-01  6.062e-02  -3.064 0.002256 ** 
## R.med         4.203e-01  8.739e-02   4.810 1.81e-06 ***
## SP           -7.258e-02  3.032e-02  -2.394 0.016900 *  
## density.corr  8.912e+00  4.637e+01   0.192 0.847637    
## density       4.190e+01  1.131e+01   3.705 0.000226 ***
## phi.core      3.199e+02  2.200e+01  14.538  < 2e-16 ***
## FaciesF10     9.007e+00  3.461e+00   2.602 0.009427 ** 
## FaciesF2      7.261e+00  5.609e+00   1.294 0.195873    
## FaciesF3      2.112e+00  3.224e+00   0.655 0.512716    
## FaciesF5      6.594e+00  3.305e+00   1.995 0.046334 *  
## FaciesF7      5.971e+00  5.536e+00   1.079 0.281127    
## FaciesF8     -7.492e+00  3.786e+00  -1.979 0.048190 *  
## FaciesF9     -2.571e+01  4.143e+00  -6.206 8.73e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.16 on 799 degrees of freedom
## Multiple R-squared:  0.7684, Adjusted R-squared:  0.7629 
## F-statistic: 139.5 on 19 and 799 DF,  p-value: < 2.2e-16
model3.red <- lm(((karpur$k.core^best.lam-1)/best.lam)~CphiL+depth+gamma+phi.N+R.deep+R.med+
                   SP+density+phi.core+Facies, data = karpur)
C_PERM_L3 <- predict(model3.red, karpur)
C_PERM_L3 <- exp(log(best.lam*C_PERM_L3+1)/best.lam)
AdjR.sq3 <- 1-sum((C_PERM_L3 - karpur$k.core)^2)/sum((karpur$k.core-mean(karpur$k.core))^2)
AdjR.sq3
## [1] 0.9479614
rmse.model3 <- sqrt(sum((C_PERM_L3 - karpur$k.core)^2)/nrow(karpur))
rmse.model3
## [1] 509.675

let plot each predicted value with core K

par(mfrow=c(1,3))
plot(y=y<-(karpur$depth),ylim=rev(range(karpur$depth)),x=x<-(karpur$k.core),
     type="l", col="black", lwd = 5, pch=17, xlab='core k and corrected core k ',
     ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2,col.axis="200",col.lab="darkblue" ,cex.main=0.8, main = 'Adjusted R-squared=0.8219384 & RMSE= 942.7917 ')
lines(C_PERM_L,karpur$depth, type="l", col="92",lwd=5)
grid(nx= NULL, ny= NULL, lty=2,col="gray",lwd=1)
plot(y=y<-(karpur$depth),ylim=rev(range(karpur$depth)),x=x<-(karpur$k.core),
     type="l", col="black", lwd = 5, pch=17, xlab=' by log transformation ',
     ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5, cex.axis=1.2,col.axis="200",col.lab="darkblue" ,cex.main=0.8, main ='Adjusted R-squared=0.7185139 & RMSE=1185.384' )
lines(C_PERM_L2,karpur$depth, type="l", col="120",lwd=5)
grid(nx= NULL, ny= NULL, lty=2,col="gray",lwd=1)
plot(y=y<-(karpur$depth),ylim=rev(range(karpur$depth)),x=x<-(karpur$k.core),
     type="l", col="black", lwd = 5, pch=17, xlab=' by box cox transformation ',
     ylab='Depth, m', xlim=c(0,16000), cex=1.5, cex.lab=1.5,cex.main=0.8, cex.axis=1.2,col.axis="200",col.lab="darkblue" , main ='Adjusted R-squared=0.9479614 & RMSE=509.675')
lines(C_PERM_L3,karpur$depth, type="l", col="170",lwd=5)
grid(nx= NULL, ny= NULL, lty=2,col="gray",lwd=1)