Conduct MLR to model and predict permeability in multiple models
Ahmed Wasfi -BUOG 4stage
2024-11-29
1st step: Set data and take a knowledge for it
data3<-read.csv("karpur.csv")
karpur_data <- read.csv("karpur.csv")str(data3)## 'data.frame': 819 obs. of 15 variables:
## $ depth : num 5667 5668 5668 5668 5669 ...
## $ caliper : num 8.69 8.69 8.69 8.69 8.69 ...
## $ ind.deep : num 618 498 385 278 184 ...
## $ ind.med : num 570 419 300 205 131 ...
## $ gamma : num 98.8 90.6 78.1 66.2 59.8 ...
## $ phi.N : num 0.41 0.307 0.203 0.119 0.069 0.048 0.047 0.055 0.066 0.074 ...
## $ R.deep : num 1.62 2.01 2.6 3.59 5.44 ...
## $ R.med : num 1.75 2.38 3.33 4.87 7.62 ...
## $ SP : num -56.6 -61.9 -55.9 -41.9 -34.9 ...
## $ density.corr : num -0.033 -0.067 -0.064 -0.053 -0.054 -0.058 -0.056 -0.046 -0.04 -0.043 ...
## $ density : num 2.21 2.04 1.89 1.79 1.76 ...
## $ phi.core : num 33.9 33.4 33.1 34.9 35.1 ...
## $ k.core : num 2443 3007 3370 2270 2531 ...
## $ Facies : chr "F1" "F1" "F1" "F1" ...
## $ phi.core.frac: num 0.339 0.334 0.331 0.349 0.351 ...log10_permeability <- log10(karpur_data$k.core)2nd step: Data Pre-processing:
data3$log_k_core <- log10(data3$k.core)model 1: MLR of Permeability given all well logs without Facies —- Step 1: MLR of Permeability given all well logs without Facies —-
model1 <- lm(k.core ~ . - Facies , data = karpur_data)
summary(model1)##
## Call:
## lm(formula = k.core ~ . - Facies, data = karpur_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5549.5 -755.5 -178.1 578.0 11260.8
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 60762.728 16605.360 3.659 0.000269 ***
## depth -7.398 1.446 -5.115 3.92e-07 ***
## caliper -3955.952 1055.105 -3.749 0.000190 ***
## ind.deep -14.183 2.345 -6.048 2.24e-09 ***
## ind.med 17.300 2.509 6.896 1.08e-11 ***
## gamma -77.487 5.475 -14.153 < 2e-16 ***
## phi.N -1784.704 1301.772 -1.371 0.170763
## R.deep -26.007 6.974 -3.729 0.000206 ***
## R.med 63.525 9.841 6.455 1.86e-10 ***
## SP -8.784 3.460 -2.539 0.011313 *
## density.corr -523.060 5358.876 -0.098 0.922269
## density 8011.106 1120.554 7.149 1.96e-12 ***
## phi.core 183.203 23.802 7.697 4.07e-14 ***
## phi.core.frac NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1442 on 806 degrees of freedom
## Multiple R-squared: 0.5903, Adjusted R-squared: 0.5842
## F-statistic: 96.77 on 12 and 806 DF, p-value: < 2.2e-16adjusted_r2_model1<- summary(model1)$adj.r.squared
rmse_model1 <- sqrt(mean(residuals(model1)^2))
cat("Adjusted R2:", adjusted_r2_model1, " | RMSE:", rmse_model1, "\n")## Adjusted R2: 0.5841845 | RMSE: 1430.118Plot measured vs. predicted permeability
predicted1 <- predict(model1, newdata = karpur_data)
plot(karpur_data$k.core, predicted1, xlab = "Measured Permeability", ylab = "Predicted Permeability",
main = "Measured vs. Predicted Permeability (Model 1)")
—- Step 2: Stepwise Elimination (Model 1) —-
model2 <- step(model1 , direction = "both")## Start: AIC=11926.91
## k.core ~ (depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core +
## Facies + phi.core.frac) - Facies
##
##
## Step: AIC=11926.91
## k.core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core
##
## Df Sum of Sq RSS AIC
## - density.corr 1 19799 1675068713 11925
## - phi.N 1 3906205 1678955118 11927
## <none> 1675048914 11927
## - SP 1 13394190 1688443104 11931
## - R.deep 1 28897686 1703946599 11939
## - caliper 1 29214826 1704263740 11939
## - depth 1 54372650 1729421563 11951
## - ind.deep 1 76022788 1751071701 11961
## - R.med 1 86603706 1761652619 11966
## - ind.med 1 98823752 1773872666 11972
## - density 1 106221406 1781270319 11975
## - phi.core 1 123125117 1798174031 11983
## - gamma 1 416312526 2091361440 12107
##
## Step: AIC=11924.92
## k.core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density + phi.core
##
## Df Sum of Sq RSS AIC
## <none> 1675068713 11925
## - phi.N 1 4564880 1679633593 11925
## + density.corr 1 19799 1675048914 11927
## - SP 1 13491079 1688559792 11930
## - R.deep 1 28896144 1703964857 11937
## - caliper 1 29253869 1704322581 11937
## - depth 1 54825159 1729893872 11949
## - ind.deep 1 77573926 1752642639 11960
## - R.med 1 86772220 1761840933 11964
## - ind.med 1 100740701 1775809413 11971
## - density 1 114209586 1789278299 11977
## - phi.core 1 124694278 1799762991 11982
## - gamma 1 417015194 2092083907 12105adjusted_r2_step2 <- summary(model2)$adj.r.squared
rmse_step2 <- sqrt(mean(residuals(model2)^2))
cat("Adjusted R2:", adjusted_r2_step2, " | RMSE:", rmse_step2, "\n")## Adjusted R2: 0.5846949 | RMSE: 1430.126Plot measured vs. predicted permeability
predicted2 <- predict(model2, newdata = karpur_data)
plot(karpur_data$k.core, predicted2, xlab = "Measured Permeability", ylab = "Predicted Permeability",
main = "Measured vs. Predicted Permeability (Model 2)")
—- Step 3: MLR of Permeability given all well logs with Facies —-
model3 <- lm(k.core ~ . , data = karpur_data)adjusted_r2_model3 <- summary(model3)$adj.r.squared
rmse_model3 <- sqrt(mean(residuals(model3)^2))
cat("Adjusted R2:", adjusted_r2_model3, " | RMSE:", rmse_model3, "\n")## Adjusted R2: 0.6814911 | RMSE: 1246.201Plot measured vs. predicted permeability
predicted3 <- predict(model3, newdata = karpur_data)
plot(karpur_data$k.core, predicted3, xlab = "Measured Permeability", ylab = "Predicted Permeability",
main = "Measured vs. Predicted Permeability (Model 3)")
—- Step 4: Stepwise Elimination (Model 3) —-
model4 <- step(model3, direction = "both")## Start: AIC=11715.43
## k.core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core +
## Facies + phi.core.frac
##
##
## Step: AIC=11715.43
## k.core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core +
## Facies
##
## Df Sum of Sq RSS AIC
## - ind.deep 1 16793 1271937992 11713
## - ind.med 1 356746 1272277945 11714
## - density.corr 1 453661 1272374861 11714
## - phi.N 1 2953609 1274874809 11715
## - caliper 1 3063007 1274984206 11715
## <none> 1271921199 11715
## - density 1 6217927 1278139127 11717
## - SP 1 8171834 1280093033 11719
## - R.deep 1 22117394 1294038593 11728
## - depth 1 36466976 1308388176 11737
## - R.med 1 61690461 1333611660 11752
## - gamma 1 92579723 1364500923 11771
## - phi.core 1 112793101 1384714301 11783
## - Facies 7 403127714 1675048914 11927
##
## Step: AIC=11713.44
## k.core ~ depth + caliper + ind.med + gamma + phi.N + R.deep +
## R.med + SP + density.corr + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - density.corr 1 437546 1272375538 11712
## - phi.N 1 2938766 1274876758 11713
## - caliper 1 3074396 1275012389 11713
## <none> 1271937992 11713
## + ind.deep 1 16793 1271921199 11715
## - density 1 6228928 1278166920 11715
## - ind.med 1 6905855 1278843848 11716
## - SP 1 8191802 1280129794 11717
## - R.deep 1 22125695 1294063687 11726
## - depth 1 39139470 1311077462 11736
## - R.med 1 61773953 1333711946 11750
## - gamma 1 92865220 1364803212 11769
## - phi.core 1 112960440 1384898432 11781
## - Facies 7 479133709 1751071701 11961
##
## Step: AIC=11711.72
## k.core ~ depth + caliper + ind.med + gamma + phi.N + R.deep +
## R.med + SP + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - caliper 1 2980713 1275356252 11712
## <none> 1272375538 11712
## - phi.N 1 3279032 1275654571 11712
## + density.corr 1 437546 1271937992 11713
## - density 1 5792837 1278168375 11713
## + ind.deep 1 677 1272374861 11714
## - ind.med 1 6813959 1279189497 11714
## - SP 1 8391302 1280766840 11715
## - R.deep 1 22009402 1294384940 11724
## - depth 1 38705776 1311081314 11734
## - R.med 1 61436819 1333812357 11748
## - gamma 1 93974329 1366349868 11768
## - phi.core 1 115336515 1387712053 11781
## - Facies 7 480267100 1752642639 11960
##
## Step: AIC=11711.64
## k.core ~ depth + ind.med + gamma + phi.N + R.deep + R.med + SP +
## density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - phi.N 1 2534906 1277891157 11711
## <none> 1275356252 11712
## + caliper 1 2980713 1272375538 11712
## + density.corr 1 343863 1275012389 11713
## + ind.deep 1 5597 1275350654 11714
## - density 1 7270311 1282626562 11714
## - SP 1 8733336 1284089587 11715
## - ind.med 1 12924050 1288280301 11718
## - R.deep 1 22449117 1297805369 11724
## - depth 1 51507476 1326863728 11742
## - R.med 1 60137982 1335494234 11747
## - phi.core 1 112564835 1387921086 11779
## - gamma 1 141535555 1416891807 11796
## - Facies 7 520094756 1795451008 11978
##
## Step: AIC=11711.26
## k.core ~ depth + ind.med + gamma + R.deep + R.med + SP + density +
## phi.core + Facies
##
## Df Sum of Sq RSS AIC
## <none> 1277891157 11711
## + phi.N 1 2534906 1275356252 11712
## + caliper 1 2236587 1275654571 11712
## - density 1 5155969 1283047127 11713
## + density.corr 1 624807 1277266351 11713
## + ind.deep 1 1762 1277889395 11713
## - SP 1 8515796 1286406953 11715
## - ind.med 1 10944937 1288836095 11716
## - R.deep 1 23273312 1301164469 11724
## - depth 1 49725248 1327616405 11740
## - R.med 1 59454645 1337345802 11746
## - phi.core 1 110154394 1388045551 11777
## - gamma 1 219059092 1496950249 11839
## - Facies 7 526383446 1804274603 11980adjusted_r2_step4 <- summary(model4)$adj.r.squared
rmse_step4 <- sqrt(mean(residuals(model4)^2))
cat("Adjusted R2:", adjusted_r2_step4, " | RMSE:", rmse_step4, "\n")## Adjusted R2: 0.6815901 | RMSE: 1249.122Plot measured vs. predicted permeability
predicted4 <- predict(model4, newdata = karpur_data)
plot(karpur_data$k.core, predicted4, xlab = "Measured Permeability", ylab = "Predicted Permeability",
main = "Measured vs. Predicted Permeability (Model 4)")
—- Step 5: MLR of Log10(Permeability) with all well logs and Facies —-
model5 <- lm(log10_permeability ~ ., data = karpur_data)adjusted_r2_model5 <- summary(model5)$adj.r.squared
rmse_model5 <- sqrt(mean(residuals(model5)^2))
cat("Adjusted R2:", adjusted_r2_model5, " | RMSE:", rmse_model5, "\n")## Adjusted R2: 0.7456542 | RMSE: 0.2903109Plot measured vs. predicted log10(permeability)
predicted5 <- predict(model5, newdata = karpur_data)
plot(log10_permeability, predicted5, xlab = "Measured log10(Permeability)", ylab = "Predicted log10(Permeability)",
main = "Measured vs. Predicted log10(Permeability) (Model 5)")
—- Step 6: Stepwise Elimination (Model 5) —-
model6 <- step(model5, direction = "both")## Start: AIC=-1983.88
## log10_permeability ~ depth + caliper + ind.deep + ind.med + gamma +
## phi.N + R.deep + R.med + SP + density.corr + density + phi.core +
## k.core + Facies + phi.core.frac
##
##
## Step: AIC=-1983.88
## log10_permeability ~ depth + caliper + ind.deep + ind.med + gamma +
## phi.N + R.deep + R.med + SP + density.corr + density + phi.core +
## k.core + Facies
##
## Df Sum of Sq RSS AIC
## - Facies 7 0.9845 70.010 -1986.3
## - R.deep 1 0.0046 69.030 -1985.8
## - depth 1 0.0511 69.077 -1985.3
## - ind.med 1 0.0749 69.101 -1985.0
## - SP 1 0.1033 69.129 -1984.7
## - R.med 1 0.1287 69.154 -1984.4
## - ind.deep 1 0.1681 69.194 -1983.9
## <none> 69.026 -1983.9
## - density.corr 1 0.2148 69.240 -1983.3
## - gamma 1 0.4759 69.502 -1980.3
## - caliper 1 0.6209 69.647 -1978.5
## - phi.N 1 1.6663 70.692 -1966.3
## - density 1 2.0216 71.047 -1962.2
## - phi.core 1 14.0977 83.123 -1833.7
## - k.core 1 19.8344 88.860 -1779.0
##
## Step: AIC=-1986.28
## log10_permeability ~ depth + caliper + ind.deep + ind.med + gamma +
## phi.N + R.deep + R.med + SP + density.corr + density + phi.core +
## k.core
##
## Df Sum of Sq RSS AIC
## - R.deep 1 0.0029 70.013 -1988.2
## - SP 1 0.0353 70.045 -1987.9
## - ind.med 1 0.0527 70.063 -1987.7
## - depth 1 0.0864 70.097 -1987.3
## - R.med 1 0.1528 70.163 -1986.5
## - ind.deep 1 0.1581 70.168 -1986.4
## <none> 70.010 -1986.3
## - density.corr 1 0.1915 70.202 -1986.0
## + Facies 7 0.9845 69.026 -1983.9
## - gamma 1 0.9247 70.935 -1977.5
## - caliper 1 1.1696 71.180 -1974.7
## - phi.N 1 2.2434 72.254 -1962.5
## - density 1 2.3311 72.341 -1961.5
## - phi.core 1 16.9538 86.964 -1810.7
## - k.core 1 25.9257 95.936 -1730.3
##
## Step: AIC=-1988.25
## log10_permeability ~ depth + caliper + ind.deep + ind.med + gamma +
## phi.N + R.med + SP + density.corr + density + phi.core +
## k.core
##
## Df Sum of Sq RSS AIC
## - SP 1 0.0420 70.055 -1989.8
## - ind.med 1 0.0582 70.071 -1989.6
## - depth 1 0.0862 70.099 -1989.2
## - ind.deep 1 0.1671 70.180 -1988.3
## <none> 70.013 -1988.2
## - density.corr 1 0.1896 70.203 -1988.0
## + R.deep 1 0.0029 70.010 -1986.3
## + Facies 7 0.9828 69.030 -1985.8
## - gamma 1 0.9416 70.955 -1979.3
## - R.med 1 0.9727 70.986 -1979.0
## - caliper 1 1.1748 71.188 -1976.6
## - phi.N 1 2.2449 72.258 -1964.4
## - density 1 2.4035 72.416 -1962.6
## - phi.core 1 16.9523 86.965 -1812.7
## - k.core 1 26.3009 96.314 -1729.0
##
## Step: AIC=-1989.76
## log10_permeability ~ depth + caliper + ind.deep + ind.med + gamma +
## phi.N + R.med + density.corr + density + phi.core + k.core
##
## Df Sum of Sq RSS AIC
## - ind.med 1 0.0543 70.109 -1991.1
## - depth 1 0.0831 70.138 -1990.8
## - ind.deep 1 0.1603 70.215 -1989.9
## <none> 70.055 -1989.8
## - density.corr 1 0.1785 70.234 -1989.7
## + SP 1 0.0420 70.013 -1988.2
## + R.deep 1 0.0096 70.045 -1987.9
## + Facies 7 0.9082 69.147 -1986.5
## - gamma 1 0.9074 70.962 -1981.2
## - R.med 1 0.9323 70.987 -1980.9
## - caliper 1 1.1514 71.206 -1978.4
## - phi.N 1 2.3482 72.403 -1964.8
## - density 1 2.3882 72.443 -1964.3
## - phi.core 1 16.9572 87.012 -1814.2
## - k.core 1 26.5342 96.589 -1728.7
##
## Step: AIC=-1991.13
## log10_permeability ~ depth + caliper + ind.deep + gamma + phi.N +
## R.med + density.corr + density + phi.core + k.core
##
## Df Sum of Sq RSS AIC
## - depth 1 0.0758 70.185 -1992.2
## <none> 70.109 -1991.1
## - density.corr 1 0.2130 70.322 -1990.6
## + ind.med 1 0.0543 70.055 -1989.8
## + SP 1 0.0381 70.071 -1989.6
## + R.deep 1 0.0172 70.092 -1989.3
## + Facies 7 0.9040 69.205 -1987.8
## - ind.deep 1 0.8204 70.930 -1983.6
## - gamma 1 0.8531 70.962 -1983.2
## - R.med 1 0.9993 71.109 -1981.5
## - caliper 1 1.1570 71.266 -1979.7
## - phi.N 1 2.4295 72.539 -1965.2
## - density 1 2.5137 72.623 -1964.3
## - phi.core 1 16.9117 87.021 -1816.1
## - k.core 1 28.4075 98.517 -1714.5
##
## Step: AIC=-1992.24
## log10_permeability ~ caliper + ind.deep + gamma + phi.N + R.med +
## density.corr + density + phi.core + k.core
##
## Df Sum of Sq RSS AIC
## <none> 70.185 -1992.2
## - density.corr 1 0.1945 70.380 -1992.0
## + depth 1 0.0758 70.109 -1991.1
## + ind.med 1 0.0470 70.138 -1990.8
## + SP 1 0.0355 70.150 -1990.7
## + R.deep 1 0.0156 70.170 -1990.4
## + Facies 7 0.9638 69.221 -1989.6
## - R.med 1 0.9436 71.129 -1983.3
## - gamma 1 1.0564 71.241 -1982.0
## - caliper 1 1.9123 72.097 -1972.2
## - ind.deep 1 2.2970 72.482 -1967.9
## - density 1 2.4386 72.624 -1966.3
## - phi.N 1 2.9529 73.138 -1960.5
## - phi.core 1 17.0365 87.222 -1816.3
## - k.core 1 29.7789 99.964 -1704.6adjusted_r2_step6 <- summary(model6)$adj.r.squared
rmse_step6 <- sqrt(mean(residuals(model6)^2))
cat("Adjusted R2:", adjusted_r2_step6, " | RMSE:", rmse_step6, "\n")## Adjusted R2: 0.7448982 | RMSE: 0.292739Plot measured vs. predicted log10(permeability)
predicted6 <- predict(model6, newdata = karpur_data)
plot(log10_permeability, predicted6, xlab = "Measured log10(Permeability)", ylab = "Predicted log10(Permeability)",
main = "Measured vs. Predicted log10(Permeability) (Model 6)")
model 7 Random Sub-sampling Cross-Validation (CV) applied on MLR of Log10(Permeability) given all well logs with Facies.
data3$log_k_core <- log10(data3$k.core)
library(caret)## Warning: package 'caret' was built under R version 4.4.2## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 4.4.2## Loading required package: latticeset.seed(123)
train_index = createDataPartition(data3$log_k_core, p = 0.67, list = FALSE)
train_data = data3[train_index, ]
test_data = data3[-train_index, ]Predicted_Permeabiity_Model_4<- lm(log_k_core~.-k.core,data=train_data)
summary(Predicted_Permeabiity_Model_4)##
## Call:
## lm(formula = log_k_core ~ . - k.core, data = train_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.63072 -0.11223 0.03652 0.14171 0.72653
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.1528438 5.8994071 -0.534 0.593265
## depth 0.0009582 0.0006110 1.568 0.117431
## caliper -0.4446846 0.3409032 -1.304 0.192652
## ind.deep -0.0009556 0.0007647 -1.250 0.211954
## ind.med 0.0008752 0.0008445 1.036 0.300512
## gamma -0.0078715 0.0020532 -3.834 0.000141 ***
## phi.N -1.9479851 0.5069395 -3.843 0.000136 ***
## R.deep -0.0031459 0.0020084 -1.566 0.117864
## R.med 0.0055215 0.0029157 1.894 0.058804 .
## SP -0.0015514 0.0010083 -1.539 0.124476
## density.corr 1.1393219 1.6338379 0.697 0.485902
## density 1.2975774 0.3976294 3.263 0.001172 **
## phi.core 0.0937129 0.0076810 12.201 < 2e-16 ***
## FaciesF10 0.2190849 0.1213529 1.805 0.071586 .
## FaciesF2 0.0950972 0.1810512 0.525 0.599629
## FaciesF3 0.0570353 0.1152831 0.495 0.620987
## FaciesF5 0.1668566 0.1117783 1.493 0.136098
## FaciesF7 0.3625122 0.2347997 1.544 0.123203
## FaciesF8 -0.0468921 0.1320336 -0.355 0.722616
## FaciesF9 -0.3011142 0.1452945 -2.072 0.038706 *
## phi.core.frac NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3398 on 531 degrees of freedom
## Multiple R-squared: 0.6706, Adjusted R-squared: 0.6589
## F-statistic: 56.91 on 19 and 531 DF, p-value: < 2.2e-16Predicted_log10_permeability_7<-predict(Predicted_Permeabiity_Model_4,newdata=test_data)
Predicted_permeability_7<-10^Predicted_log10_permeability_7
plot(Predicted_permeability_7,test_data$k.core,main="Measured permeability vs Predicted permeability",ylab="Predicted permeability",xlab="Measured permeability")
model 8 :Applying step wise elimination to this model.
Stepwise_Model_4<-step(Predicted_Permeabiity_Model_4, direction = "backward")## Start: AIC=-1169.74
## log_k_core ~ (depth + caliper + ind.deep + ind.med + gamma +
## phi.N + R.deep + R.med + SP + density.corr + density + phi.core +
## k.core + Facies + phi.core.frac) - k.core
##
##
## Step: AIC=-1169.74
## log_k_core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density.corr + density + phi.core +
## Facies
##
## Df Sum of Sq RSS AIC
## - density.corr 1 0.0562 61.382 -1171.2
## - ind.med 1 0.1240 61.450 -1170.6
## - ind.deep 1 0.1804 61.506 -1170.1
## - caliper 1 0.1965 61.523 -1170.0
## <none> 61.326 -1169.7
## - SP 1 0.2734 61.599 -1169.3
## - R.deep 1 0.2834 61.609 -1169.2
## - depth 1 0.2840 61.610 -1169.2
## - R.med 1 0.4142 61.740 -1168.0
## - density 1 1.2299 62.556 -1160.8
## - gamma 1 1.6975 63.023 -1156.7
## - phi.N 1 1.7053 63.031 -1156.6
## - Facies 7 5.0474 66.373 -1140.2
## - phi.core 1 17.1913 78.517 -1035.6
##
## Step: AIC=-1171.23
## log_k_core ~ depth + caliper + ind.deep + ind.med + gamma + phi.N +
## R.deep + R.med + SP + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - ind.med 1 0.1459 61.528 -1171.9
## - caliper 1 0.1976 61.580 -1171.5
## - ind.deep 1 0.2054 61.588 -1171.4
## <none> 61.382 -1171.2
## - SP 1 0.2683 61.650 -1170.8
## - R.deep 1 0.2878 61.670 -1170.7
## - depth 1 0.2908 61.673 -1170.6
## - R.med 1 0.4241 61.806 -1169.4
## - density 1 1.4632 62.845 -1160.2
## - phi.N 1 1.6495 63.032 -1158.6
## - gamma 1 1.6777 63.060 -1158.4
## - Facies 7 5.0922 66.474 -1141.3
## - phi.core 1 17.1602 78.542 -1037.4
##
## Step: AIC=-1171.93
## log_k_core ~ depth + caliper + ind.deep + gamma + phi.N + R.deep +
## R.med + SP + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - caliper 1 0.1611 61.689 -1172.5
## - ind.deep 1 0.1751 61.703 -1172.4
## - SP 1 0.2185 61.747 -1172.0
## <none> 61.528 -1171.9
## - R.deep 1 0.2592 61.787 -1171.6
## - R.med 1 0.3813 61.909 -1170.5
## - depth 1 0.5263 62.054 -1169.2
## - density 1 1.4745 63.003 -1160.9
## - phi.N 1 1.5625 63.091 -1160.1
## - gamma 1 1.5734 63.101 -1160.0
## - Facies 7 6.9521 68.480 -1126.9
## - phi.core 1 17.0279 78.556 -1039.3
##
## Step: AIC=-1172.48
## log_k_core ~ depth + ind.deep + gamma + phi.N + R.deep + R.med +
## SP + density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - SP 1 0.2025 61.892 -1172.7
## <none> 61.689 -1172.5
## - R.deep 1 0.2564 61.946 -1172.2
## - ind.deep 1 0.3838 62.073 -1171.1
## - R.med 1 0.4260 62.115 -1170.7
## - density 1 1.3593 63.048 -1162.5
## - gamma 1 1.4473 63.136 -1161.7
## - phi.N 1 1.7777 63.467 -1158.8
## - depth 1 2.0564 63.746 -1156.4
## - Facies 7 8.8789 70.568 -1112.4
## - phi.core 1 17.7780 79.467 -1035.0
##
## Step: AIC=-1172.68
## log_k_core ~ depth + ind.deep + gamma + phi.N + R.deep + R.med +
## density + phi.core + Facies
##
## Df Sum of Sq RSS AIC
## - R.deep 1 0.1913 62.083 -1173.0
## <none> 61.892 -1172.7
## - R.med 1 0.3613 62.253 -1171.5
## - ind.deep 1 0.4313 62.323 -1170.8
## - density 1 1.3322 63.224 -1162.9
## - gamma 1 1.4881 63.380 -1161.6
## - phi.N 1 1.7508 63.642 -1159.3
## - depth 1 2.0065 63.898 -1157.1
## - Facies 7 8.7603 70.652 -1113.7
## - phi.core 1 17.9425 79.834 -1034.4
##
## Step: AIC=-1172.98
## log_k_core ~ depth + ind.deep + gamma + phi.N + R.med + density +
## phi.core + Facies
##
## Df Sum of Sq RSS AIC
## <none> 62.083 -1173.0
## - R.med 1 0.3001 62.383 -1172.3
## - ind.deep 1 0.4671 62.550 -1170.8
## - density 1 1.2358 63.319 -1164.1
## - gamma 1 1.4180 63.501 -1162.5
## - phi.N 1 1.8386 63.922 -1158.9
## - depth 1 1.8421 63.925 -1158.9
## - Facies 7 8.7262 70.809 -1114.5
## - phi.core 1 18.3618 80.445 -1032.2summary(Stepwise_Model_4)##
## Call:
## lm(formula = log_k_core ~ depth + ind.deep + gamma + phi.N +
## R.med + density + phi.core + Facies, data = train_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.67933 -0.11096 0.02422 0.15624 0.69126
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.046e+01 2.167e+00 -4.827 1.81e-06 ***
## depth 1.571e-03 3.940e-04 3.988 7.59e-05 ***
## ind.deep -2.619e-04 1.304e-04 -2.008 0.045120 *
## gamma -6.326e-03 1.808e-03 -3.499 0.000506 ***
## phi.N -1.950e+00 4.894e-01 -3.984 7.71e-05 ***
## R.med 1.614e-03 1.002e-03 1.610 0.108082
## density 1.234e+00 3.776e-01 3.266 0.001159 **
## phi.core 9.499e-02 7.545e-03 12.591 < 2e-16 ***
## FaciesF10 2.189e-01 1.190e-01 1.840 0.066322 .
## FaciesF2 1.156e-01 1.792e-01 0.645 0.519036
## FaciesF3 2.352e-02 1.109e-01 0.212 0.832064
## FaciesF5 1.803e-01 1.051e-01 1.716 0.086768 .
## FaciesF7 3.143e-01 2.254e-01 1.394 0.163764
## FaciesF8 -6.347e-02 1.166e-01 -0.544 0.586536
## FaciesF9 -3.582e-01 1.256e-01 -2.851 0.004529 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3403 on 536 degrees of freedom
## Multiple R-squared: 0.6666, Adjusted R-squared: 0.6579
## F-statistic: 76.54 on 14 and 536 DF, p-value: < 2.2e-16Let’s plot the predicted vs measured permeability.
Predicted_log10_permeability_8 <-predict(Stepwise_Model_4,newdata=test_data)
Predicted_permeability_8<-10^Predicted_log10_permeability_8
plot(Predicted_permeability_8,test_data$k.core,main="Measured permeability vs Predicted permeability",xlab="Measured permeability",ylab="Predicted permeability")