title: “Project 2”
author: “Deepa Sharma/William Aiken”
date: “2024-11-13”
output: html_document
Data Acquisition
Here we can preview the data structure:
student_train = read.csv('https://raw.githubusercontent.com/deepasharma06/Data-624/refs/heads/main/StudentData_training.csv')
student_eval = read.csv('https://raw.githubusercontent.com/deepasharma06/Data-624/refs/heads/main/StudentEvaluation_test.csv')
head(student_train) %>% kable()| Brand.Code | Carb.Volume | Fill.Ounces | PC.Volume | Carb.Pressure | Carb.Temp | PSC | PSC.Fill | PSC.CO2 | Mnf.Flow | Carb.Pressure1 | Fill.Pressure | Hyd.Pressure1 | Hyd.Pressure2 | Hyd.Pressure3 | Hyd.Pressure4 | Filler.Level | Filler.Speed | Temperature | Usage.cont | Carb.Flow | Density | MFR | Balling | Pressure.Vacuum | PH | Oxygen.Filler | Bowl.Setpoint | Pressure.Setpoint | Air.Pressurer | Alch.Rel | Carb.Rel | Balling.Lvl |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B | 5.340000 | 23.96667 | 0.2633333 | 68.2 | 141.2 | 0.104 | 0.26 | 0.04 | -100 | 118.8 | 46.0 | 0 | NA | NA | 118 | 121.2 | 4002 | 66.0 | 16.18 | 2932 | 0.88 | 725.0 | 1.398 | -4.0 | 8.36 | 0.022 | 120 | 46.4 | 142.6 | 6.58 | 5.32 | 1.48 |
| A | 5.426667 | 24.00667 | 0.2386667 | 68.4 | 139.6 | 0.124 | 0.22 | 0.04 | -100 | 121.6 | 46.0 | 0 | NA | NA | 106 | 118.6 | 3986 | 67.6 | 19.90 | 3144 | 0.92 | 726.8 | 1.498 | -4.0 | 8.26 | 0.026 | 120 | 46.8 | 143.0 | 6.56 | 5.30 | 1.56 |
| B | 5.286667 | 24.06000 | 0.2633333 | 70.8 | 144.8 | 0.090 | 0.34 | 0.16 | -100 | 120.2 | 46.0 | 0 | NA | NA | 82 | 120.0 | 4020 | 67.0 | 17.76 | 2914 | 1.58 | 735.0 | 3.142 | -3.8 | 8.94 | 0.024 | 120 | 46.6 | 142.0 | 7.66 | 5.84 | 3.28 |
| A | 5.440000 | 24.00667 | 0.2933333 | 63.0 | 132.6 | NA | 0.42 | 0.04 | -100 | 115.2 | 46.4 | 0 | 0 | 0 | 92 | 117.8 | 4012 | 65.6 | 17.42 | 3062 | 1.54 | 730.6 | 3.042 | -4.4 | 8.24 | 0.030 | 120 | 46.0 | 146.2 | 7.14 | 5.42 | 3.04 |
| A | 5.486667 | 24.31333 | 0.1113333 | 67.2 | 136.8 | 0.026 | 0.16 | 0.12 | -100 | 118.4 | 45.8 | 0 | 0 | 0 | 92 | 118.6 | 4010 | 65.6 | 17.68 | 3054 | 1.54 | 722.8 | 3.042 | -4.4 | 8.26 | 0.030 | 120 | 46.0 | 146.2 | 7.14 | 5.44 | 3.04 |
| A | 5.380000 | 23.92667 | 0.2693333 | 66.6 | 138.4 | 0.090 | 0.24 | 0.04 | -100 | 119.6 | 45.6 | 0 | 0 | 0 | 116 | 120.2 | 4014 | 66.2 | 23.82 | 2948 | 1.52 | 738.8 | 2.992 | -4.4 | 8.32 | 0.024 | 120 | 46.0 | 146.6 | 7.16 | 5.44 | 3.02 |
Missing values
colSums(is.na(student_train))## Brand.Code Carb.Volume Fill.Ounces PC.Volume
## 0 10 38 39
## Carb.Pressure Carb.Temp PSC PSC.Fill
## 27 26 33 23
## PSC.CO2 Mnf.Flow Carb.Pressure1 Fill.Pressure
## 39 2 32 22
## Hyd.Pressure1 Hyd.Pressure2 Hyd.Pressure3 Hyd.Pressure4
## 11 15 15 30
## Filler.Level Filler.Speed Temperature Usage.cont
## 20 57 14 5
## Carb.Flow Density MFR Balling
## 2 1 212 1
## Pressure.Vacuum PH Oxygen.Filler Bowl.Setpoint
## 0 4 12 2
## Pressure.Setpoint Air.Pressurer Alch.Rel Carb.Rel
## 12 0 9 10
## Balling.Lvl
## 1Correlation Plot
# Select only numeric columns
numeric_data <- student_train %>% select(where(is.numeric))
# Calculate the correlation matrix
correlation_matrix <- cor(numeric_data, use = "pairwise.complete.obs")
# Create the correlation plot
corrplot(correlation_matrix, tl.col = "black", tl.cex = 0.6, order = 'AOE')
Distribution Visualization
mlt.train <- student_train # Use your actual dataframe name
mlt.train$ID <- rownames(mlt.train) # Assign row names to ID
mlt.train <- melt(mlt.train, id.vars = "ID") # Melt the data
# Convert the value column to numeric
mlt.train$value <- as.numeric(mlt.train$value)
# Create histograms of the predictors
ggplot(data = mlt.train, aes(x = value)) +
geom_histogram(binwidth = 6, fill = "skyblue", color = "black", alpha = 0.8) + # Adjust binwidth as needed
facet_wrap(~ variable, scales = "free") +
labs(title = "Distributions of Predictors", x = "Predictors", y = "Frequency") +
theme_minimal(base_size = 9) + # Use a minimal theme for better clarity
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank()) # Clean up grid lines
Build initial linear regression model and access the VIF
library(car)
library(caret)
# Setting up the model
model <- lm(PH ~ ., data = student_train)
summary(model)##
## Call:
## lm(formula = PH ~ ., data = student_train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.54899 -0.07379 0.00727 0.08502 0.44635
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.190e+01 1.275e+00 9.328 < 2e-16 ***
## Brand.CodeA -7.697e-02 3.371e-02 -2.284 0.022496 *
## Brand.CodeB 5.798e-02 1.549e-02 3.744 0.000186 ***
## Brand.CodeC -9.798e-02 1.672e-02 -5.862 5.31e-09 ***
## Brand.CodeD -2.011e-02 3.827e-02 -0.525 0.599363
## Carb.Volume -2.249e-01 1.138e-01 -1.976 0.048259 *
## Fill.Ounces -1.101e-01 3.551e-02 -3.100 0.001959 **
## PC.Volume 1.751e-02 6.417e-02 0.273 0.784990
## Carb.Pressure 7.195e-03 5.337e-03 1.348 0.177725
## Carb.Temp -5.106e-03 4.180e-03 -1.221 0.222073
## PSC -3.704e-02 6.208e-02 -0.597 0.550794
## PSC.Fill -1.856e-02 2.476e-02 -0.749 0.453717
## PSC.CO2 -1.158e-01 6.923e-02 -1.672 0.094683 .
## Mnf.Flow -6.998e-04 5.075e-05 -13.789 < 2e-16 ***
## Carb.Pressure1 6.039e-03 7.571e-04 7.976 2.46e-15 ***
## Fill.Pressure -3.697e-03 1.893e-03 -1.953 0.050927 .
## Hyd.Pressure1 1.355e-04 3.922e-04 0.345 0.729793
## Hyd.Pressure2 -1.720e-03 5.634e-04 -3.053 0.002298 **
## Hyd.Pressure3 3.569e-03 6.409e-04 5.569 2.89e-08 ***
## Hyd.Pressure4 1.962e-04 4.214e-04 0.466 0.641613
## Filler.Level -8.615e-04 8.986e-04 -0.959 0.337821
## Filler.Speed 1.672e-05 2.706e-05 0.618 0.536787
## Temperature -1.680e-02 3.191e-03 -5.264 1.55e-07 ***
## Usage.cont -7.156e-03 1.271e-03 -5.630 2.04e-08 ***
## Carb.Flow 1.166e-05 4.638e-06 2.514 0.011999 *
## Density -1.252e-01 3.010e-02 -4.161 3.30e-05 ***
## MFR -9.439e-05 1.460e-04 -0.647 0.518019
## Balling -1.944e-01 3.909e-02 -4.973 7.11e-07 ***
## Pressure.Vacuum -5.030e-02 1.004e-02 -5.010 5.91e-07 ***
## Oxygen.Filler -4.289e-01 8.473e-02 -5.062 4.52e-07 ***
## Bowl.Setpoint 2.779e-03 9.281e-04 2.994 0.002788 **
## Pressure.Setpoint -2.866e-03 2.536e-03 -1.130 0.258485
## Air.Pressurer -1.245e-03 2.528e-03 -0.492 0.622521
## Alch.Rel 6.719e-02 3.211e-02 2.092 0.036534 *
## Carb.Rel 1.492e-01 6.102e-02 2.444 0.014589 *
## Balling.Lvl 2.585e-01 4.525e-02 5.712 1.27e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1282 on 2093 degrees of freedom
## (442 observations deleted due to missingness)
## Multiple R-squared: 0.4488, Adjusted R-squared: 0.4396
## F-statistic: 48.7 on 35 and 2093 DF, p-value: < 2.2e-16We see that ‘Brand.Code’ is highly collinear
# Calculating VIF
vif_values <- vif(model)
vif_values## GVIF Df GVIF^(1/(2*Df))
## Brand.Code 161.462006 4 1.888030
## Carb.Volume 17.895899 1 4.230354
## Fill.Ounces 1.181213 1 1.086836
## PC.Volume 1.712473 1 1.308615
## Carb.Pressure 43.629727 1 6.605280
## Carb.Temp 35.744235 1 5.978648
## PSC 1.163257 1 1.078544
## PSC.Fill 1.112048 1 1.054537
## PSC.CO2 1.067962 1 1.033423
## Mnf.Flow 4.979607 1 2.231503
## Carb.Pressure1 1.467316 1 1.211328
## Fill.Pressure 3.741073 1 1.934185
## Hyd.Pressure1 3.000519 1 1.732201
## Hyd.Pressure2 10.635457 1 3.261205
## Hyd.Pressure3 12.964503 1 3.600625
## Hyd.Pressure4 2.686600 1 1.639085
## Filler.Level 25.385854 1 5.038438
## Filler.Speed 11.224377 1 3.350280
## Temperature 1.390864 1 1.179349
## Usage.cont 1.773788 1 1.331836
## Carb.Flow 2.256335 1 1.502110
## Density 16.438808 1 4.054480
## MFR 11.435430 1 3.381631
## Balling 168.721067 1 12.989267
## Pressure.Vacuum 4.289511 1 2.071113
## Oxygen.Filler 1.579977 1 1.256971
## Bowl.Setpoint 26.051364 1 5.104054
## Pressure.Setpoint 3.486682 1 1.867266
## Air.Pressurer 1.234829 1 1.111229
## Alch.Rel 33.466584 1 5.785031
## Carb.Rel 7.483881 1 2.735668
## Balling.Lvl 196.699873 1 14.024973We see that Brand B appears to have a different relationship than the other brands, Brand B has a R-squared of ~0.7 while all the other brands have a R-squared of ~0.3. We can replace all the brands with a binary variable of whether it is Brand B or not.
I’m also replacing all the missing values with zeros
student_train_0 <- student_train |> mutate(BCB = as.numeric(Brand.Code =='B')) |> select(-Brand.Code)
student_eval_0 <- student_eval |> mutate(BCB = as.numeric(Brand.Code =='B')) |> select(-Brand.Code)
student_train_0[is.na(student_train_0)] <- 0
student_eval_0[is.na(student_eval_0)] <- 0Next we check if any of the variables have a near zero variance and surprisingly only one variable is identified by default. I changed the parameters ‘freqCut’ and ‘uniqueCut’ but it required large changes to pick up other variables.
nearZeroVar(student_train_0, freqCut = 60/40, uniqueCut = 40, names = TRUE)## [1] "PC.Volume" "Fill.Pressure" "Hyd.Pressure1" "Hyd.Pressure2"
## [5] "Hyd.Pressure3" "Carb.Flow" "MFR" "Bowl.Setpoint"Just by removing the ‘Brand.Code’ variable we reduce a lot of the multicollinearity. Here I create a new linear model without ‘Brand.Code’ and check the VIF again.
model <- lm(PH ~ ., data = student_train_0)
summary(model)##
## Call:
## lm(formula = PH ~ ., data = student_train_0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.2484 -0.1000 0.0063 0.1082 4.3610
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.533e+00 8.238e-01 6.717 2.28e-11 ***
## Carb.Volume -1.142e-02 1.900e-02 -0.601 0.547971
## Fill.Ounces -4.544e-04 2.133e-03 -0.213 0.831266
## PC.Volume 2.736e-01 9.988e-02 2.740 0.006193 **
## Carb.Pressure -3.057e-04 8.905e-04 -0.343 0.731420
## Carb.Temp -2.178e-04 4.450e-04 -0.489 0.624539
## PSC -1.324e-01 1.270e-01 -1.042 0.297427
## PSC.Fill -1.249e-01 5.286e-02 -2.363 0.018202 *
## PSC.CO2 -7.328e-02 1.433e-01 -0.511 0.609141
## Mnf.Flow -8.741e-04 1.061e-04 -8.239 2.75e-16 ***
## Carb.Pressure1 2.181e-03 4.597e-04 4.744 2.21e-06 ***
## Fill.Pressure 1.035e-02 1.422e-03 7.283 4.35e-13 ***
## Hyd.Pressure1 -1.115e-03 8.292e-04 -1.345 0.178899
## Hyd.Pressure2 3.253e-03 1.220e-03 2.666 0.007717 **
## Hyd.Pressure3 -1.113e-03 1.330e-03 -0.837 0.402719
## Hyd.Pressure4 2.497e-03 4.144e-04 6.025 1.94e-09 ***
## Filler.Level 5.257e-03 6.719e-04 7.825 7.39e-15 ***
## Filler.Speed -8.270e-06 2.691e-05 -0.307 0.758608
## Temperature 8.146e-03 1.282e-03 6.354 2.48e-10 ***
## Usage.cont -4.710e-03 2.412e-03 -1.953 0.050988 .
## Carb.Flow 3.148e-05 8.443e-06 3.729 0.000197 ***
## Density -9.107e-02 6.321e-02 -1.441 0.149777
## MFR -1.414e-04 1.217e-04 -1.161 0.245598
## Balling 5.935e-01 4.942e-02 12.010 < 2e-16 ***
## Pressure.Vacuum 1.073e-01 1.706e-02 6.288 3.76e-10 ***
## Oxygen.Filler -1.589e+00 1.576e-01 -10.085 < 2e-16 ***
## Bowl.Setpoint -2.398e-03 8.268e-04 -2.901 0.003753 **
## Pressure.Setpoint -1.634e-03 1.752e-03 -0.933 0.351111
## Air.Pressurer 2.809e-03 5.417e-03 0.519 0.604140
## Alch.Rel 1.694e-01 1.811e-02 9.353 < 2e-16 ***
## Carb.Rel 9.053e-02 2.165e-02 4.181 3.01e-05 ***
## Balling.Lvl -5.907e-01 4.896e-02 -12.065 < 2e-16 ***
## BCB 1.079e-01 1.798e-02 5.999 2.27e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.307 on 2538 degrees of freedom
## Multiple R-squared: 0.3502, Adjusted R-squared: 0.342
## F-statistic: 42.75 on 32 and 2538 DF, p-value: < 2.2e-16# Calculating VIF
vif_values <- vif(model)
vif_values## Carb.Volume Fill.Ounces PC.Volume Carb.Pressure
## 1.212068 1.039624 1.299425 1.313630
## Carb.Temp PSC PSC.Fill PSC.CO2
## 1.163947 1.094245 1.073751 1.048554
## Mnf.Flow Carb.Pressure1 Fill.Pressure Hyd.Pressure1
## 4.379200 1.193121 1.626473 2.899194
## Hyd.Pressure2 Hyd.Pressure3 Hyd.Pressure4 Filler.Level
## 10.943147 12.358010 1.298333 4.145435
## Filler.Speed Temperature Usage.cont Carb.Flow
## 17.298895 1.142105 1.540381 2.249256
## Density MFR Balling Pressure.Vacuum
## 15.585262 17.190024 57.847514 2.578797
## Oxygen.Filler Bowl.Setpoint Pressure.Setpoint Air.Pressurer
## 1.473160 4.536445 1.228467 1.175515
## Alch.Rel Carb.Rel Balling.Lvl BCB
## 3.761892 1.676540 49.610553 2.203483There are still a couple variables to be addressed but first we are going to a step-wise feature reduction.
stats::step(model)## Start: AIC=-6040.25
## PH ~ Carb.Volume + Fill.Ounces + PC.Volume + Carb.Pressure +
## Carb.Temp + PSC + PSC.Fill + PSC.CO2 + Mnf.Flow + Carb.Pressure1 +
## Fill.Pressure + Hyd.Pressure1 + Hyd.Pressure2 + Hyd.Pressure3 +
## Hyd.Pressure4 + Filler.Level + Filler.Speed + Temperature +
## Usage.cont + Carb.Flow + Density + MFR + Balling + Pressure.Vacuum +
## Oxygen.Filler + Bowl.Setpoint + Pressure.Setpoint + Air.Pressurer +
## Alch.Rel + Carb.Rel + Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - Fill.Ounces 1 0.0043 239.13 -6042.2
## - Filler.Speed 1 0.0089 239.14 -6042.2
## - Carb.Pressure 1 0.0111 239.14 -6042.1
## - Carb.Temp 1 0.0226 239.15 -6042.0
## - PSC.CO2 1 0.0246 239.15 -6042.0
## - Air.Pressurer 1 0.0253 239.15 -6042.0
## - Carb.Volume 1 0.0340 239.16 -6041.9
## - Hyd.Pressure3 1 0.0660 239.19 -6041.5
## - Pressure.Setpoint 1 0.0819 239.21 -6041.4
## - PSC 1 0.1023 239.23 -6041.1
## - MFR 1 0.1271 239.26 -6040.9
## - Hyd.Pressure1 1 0.1703 239.30 -6040.4
## <none> 239.13 -6040.2
## - Density 1 0.1956 239.32 -6040.1
## - Usage.cont 1 0.3592 239.49 -6038.4
## - PSC.Fill 1 0.5261 239.66 -6036.6
## - Hyd.Pressure2 1 0.6698 239.80 -6035.1
## - PC.Volume 1 0.7072 239.84 -6034.7
## - Bowl.Setpoint 1 0.7929 239.92 -6033.7
## - Carb.Flow 1 1.3100 240.44 -6028.2
## - Carb.Rel 1 1.6466 240.78 -6024.6
## - Carb.Pressure1 1 2.1207 241.25 -6019.5
## - BCB 1 3.3904 242.52 -6006.1
## - Hyd.Pressure4 1 3.4202 242.55 -6005.7
## - Pressure.Vacuum 1 3.7259 242.85 -6002.5
## - Temperature 1 3.8040 242.93 -6001.7
## - Fill.Pressure 1 4.9969 244.13 -5989.1
## - Filler.Level 1 5.7690 244.90 -5981.0
## - Mnf.Flow 1 6.3959 245.53 -5974.4
## - Alch.Rel 1 8.2425 247.37 -5955.1
## - Oxygen.Filler 1 9.5821 248.71 -5941.2
## - Balling 1 13.5903 252.72 -5900.1
## - Balling.Lvl 1 13.7153 252.84 -5898.9
##
## Step: AIC=-6042.2
## PH ~ Carb.Volume + PC.Volume + Carb.Pressure + Carb.Temp + PSC +
## PSC.Fill + PSC.CO2 + Mnf.Flow + Carb.Pressure1 + Fill.Pressure +
## Hyd.Pressure1 + Hyd.Pressure2 + Hyd.Pressure3 + Hyd.Pressure4 +
## Filler.Level + Filler.Speed + Temperature + Usage.cont +
## Carb.Flow + Density + MFR + Balling + Pressure.Vacuum + Oxygen.Filler +
## Bowl.Setpoint + Pressure.Setpoint + Air.Pressurer + Alch.Rel +
## Carb.Rel + Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - Filler.Speed 1 0.0090 239.14 -6044.1
## - Carb.Pressure 1 0.0112 239.14 -6044.1
## - Carb.Temp 1 0.0228 239.16 -6044.0
## - PSC.CO2 1 0.0244 239.16 -6043.9
## - Air.Pressurer 1 0.0251 239.16 -6043.9
## - Carb.Volume 1 0.0365 239.17 -6043.8
## - Hyd.Pressure3 1 0.0657 239.20 -6043.5
## - Pressure.Setpoint 1 0.0817 239.22 -6043.3
## - PSC 1 0.1024 239.24 -6043.1
## - MFR 1 0.1273 239.26 -6042.8
## - Hyd.Pressure1 1 0.1692 239.30 -6042.4
## <none> 239.13 -6042.2
## - Density 1 0.1945 239.33 -6042.1
## - Usage.cont 1 0.3589 239.49 -6040.3
## - PSC.Fill 1 0.5321 239.66 -6038.5
## - Hyd.Pressure2 1 0.6679 239.80 -6037.0
## - PC.Volume 1 0.7029 239.84 -6036.7
## - Bowl.Setpoint 1 0.7892 239.92 -6035.7
## - Carb.Flow 1 1.3194 240.45 -6030.1
## - Carb.Rel 1 1.6486 240.78 -6026.5
## - Carb.Pressure1 1 2.1235 241.26 -6021.5
## - BCB 1 3.3884 242.52 -6008.0
## - Hyd.Pressure4 1 3.4576 242.59 -6007.3
## - Pressure.Vacuum 1 3.7305 242.86 -6004.4
## - Temperature 1 3.8034 242.94 -6003.6
## - Fill.Pressure 1 4.9942 244.13 -5991.1
## - Filler.Level 1 5.7700 244.90 -5982.9
## - Mnf.Flow 1 6.4031 245.54 -5976.3
## - Alch.Rel 1 8.2531 247.39 -5957.0
## - Oxygen.Filler 1 9.5835 248.72 -5943.2
## - Balling 1 13.6369 252.77 -5901.6
## - Balling.Lvl 1 13.7832 252.92 -5900.1
##
## Step: AIC=-6044.11
## PH ~ Carb.Volume + PC.Volume + Carb.Pressure + Carb.Temp + PSC +
## PSC.Fill + PSC.CO2 + Mnf.Flow + Carb.Pressure1 + Fill.Pressure +
## Hyd.Pressure1 + Hyd.Pressure2 + Hyd.Pressure3 + Hyd.Pressure4 +
## Filler.Level + Temperature + Usage.cont + Carb.Flow + Density +
## MFR + Balling + Pressure.Vacuum + Oxygen.Filler + Bowl.Setpoint +
## Pressure.Setpoint + Air.Pressurer + Alch.Rel + Carb.Rel +
## Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - Carb.Pressure 1 0.0105 239.15 -6046.0
## - Carb.Temp 1 0.0232 239.16 -6045.9
## - PSC.CO2 1 0.0251 239.17 -6045.8
## - Air.Pressurer 1 0.0260 239.17 -6045.8
## - Carb.Volume 1 0.0386 239.18 -6045.7
## - Hyd.Pressure3 1 0.0660 239.21 -6045.4
## - Pressure.Setpoint 1 0.0828 239.22 -6045.2
## - PSC 1 0.1017 239.24 -6045.0
## - Hyd.Pressure1 1 0.1654 239.31 -6044.3
## <none> 239.14 -6044.1
## - Density 1 0.1920 239.33 -6044.0
## - Usage.cont 1 0.3628 239.50 -6042.2
## - PSC.Fill 1 0.5304 239.67 -6040.4
## - Hyd.Pressure2 1 0.6602 239.80 -6039.0
## - PC.Volume 1 0.7104 239.85 -6038.5
## - Bowl.Setpoint 1 0.7804 239.92 -6037.7
## - Carb.Flow 1 1.3130 240.46 -6032.0
## - MFR 1 1.4836 240.63 -6030.2
## - Carb.Rel 1 1.6492 240.79 -6028.4
## - Carb.Pressure1 1 2.1176 241.26 -6023.4
## - BCB 1 3.3888 242.53 -6009.9
## - Hyd.Pressure4 1 3.5250 242.67 -6008.5
## - Pressure.Vacuum 1 3.7340 242.88 -6006.3
## - Temperature 1 3.8012 242.94 -6005.6
## - Fill.Pressure 1 4.9861 244.13 -5993.1
## - Filler.Level 1 5.8536 245.00 -5983.9
## - Mnf.Flow 1 6.4037 245.55 -5978.2
## - Alch.Rel 1 8.2444 247.39 -5959.0
## - Oxygen.Filler 1 9.6358 248.78 -5944.5
## - Balling 1 13.6513 252.79 -5903.4
## - Balling.Lvl 1 13.7995 252.94 -5901.9
##
## Step: AIC=-6045.99
## PH ~ Carb.Volume + PC.Volume + Carb.Temp + PSC + PSC.Fill + PSC.CO2 +
## Mnf.Flow + Carb.Pressure1 + Fill.Pressure + Hyd.Pressure1 +
## Hyd.Pressure2 + Hyd.Pressure3 + Hyd.Pressure4 + Filler.Level +
## Temperature + Usage.cont + Carb.Flow + Density + MFR + Balling +
## Pressure.Vacuum + Oxygen.Filler + Bowl.Setpoint + Pressure.Setpoint +
## Air.Pressurer + Alch.Rel + Carb.Rel + Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - Air.Pressurer 1 0.0258 239.18 -6047.7
## - PSC.CO2 1 0.0259 239.18 -6047.7
## - Carb.Temp 1 0.0400 239.19 -6047.6
## - Carb.Volume 1 0.0566 239.21 -6047.4
## - Hyd.Pressure3 1 0.0673 239.22 -6047.3
## - Pressure.Setpoint 1 0.0827 239.24 -6047.1
## - PSC 1 0.0987 239.25 -6046.9
## - Hyd.Pressure1 1 0.1646 239.32 -6046.2
## <none> 239.15 -6046.0
## - Density 1 0.1906 239.34 -6045.9
## - Usage.cont 1 0.3647 239.52 -6044.1
## - PSC.Fill 1 0.5276 239.68 -6042.3
## - Hyd.Pressure2 1 0.6642 239.82 -6040.9
## - PC.Volume 1 0.7069 239.86 -6040.4
## - Bowl.Setpoint 1 0.7797 239.93 -6039.6
## - Carb.Flow 1 1.3060 240.46 -6034.0
## - MFR 1 1.4807 240.63 -6032.1
## - Carb.Rel 1 1.6508 240.80 -6030.3
## - Carb.Pressure1 1 2.1170 241.27 -6025.3
## - BCB 1 3.3825 242.53 -6011.9
## - Hyd.Pressure4 1 3.5220 242.68 -6010.4
## - Pressure.Vacuum 1 3.7394 242.89 -6008.1
## - Temperature 1 3.7970 242.95 -6007.5
## - Fill.Pressure 1 4.9947 244.15 -5994.9
## - Filler.Level 1 5.8503 245.00 -5985.9
## - Mnf.Flow 1 6.4001 245.55 -5980.1
## - Alch.Rel 1 8.2436 247.40 -5960.9
## - Oxygen.Filler 1 9.6312 248.78 -5946.5
## - Balling 1 13.6427 252.79 -5905.4
## - Balling.Lvl 1 13.8074 252.96 -5903.7
##
## Step: AIC=-6047.72
## PH ~ Carb.Volume + PC.Volume + Carb.Temp + PSC + PSC.Fill + PSC.CO2 +
## Mnf.Flow + Carb.Pressure1 + Fill.Pressure + Hyd.Pressure1 +
## Hyd.Pressure2 + Hyd.Pressure3 + Hyd.Pressure4 + Filler.Level +
## Temperature + Usage.cont + Carb.Flow + Density + MFR + Balling +
## Pressure.Vacuum + Oxygen.Filler + Bowl.Setpoint + Pressure.Setpoint +
## Alch.Rel + Carb.Rel + Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - PSC.CO2 1 0.0262 239.21 -6049.4
## - Carb.Temp 1 0.0394 239.22 -6049.3
## - Hyd.Pressure3 1 0.0544 239.23 -6049.1
## - Carb.Volume 1 0.0557 239.23 -6049.1
## - Pressure.Setpoint 1 0.0826 239.26 -6048.8
## - PSC 1 0.0963 239.28 -6048.7
## - Hyd.Pressure1 1 0.1770 239.35 -6047.8
## <none> 239.18 -6047.7
## - Density 1 0.1877 239.37 -6047.7
## - Usage.cont 1 0.3833 239.56 -6045.6
## - PSC.Fill 1 0.5341 239.71 -6044.0
## - Hyd.Pressure2 1 0.6393 239.82 -6042.9
## - PC.Volume 1 0.7118 239.89 -6042.1
## - Bowl.Setpoint 1 0.8129 239.99 -6041.0
## - Carb.Flow 1 1.3128 240.49 -6035.6
## - MFR 1 1.4860 240.66 -6033.8
## - Carb.Rel 1 1.6417 240.82 -6032.1
## - Carb.Pressure1 1 2.1588 241.34 -6026.6
## - BCB 1 3.4128 242.59 -6013.3
## - Hyd.Pressure4 1 3.5368 242.72 -6012.0
## - Temperature 1 3.8036 242.98 -6009.2
## - Pressure.Vacuum 1 3.9212 243.10 -6007.9
## - Fill.Pressure 1 4.9848 244.16 -5996.7
## - Filler.Level 1 5.8677 245.05 -5987.4
## - Mnf.Flow 1 6.4078 245.59 -5981.7
## - Alch.Rel 1 8.2751 247.45 -5962.3
## - Oxygen.Filler 1 9.6085 248.79 -5948.5
## - Balling 1 13.6446 252.82 -5907.1
## - Balling.Lvl 1 13.8371 253.01 -5905.1
##
## Step: AIC=-6049.43
## PH ~ Carb.Volume + PC.Volume + Carb.Temp + PSC + PSC.Fill + Mnf.Flow +
## Carb.Pressure1 + Fill.Pressure + Hyd.Pressure1 + Hyd.Pressure2 +
## Hyd.Pressure3 + Hyd.Pressure4 + Filler.Level + Temperature +
## Usage.cont + Carb.Flow + Density + MFR + Balling + Pressure.Vacuum +
## Oxygen.Filler + Bowl.Setpoint + Pressure.Setpoint + Alch.Rel +
## Carb.Rel + Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - Carb.Temp 1 0.0404 239.25 -6051.0
## - Hyd.Pressure3 1 0.0574 239.26 -6050.8
## - Carb.Volume 1 0.0586 239.26 -6050.8
## - Pressure.Setpoint 1 0.0836 239.29 -6050.5
## - PSC 1 0.0977 239.30 -6050.4
## - Hyd.Pressure1 1 0.1750 239.38 -6049.6
## <none> 239.21 -6049.4
## - Density 1 0.1895 239.39 -6049.4
## - Usage.cont 1 0.3867 239.59 -6047.3
## - PSC.Fill 1 0.5879 239.79 -6045.1
## - Hyd.Pressure2 1 0.6476 239.85 -6044.5
## - PC.Volume 1 0.7178 239.92 -6043.7
## - Bowl.Setpoint 1 0.8168 240.02 -6042.7
## - Carb.Flow 1 1.3073 240.51 -6037.4
## - MFR 1 1.4803 240.69 -6035.6
## - Carb.Rel 1 1.6575 240.86 -6033.7
## - Carb.Pressure1 1 2.1759 241.38 -6028.2
## - BCB 1 3.4276 242.63 -6014.9
## - Hyd.Pressure4 1 3.5224 242.73 -6013.9
## - Temperature 1 3.7879 242.99 -6011.0
## - Pressure.Vacuum 1 3.9129 243.12 -6009.7
## - Fill.Pressure 1 4.9653 244.17 -5998.6
## - Filler.Level 1 5.8774 245.08 -5989.0
## - Mnf.Flow 1 6.4152 245.62 -5983.4
## - Alch.Rel 1 8.2742 247.48 -5964.0
## - Oxygen.Filler 1 9.6002 248.81 -5950.3
## - Balling 1 13.6483 252.85 -5908.8
## - Balling.Lvl 1 13.8254 253.03 -5907.0
##
## Step: AIC=-6051
## PH ~ Carb.Volume + PC.Volume + PSC + PSC.Fill + Mnf.Flow + Carb.Pressure1 +
## Fill.Pressure + Hyd.Pressure1 + Hyd.Pressure2 + Hyd.Pressure3 +
## Hyd.Pressure4 + Filler.Level + Temperature + Usage.cont +
## Carb.Flow + Density + MFR + Balling + Pressure.Vacuum + Oxygen.Filler +
## Bowl.Setpoint + Pressure.Setpoint + Alch.Rel + Carb.Rel +
## Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - Hyd.Pressure3 1 0.0616 239.31 -6052.3
## - Carb.Volume 1 0.0709 239.32 -6052.2
## - Pressure.Setpoint 1 0.0812 239.33 -6052.1
## - PSC 1 0.0933 239.34 -6052.0
## - Hyd.Pressure1 1 0.1754 239.42 -6051.1
## <none> 239.25 -6051.0
## - Density 1 0.1933 239.44 -6050.9
## - Usage.cont 1 0.3859 239.63 -6048.9
## - PSC.Fill 1 0.5895 239.83 -6046.7
## - Hyd.Pressure2 1 0.6615 239.91 -6045.9
## - PC.Volume 1 0.7125 239.96 -6045.4
## - Bowl.Setpoint 1 0.8196 240.06 -6044.2
## - Carb.Flow 1 1.3190 240.56 -6038.9
## - MFR 1 1.4957 240.74 -6037.0
## - Carb.Rel 1 1.6667 240.91 -6035.2
## - Carb.Pressure1 1 2.1805 241.43 -6029.7
## - BCB 1 3.4263 242.67 -6016.4
## - Hyd.Pressure4 1 3.5188 242.76 -6015.5
## - Temperature 1 3.7572 243.00 -6012.9
## - Pressure.Vacuum 1 3.9054 243.15 -6011.4
## - Fill.Pressure 1 4.9599 244.21 -6000.2
## - Filler.Level 1 5.9140 245.16 -5990.2
## - Mnf.Flow 1 6.3855 245.63 -5985.3
## - Alch.Rel 1 8.2780 247.52 -5965.5
## - Oxygen.Filler 1 9.5887 248.83 -5952.0
## - Balling 1 13.6641 252.91 -5910.2
## - Balling.Lvl 1 13.8277 253.07 -5908.5
##
## Step: AIC=-6052.34
## PH ~ Carb.Volume + PC.Volume + PSC + PSC.Fill + Mnf.Flow + Carb.Pressure1 +
## Fill.Pressure + Hyd.Pressure1 + Hyd.Pressure2 + Hyd.Pressure4 +
## Filler.Level + Temperature + Usage.cont + Carb.Flow + Density +
## MFR + Balling + Pressure.Vacuum + Oxygen.Filler + Bowl.Setpoint +
## Pressure.Setpoint + Alch.Rel + Carb.Rel + Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - Carb.Volume 1 0.0662 239.37 -6053.6
## - PSC 1 0.0914 239.40 -6053.4
## - Pressure.Setpoint 1 0.1089 239.41 -6053.2
## - Density 1 0.1518 239.46 -6052.7
## - Hyd.Pressure1 1 0.1862 239.49 -6052.3
## <none> 239.31 -6052.3
## - Usage.cont 1 0.3630 239.67 -6050.4
## - PSC.Fill 1 0.5873 239.89 -6048.0
## - PC.Volume 1 0.7005 240.01 -6046.8
## - Bowl.Setpoint 1 0.8013 240.11 -6045.7
## - Hyd.Pressure2 1 0.8523 240.16 -6045.2
## - Carb.Flow 1 1.2797 240.59 -6040.6
## - MFR 1 1.5349 240.84 -6037.9
## - Carb.Rel 1 1.6441 240.95 -6036.7
## - Carb.Pressure1 1 2.1750 241.48 -6031.1
## - BCB 1 3.4661 242.77 -6017.4
## - Hyd.Pressure4 1 3.5049 242.81 -6017.0
## - Temperature 1 3.7488 243.06 -6014.4
## - Pressure.Vacuum 1 4.0215 243.33 -6011.5
## - Fill.Pressure 1 4.8986 244.21 -6002.2
## - Filler.Level 1 6.0363 245.34 -5990.3
## - Mnf.Flow 1 7.8551 247.16 -5971.3
## - Alch.Rel 1 8.3168 247.62 -5966.5
## - Oxygen.Filler 1 9.6667 248.97 -5952.5
## - Balling 1 13.7614 253.07 -5910.6
## - Balling.Lvl 1 13.7782 253.09 -5910.4
##
## Step: AIC=-6053.63
## PH ~ PC.Volume + PSC + PSC.Fill + Mnf.Flow + Carb.Pressure1 +
## Fill.Pressure + Hyd.Pressure1 + Hyd.Pressure2 + Hyd.Pressure4 +
## Filler.Level + Temperature + Usage.cont + Carb.Flow + Density +
## MFR + Balling + Pressure.Vacuum + Oxygen.Filler + Bowl.Setpoint +
## Pressure.Setpoint + Alch.Rel + Carb.Rel + Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - PSC 1 0.0926 239.47 -6054.6
## - Pressure.Setpoint 1 0.1051 239.48 -6054.5
## - Density 1 0.1512 239.52 -6054.0
## - Hyd.Pressure1 1 0.1804 239.55 -6053.7
## <none> 239.37 -6053.6
## - Usage.cont 1 0.3616 239.73 -6051.7
## - PSC.Fill 1 0.5910 239.96 -6049.3
## - PC.Volume 1 0.6764 240.05 -6048.4
## - Bowl.Setpoint 1 0.8071 240.18 -6047.0
## - Hyd.Pressure2 1 0.8532 240.23 -6046.5
## - Carb.Flow 1 1.2787 240.65 -6041.9
## - MFR 1 1.5238 240.90 -6039.3
## - Carb.Rel 1 1.6575 241.03 -6037.9
## - Carb.Pressure1 1 2.1786 241.55 -6032.3
## - BCB 1 3.4490 242.82 -6018.8
## - Hyd.Pressure4 1 3.5552 242.93 -6017.7
## - Temperature 1 3.6982 243.07 -6016.2
## - Pressure.Vacuum 1 4.0239 243.40 -6012.8
## - Fill.Pressure 1 4.8527 244.22 -6004.0
## - Filler.Level 1 6.0737 245.45 -5991.2
## - Mnf.Flow 1 7.8836 247.26 -5972.3
## - Alch.Rel 1 8.3403 247.71 -5967.6
## - Oxygen.Filler 1 9.6660 249.04 -5953.8
## - Balling 1 13.7253 253.10 -5912.3
## - Balling.Lvl 1 13.8191 253.19 -5911.3
##
## Step: AIC=-6054.63
## PH ~ PC.Volume + PSC.Fill + Mnf.Flow + Carb.Pressure1 + Fill.Pressure +
## Hyd.Pressure1 + Hyd.Pressure2 + Hyd.Pressure4 + Filler.Level +
## Temperature + Usage.cont + Carb.Flow + Density + MFR + Balling +
## Pressure.Vacuum + Oxygen.Filler + Bowl.Setpoint + Pressure.Setpoint +
## Alch.Rel + Carb.Rel + Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - Pressure.Setpoint 1 0.1046 239.57 -6055.5
## - Density 1 0.1514 239.62 -6055.0
## - Hyd.Pressure1 1 0.1769 239.64 -6054.7
## <none> 239.47 -6054.6
## - Usage.cont 1 0.3757 239.84 -6052.6
## - PC.Volume 1 0.6101 240.07 -6050.1
## - PSC.Fill 1 0.6906 240.16 -6049.2
## - Bowl.Setpoint 1 0.8034 240.27 -6048.0
## - Hyd.Pressure2 1 0.8756 240.34 -6047.2
## - Carb.Flow 1 1.2928 240.76 -6042.8
## - MFR 1 1.5506 241.02 -6040.0
## - Carb.Rel 1 1.6425 241.11 -6039.1
## - Carb.Pressure1 1 2.1935 241.66 -6033.2
## - BCB 1 3.4631 242.93 -6019.7
## - Hyd.Pressure4 1 3.5462 243.01 -6018.8
## - Temperature 1 3.6758 243.14 -6017.5
## - Pressure.Vacuum 1 3.9588 243.42 -6014.5
## - Fill.Pressure 1 4.8292 244.29 -6005.3
## - Filler.Level 1 6.0535 245.52 -5992.4
## - Mnf.Flow 1 8.1194 247.59 -5970.9
## - Alch.Rel 1 8.3169 247.78 -5968.9
## - Oxygen.Filler 1 9.6845 249.15 -5954.7
## - Balling 1 13.7030 253.17 -5913.6
## - Balling.Lvl 1 13.7754 253.24 -5912.8
##
## Step: AIC=-6055.51
## PH ~ PC.Volume + PSC.Fill + Mnf.Flow + Carb.Pressure1 + Fill.Pressure +
## Hyd.Pressure1 + Hyd.Pressure2 + Hyd.Pressure4 + Filler.Level +
## Temperature + Usage.cont + Carb.Flow + Density + MFR + Balling +
## Pressure.Vacuum + Oxygen.Filler + Bowl.Setpoint + Alch.Rel +
## Carb.Rel + Balling.Lvl + BCB
##
## Df Sum of Sq RSS AIC
## - Density 1 0.1384 239.71 -6056.0
## - Hyd.Pressure1 1 0.1767 239.75 -6055.6
## <none> 239.57 -6055.5
## - Usage.cont 1 0.3808 239.95 -6053.4
## - PC.Volume 1 0.5934 240.16 -6051.1
## - PSC.Fill 1 0.6894 240.26 -6050.1
## - Bowl.Setpoint 1 0.7908 240.36 -6049.0
## - Hyd.Pressure2 1 0.8833 240.45 -6048.0
## - Carb.Flow 1 1.3275 240.90 -6043.3
## - MFR 1 1.5504 241.12 -6040.9
## - Carb.Rel 1 1.6409 241.21 -6040.0
## - Carb.Pressure1 1 2.2268 241.80 -6033.7
## - BCB 1 3.4063 242.98 -6021.2
## - Hyd.Pressure4 1 3.6050 243.18 -6019.1
## - Temperature 1 3.7213 243.29 -6017.9
## - Pressure.Vacuum 1 3.9945 243.56 -6015.0
## - Fill.Pressure 1 4.7757 244.35 -6006.8
## - Filler.Level 1 6.3022 245.87 -5990.8
## - Mnf.Flow 1 8.1603 247.73 -5971.4
## - Alch.Rel 1 8.3671 247.94 -5969.2
## - Oxygen.Filler 1 9.7054 249.28 -5955.4
## - Balling 1 13.7275 253.30 -5914.3
## - Balling.Lvl 1 13.8742 253.44 -5912.8
##
## Step: AIC=-6056.02
## PH ~ PC.Volume + PSC.Fill + Mnf.Flow + Carb.Pressure1 + Fill.Pressure +
## Hyd.Pressure1 + Hyd.Pressure2 + Hyd.Pressure4 + Filler.Level +
## Temperature + Usage.cont + Carb.Flow + MFR + Balling + Pressure.Vacuum +
## Oxygen.Filler + Bowl.Setpoint + Alch.Rel + Carb.Rel + Balling.Lvl +
## BCB
##
## Df Sum of Sq RSS AIC
## - Hyd.Pressure1 1 0.1657 239.87 -6056.2
## <none> 239.71 -6056.0
## - Usage.cont 1 0.3499 240.06 -6054.3
## - PC.Volume 1 0.5919 240.30 -6051.7
## - PSC.Fill 1 0.6804 240.39 -6050.7
## - Bowl.Setpoint 1 0.7360 240.44 -6050.1
## - Hyd.Pressure2 1 0.8224 240.53 -6049.2
## - Carb.Flow 1 1.2086 240.92 -6045.1
## - MFR 1 1.4817 241.19 -6042.2
## - Carb.Rel 1 1.5681 241.28 -6041.3
## - Carb.Pressure1 1 2.2355 241.94 -6034.2
## - BCB 1 3.3972 243.10 -6021.8
## - Hyd.Pressure4 1 3.5846 243.29 -6019.9
## - Temperature 1 3.6888 243.40 -6018.8
## - Pressure.Vacuum 1 3.8839 243.59 -6016.7
## - Fill.Pressure 1 4.8494 244.56 -6006.5
## - Filler.Level 1 6.3042 246.01 -5991.3
## - Mnf.Flow 1 8.0221 247.73 -5973.4
## - Alch.Rel 1 8.3983 248.11 -5969.5
## - Oxygen.Filler 1 9.7532 249.46 -5955.5
## - Balling.Lvl 1 14.1438 253.85 -5910.6
## - Balling 1 15.4278 255.14 -5897.7
##
## Step: AIC=-6056.25
## PH ~ PC.Volume + PSC.Fill + Mnf.Flow + Carb.Pressure1 + Fill.Pressure +
## Hyd.Pressure2 + Hyd.Pressure4 + Filler.Level + Temperature +
## Usage.cont + Carb.Flow + MFR + Balling + Pressure.Vacuum +
## Oxygen.Filler + Bowl.Setpoint + Alch.Rel + Carb.Rel + Balling.Lvl +
## BCB
##
## Df Sum of Sq RSS AIC
## <none> 239.87 -6056.2
## - Usage.cont 1 0.3247 240.20 -6054.8
## - PC.Volume 1 0.5030 240.38 -6052.9
## - PSC.Fill 1 0.6857 240.56 -6050.9
## - Hyd.Pressure2 1 0.7736 240.65 -6050.0
## - Bowl.Setpoint 1 0.8663 240.74 -6049.0
## - Carb.Flow 1 1.1455 241.02 -6046.0
## - MFR 1 1.3691 241.24 -6043.6
## - Carb.Rel 1 1.5586 241.43 -6041.6
## - Carb.Pressure1 1 2.4900 242.36 -6031.7
## - BCB 1 3.4378 243.31 -6021.7
## - Hyd.Pressure4 1 3.5512 243.43 -6020.5
## - Temperature 1 3.6501 243.52 -6019.4
## - Pressure.Vacuum 1 3.7374 243.61 -6018.5
## - Fill.Pressure 1 4.9162 244.79 -6006.1
## - Filler.Level 1 6.2090 246.08 -5992.5
## - Mnf.Flow 1 8.1206 248.00 -5972.7
## - Alch.Rel 1 8.4781 248.35 -5968.9
## - Oxygen.Filler 1 9.7274 249.60 -5956.0
## - Balling.Lvl 1 14.2512 254.12 -5909.9
## - Balling 1 15.5533 255.43 -5896.7##
## Call:
## lm(formula = PH ~ PC.Volume + PSC.Fill + Mnf.Flow + Carb.Pressure1 +
## Fill.Pressure + Hyd.Pressure2 + Hyd.Pressure4 + Filler.Level +
## Temperature + Usage.cont + Carb.Flow + MFR + Balling + Pressure.Vacuum +
## Oxygen.Filler + Bowl.Setpoint + Alch.Rel + Carb.Rel + Balling.Lvl +
## BCB, data = student_train_0)
##
## Coefficients:
## (Intercept) PC.Volume PSC.Fill Mnf.Flow
## 5.6966783 0.2219495 -0.1385031 -0.0009060
## Carb.Pressure1 Fill.Pressure Hyd.Pressure2 Hyd.Pressure4
## 0.0023250 0.0098435 0.0016407 0.0025172
## Filler.Level Temperature Usage.cont Carb.Flow
## 0.0053094 0.0079330 -0.0044215 0.0000285
## MFR Balling Pressure.Vacuum Oxygen.Filler
## -0.0001667 0.5619052 0.1033532 -1.5930429
## Bowl.Setpoint Alch.Rel Carb.Rel Balling.Lvl
## -0.0024400 0.1713421 0.0875079 -0.5968109
## BCB
## 0.1081677We reduce our predictors to just those remaining after the feature reduction.
student_train_1 <- student_train_0 |> select(PH, PC.Volume , PSC.Fill , Mnf.Flow , Carb.Pressure1 ,
Fill.Pressure , Hyd.Pressure2 , Hyd.Pressure4 , Filler.Level ,
Temperature , Usage.cont , Carb.Flow , MFR , Balling ,
Pressure.Vacuum , Oxygen.Filler , Bowl.Setpoint , Alch.Rel ,
Carb.Rel , Balling.Lvl , BCB)
student_eval_1 <- student_eval_0 |> select(PH, PC.Volume , PSC.Fill , Mnf.Flow , Carb.Pressure1 ,
Fill.Pressure , Hyd.Pressure2 , Hyd.Pressure4 , Filler.Level ,
Temperature , Usage.cont , Carb.Flow , MFR , Balling ,
Pressure.Vacuum , Oxygen.Filler , Bowl.Setpoint , Alch.Rel ,
Carb.Rel , Balling.Lvl , BCB)
model <- lm(PH ~ ., data = student_train_1)
summary(model)##
## Call:
## lm(formula = PH ~ ., data = student_train_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.2646 -0.1012 0.0052 0.1088 4.3654
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.697e+00 1.843e-01 30.908 < 2e-16 ***
## PC.Volume 2.219e-01 9.598e-02 2.312 0.020836 *
## PSC.Fill -1.385e-01 5.130e-02 -2.700 0.006983 **
## Mnf.Flow -9.060e-04 9.751e-05 -9.291 < 2e-16 ***
## Carb.Pressure1 2.325e-03 4.519e-04 5.145 2.88e-07 ***
## Fill.Pressure 9.843e-03 1.362e-03 7.229 6.39e-13 ***
## Hyd.Pressure2 1.641e-03 5.721e-04 2.868 0.004168 **
## Hyd.Pressure4 2.517e-03 4.097e-04 6.144 9.30e-10 ***
## Filler.Level 5.309e-03 6.535e-04 8.124 6.93e-16 ***
## Temperature 7.933e-03 1.274e-03 6.229 5.47e-10 ***
## Usage.cont -4.422e-03 2.380e-03 -1.858 0.063293 .
## Carb.Flow 2.850e-05 8.167e-06 3.490 0.000492 ***
## MFR -1.667e-04 4.368e-05 -3.815 0.000139 ***
## Balling 5.619e-01 4.370e-02 12.859 < 2e-16 ***
## Pressure.Vacuum 1.034e-01 1.640e-02 6.303 3.42e-10 ***
## Oxygen.Filler -1.593e+00 1.567e-01 -10.169 < 2e-16 ***
## Bowl.Setpoint -2.440e-03 8.041e-04 -3.035 0.002432 **
## Alch.Rel 1.713e-01 1.805e-02 9.494 < 2e-16 ***
## Carb.Rel 8.751e-02 2.150e-02 4.071 4.83e-05 ***
## Balling.Lvl -5.968e-01 4.849e-02 -12.308 < 2e-16 ***
## BCB 1.082e-01 1.789e-02 6.045 1.71e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3067 on 2550 degrees of freedom
## Multiple R-squared: 0.3482, Adjusted R-squared: 0.3431
## F-statistic: 68.12 on 20 and 2550 DF, p-value: < 2.2e-16We evaluate the VIF again and see that Balling.Lvl and Balling are collinear, I created a new predictor by dividing Balling.Lvl by Balling.
# Calculating VIF
vif_values <- vif(model)
vif_values## PC.Volume PSC.Fill Mnf.Flow Carb.Pressure1 Fill.Pressure
## 1.202038 1.012851 3.705385 1.154856 1.494303
## Hyd.Pressure2 Hyd.Pressure4 Filler.Level Temperature Usage.cont
## 2.410119 1.270967 3.928468 1.128926 1.501908
## Carb.Flow MFR Balling Pressure.Vacuum Oxygen.Filler
## 2.107870 2.217223 45.309741 2.386455 1.458751
## Bowl.Setpoint Alch.Rel Carb.Rel Balling.Lvl BCB
## 4.297317 3.741577 1.654980 48.738174 2.184705# Visualizing the model
#plot(model, which = 1, main = "Model Fit")student_train_2 <- student_train_1 |> mutate(PT = Balling.Lvl/Balling) |> select(-c(Balling, Balling.Lvl))
student_eval_2 <- student_eval_1 |> mutate(PT = Balling.Lvl/Balling) |> select(-c(Balling, Balling.Lvl))
model <- lm(PH ~ ., data = student_train_2)
summary(model)##
## Call:
## lm(formula = PH ~ ., data = student_train_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.8265 -0.0918 0.0077 0.1043 2.9896
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.910e+00 1.854e-01 37.274 < 2e-16 ***
## PC.Volume 1.582e-01 9.068e-02 1.745 0.081139 .
## PSC.Fill -1.100e-01 4.870e-02 -2.259 0.023993 *
## Mnf.Flow -8.162e-04 9.264e-05 -8.811 < 2e-16 ***
## Carb.Pressure1 2.032e-03 4.287e-04 4.741 2.25e-06 ***
## Fill.Pressure 8.599e-03 1.290e-03 6.666 3.20e-11 ***
## Hyd.Pressure2 1.613e-03 5.426e-04 2.974 0.002968 **
## Hyd.Pressure4 1.296e-03 3.801e-04 3.410 0.000661 ***
## Filler.Level 5.568e-03 6.195e-04 8.988 < 2e-16 ***
## Temperature 4.021e-03 1.223e-03 3.287 0.001028 **
## Usage.cont -2.956e-03 2.258e-03 -1.309 0.190487
## Carb.Flow 2.530e-05 7.722e-06 3.277 0.001064 **
## MFR -1.068e-04 4.077e-05 -2.620 0.008836 **
## Pressure.Vacuum 4.958e-02 1.406e-02 3.527 0.000428 ***
## Oxygen.Filler -1.211e+00 1.505e-01 -8.041 1.35e-15 ***
## Bowl.Setpoint -2.980e-03 7.634e-04 -3.903 9.74e-05 ***
## Alch.Rel 1.400e-01 1.324e-02 10.573 < 2e-16 ***
## Carb.Rel 1.649e-02 2.059e-02 0.801 0.423272
## BCB 9.657e-02 1.426e-02 6.772 1.57e-11 ***
## PT -4.733e-01 4.340e-02 -10.907 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.291 on 2550 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.2687, Adjusted R-squared: 0.2633
## F-statistic: 49.32 on 19 and 2550 DF, p-value: < 2.2e-16This resolves our collinearity but our model still has terrible performance so we are going to build some MARS models to capture some of the nonlinear relationships
# Calculating VIF
vif_values <- vif(model)
vif_values## PC.Volume PSC.Fill Mnf.Flow Carb.Pressure1 Fill.Pressure
## 1.191026 1.013459 3.716245 1.154787 1.445729
## Hyd.Pressure2 Hyd.Pressure4 Filler.Level Temperature Usage.cont
## 2.406789 1.200213 3.869511 1.081680 1.501337
## Carb.Flow MFR Pressure.Vacuum Oxygen.Filler Bowl.Setpoint
## 2.089432 2.137275 1.949095 1.463420 4.294010
## Alch.Rel Carb.Rel BCB PT
## 2.140017 1.540402 1.541232 1.463051student_train_2[is.na(student_train_2)] <- 0
library(earth)
y = student_train_2$PH
x = student_train_2 |> select(-PH)
marsFit <- earth(x, y)
summary(marsFit)## Call: earth(x=x, y=y)
##
## coefficients
## (Intercept) 60.142179
## BCB 0.109982
## h(155.4-Mnf.Flow) 0.000713
## h(115.2-Carb.Pressure1) -0.001086
## h(Carb.Pressure1-115.2) 0.012040
## h(Carb.Pressure1-129.2) -0.032280
## h(44-Fill.Pressure) -0.010383
## h(22.8-Hyd.Pressure2) -0.003566
## h(Hyd.Pressure4-112) 0.007462
## h(65.4-Filler.Level) -0.007803
## h(Temperature-64.8) -0.020892
## h(73.2-Temperature) -0.007473
## h(Temperature-73.2) 0.357884
## h(Usage.cont-22.06) -0.036833
## h(280.4-MFR) -0.000513
## h(MFR-280.4) -0.000281
## h(Oxygen.Filler-0.0026) -199.580131
## h(Oxygen.Filler-0.224) 22.772443
## h(0.262-Oxygen.Filler) -199.212897
## h(Oxygen.Filler-0.262) 142.671213
## h(Bowl.Setpoint-90) 0.003388
## h(6.52-Alch.Rel) -0.105306
## h(Alch.Rel-6.52) 0.136097
## h(PT-0.953488) 0.544001
## h(PT-1.05341) -0.872367
##
## Selected 25 of 33 terms, and 14 of 19 predictors
## Termination condition: Reached nk 39
## Importance: Oxygen.Filler, Filler.Level, Mnf.Flow, Alch.Rel, BCB, ...
## Number of terms at each degree of interaction: 1 24 (additive model)
## GCV 0.06876423 RSS 170.1182 GRSq 0.5199934 RSq 0.5377561plotmo(marsFit)## plotmo grid: PC.Volume PSC.Fill Mnf.Flow Carb.Pressure1 Fill.Pressure
## 0.27 0.18 64.8 123 46.4
## Hyd.Pressure2 Hyd.Pressure4 Filler.Level Temperature Usage.cont Carb.Flow
## 28.6 96 118.2 65.6 21.78 3028
## MFR Pressure.Vacuum Oxygen.Filler Bowl.Setpoint Alch.Rel Carb.Rel BCB
## 721.4 -5.4 0.0334 120 6.56 5.4 0
## PT
## 0.9302326
We are going to add some 2nd order relationships and we get an R-squared of 0.89
student_train_2[is.na(student_train_2)] <- 0
library(earth)
y = student_train_2$PH
x = student_train_2 |> select(-PH)
y_eval = student_eval_2$PH
x_eval = student_eval_2 |> select(-PH)
marsFit2 <- earth(x, y, degree = 2)
summary(marsFit2)## Call: earth(x=x, y=y, degree=2)
##
## coefficients
## (Intercept) 8.390041
## BCB 0.051556
## h(0.2-Mnf.Flow) 0.001352
## h(Mnf.Flow-0.2) -0.000508
## h(115.2-Carb.Pressure1) -0.001204
## h(Carb.Pressure1-115.2) 0.010962
## h(20.2-Hyd.Pressure2) -0.004303
## h(Hyd.Pressure2-20.2) 0.002212
## h(Oxygen.Filler-0.262) -90.613327
## h(6.66-Alch.Rel) 0.338152
## Filler.Level * h(Oxygen.Filler-0.262) 0.518596
## h(Oxygen.Filler-0.262) * Carb.Rel 5.429397
## h(0.024-Oxygen.Filler) * BCB -3.529366
## h(Oxygen.Filler-0.024) * BCB -0.604163
## h(90-Bowl.Setpoint) * BCB 0.004278
## h(Bowl.Setpoint-90) * BCB 0.004900
## h(0.2-Mnf.Flow) * h(Pressure.Vacuum- -5) -0.000994
## h(0.2-Mnf.Flow) * h(-5-Pressure.Vacuum) -0.001447
## h(0.2-Mnf.Flow) * h(Alch.Rel-6.5) 0.000878
## h(Mnf.Flow-0.2) * h(Alch.Rel-6.48) 0.000530
## h(Mnf.Flow-0.2) * h(6.48-Alch.Rel) 0.003911
## h(Carb.Pressure1-115.2) * h(Usage.cont-22.06) -0.006320
## h(Carb.Pressure1-115.2) * h(22.06-Usage.cont) -0.000666
## h(Carb.Pressure1-129.2) * h(6.66-Alch.Rel) -0.088171
## h(Hyd.Pressure2-20.2) * h(Bowl.Setpoint-110) -0.000349
## h(Hyd.Pressure2-20.2) * h(110-Bowl.Setpoint) -0.000169
## h(120-Hyd.Pressure4) * h(6.66-Alch.Rel) 0.005533
## h(Hyd.Pressure4-120) * h(6.66-Alch.Rel) 0.047192
## h(0.262-Oxygen.Filler) * h(Alch.Rel-6.52) 0.475863
## h(0.262-Oxygen.Filler) * h(6.52-Alch.Rel) -3.839015
##
## Selected 30 of 36 terms, and 12 of 19 predictors
## Termination condition: Reached nk 39
## Importance: Oxygen.Filler, Filler.Level, Carb.Pressure1, Alch.Rel, ...
## Number of terms at each degree of interaction: 1 9 20
## GCV 0.01620618 RSS 39.31784 GRSq 0.8868732 RSq 0.8931658plotmo(marsFit2)## plotmo grid: PC.Volume PSC.Fill Mnf.Flow Carb.Pressure1 Fill.Pressure
## 0.27 0.18 64.8 123 46.4
## Hyd.Pressure2 Hyd.Pressure4 Filler.Level Temperature Usage.cont Carb.Flow
## 28.6 96 118.2 65.6 21.78 3028
## MFR Pressure.Vacuum Oxygen.Filler Bowl.Setpoint Alch.Rel Carb.Rel BCB
## 721.4 -5.4 0.0334 120 6.56 5.4 0
## PT
## 0.9302326
Lastly we make some predictions with our evaluation dataset
#library(Metrics)
preds <- stats::predict(marsFit2, student_eval_2)