Data624_Project2
Alexis Mekueko
12/3/2021
Project #2 (Team) Assignment
This is role playing. I am your new boss. I am in charge of production at ABC Beverage and you are a team of data scientists reporting to me. My leadership has told me that new regulations are requiring us to understand our manufacturing process, the predictive factors and be able to report to them our predictive model of PH.
Please use the historical data set I am providing. Build and report the factors in both a technical and non-technical report. I like to use Word and Excel. Please provide your non-technical report in a business friendly readable document and your predictions in an Excel readable format. The technical report should show clearly the models you tested and how you selected your final approach.
Please submit both Rpubs links and .rmd files or other readable formats for technical and non-technical reports. Also submit the excel file showing the prediction of your models for pH.
Data Structure
## 'data.frame': 2571 obs. of 33 variables:
## $ Brand.Code : chr "B" "A" "B" "A" ...
## $ Carb.Volume : num 5.34 5.43 5.29 5.44 5.49 ...
## $ Fill.Ounces : num 24 24 24.1 24 24.3 ...
## $ PC.Volume : num 0.263 0.239 0.263 0.293 0.111 ...
## $ Carb.Pressure : num 68.2 68.4 70.8 63 67.2 66.6 64.2 67.6 64.2 72 ...
## $ Carb.Temp : num 141 140 145 133 137 ...
## $ PSC : num 0.104 0.124 0.09 NA 0.026 0.09 0.128 0.154 0.132 0.014 ...
## $ PSC.Fill : num 0.26 0.22 0.34 0.42 0.16 0.24 0.4 0.34 0.12 0.24 ...
## $ PSC.CO2 : num 0.04 0.04 0.16 0.04 0.12 0.04 0.04 0.04 0.14 0.06 ...
## $ Mnf.Flow : num -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 ...
## $ Carb.Pressure1 : num 119 122 120 115 118 ...
## $ Fill.Pressure : num 46 46 46 46.4 45.8 45.6 51.8 46.8 46 45.2 ...
## $ Hyd.Pressure1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Hyd.Pressure2 : num NA NA NA 0 0 0 0 0 0 0 ...
## $ Hyd.Pressure3 : num NA NA NA 0 0 0 0 0 0 0 ...
## $ Hyd.Pressure4 : int 118 106 82 92 92 116 124 132 90 108 ...
## $ Filler.Level : num 121 119 120 118 119 ...
## $ Filler.Speed : int 4002 3986 4020 4012 4010 4014 NA 1004 4014 4028 ...
## $ Temperature : num 66 67.6 67 65.6 65.6 66.2 65.8 65.2 65.4 66.6 ...
## $ Usage.cont : num 16.2 19.9 17.8 17.4 17.7 ...
## $ Carb.Flow : int 2932 3144 2914 3062 3054 2948 30 684 2902 3038 ...
## $ Density : num 0.88 0.92 1.58 1.54 1.54 1.52 0.84 0.84 0.9 0.9 ...
## $ MFR : num 725 727 735 731 723 ...
## $ Balling : num 1.4 1.5 3.14 3.04 3.04 ...
## $ Pressure.Vacuum : num -4 -4 -3.8 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 ...
## $ PH : num 8.36 8.26 8.94 8.24 8.26 8.32 8.4 8.38 8.38 8.5 ...
## $ Oxygen.Filler : num 0.022 0.026 0.024 0.03 0.03 0.024 0.066 0.046 0.064 0.022 ...
## $ Bowl.Setpoint : int 120 120 120 120 120 120 120 120 120 120 ...
## $ Pressure.Setpoint: num 46.4 46.8 46.6 46 46 46 46 46 46 46 ...
## $ Air.Pressurer : num 143 143 142 146 146 ...
## $ Alch.Rel : num 6.58 6.56 7.66 7.14 7.14 7.16 6.54 6.52 6.52 6.54 ...
## $ Carb.Rel : num 5.32 5.3 5.84 5.42 5.44 5.44 5.38 5.34 5.34 5.34 ...
## $ Balling.Lvl : num 1.48 1.56 3.28 3.04 3.04 3.02 1.44 1.44 1.44 1.38 ...## 'data.frame': 267 obs. of 33 variables:
## $ Brand.Code : chr "D" "A" "B" "B" ...
## $ Carb.Volume : num 5.48 5.39 5.29 5.27 5.41 ...
## $ Fill.Ounces : num 24 24 23.9 23.9 24.2 ...
## $ PC.Volume : num 0.27 0.227 0.303 0.186 0.16 ...
## $ Carb.Pressure : num 65.4 63.2 66.4 64.8 69.4 73.4 65.2 67.4 66.8 72.6 ...
## $ Carb.Temp : num 135 135 140 139 142 ...
## $ PSC : num 0.236 0.042 0.068 0.004 0.04 0.078 0.088 0.076 0.246 0.146 ...
## $ PSC.Fill : num 0.4 0.22 0.1 0.2 0.3 0.22 0.14 0.1 0.48 0.1 ...
## $ PSC.CO2 : num 0.04 0.08 0.02 0.02 0.06 NA 0 0.04 0.04 0.02 ...
## $ Mnf.Flow : num -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 ...
## $ Carb.Pressure1 : num 117 119 120 125 115 ...
## $ Fill.Pressure : num 46 46.2 45.8 40 51.4 46.4 46.2 40 43.8 40.8 ...
## $ Hyd.Pressure1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Hyd.Pressure2 : num NA 0 0 0 0 0 0 0 0 0 ...
## $ Hyd.Pressure3 : num NA 0 0 0 0 0 0 0 0 0 ...
## $ Hyd.Pressure4 : int 96 112 98 132 94 94 108 108 110 106 ...
## $ Filler.Level : num 129 120 119 120 116 ...
## $ Filler.Speed : int 3986 4012 4010 NA 4018 4010 4010 NA 4010 1006 ...
## $ Temperature : num 66 65.6 65.6 74.4 66.4 66.6 66.8 NA 65.8 66 ...
## $ Usage.cont : num 21.7 17.6 24.2 18.1 21.3 ...
## $ Carb.Flow : int 2950 2916 3056 28 3214 3064 3042 1972 2502 28 ...
## $ Density : num 0.88 1.5 0.9 0.74 0.88 0.84 1.48 1.6 1.52 1.48 ...
## $ MFR : num 728 736 735 NA 752 ...
## $ Balling : num 1.4 2.94 1.45 1.06 1.4 ...
## $ Pressure.Vacuum : num -3.8 -4.4 -4.2 -4 -4 -3.8 -4.2 -4.4 -4.4 -4.2 ...
## $ PH : logi NA NA NA NA NA NA ...
## $ Oxygen.Filler : num 0.022 0.03 0.046 NA 0.082 0.064 0.042 0.096 0.046 0.096 ...
## $ Bowl.Setpoint : int 130 120 120 120 120 120 120 120 120 120 ...
## $ Pressure.Setpoint: num 45.2 46 46 46 50 46 46 46 46 46 ...
## $ Air.Pressurer : num 143 147 147 146 146 ...
## $ Alch.Rel : num 6.56 7.14 6.52 6.48 6.5 6.5 7.18 7.16 7.14 7.78 ...
## $ Carb.Rel : num 5.34 5.58 5.34 5.5 5.38 5.42 5.46 5.42 5.44 5.52 ...
## $ Balling.Lvl : num 1.48 3.04 1.46 1.48 1.46 1.44 3.02 3 3.1 3.12 ...| 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 |
| A | 5.313333 | 23.88667 | 0.2680000 | 64.2 | 136.8 | 0.128 | 0.40 | 0.04 | -100 | 122.2 | 51.8 | 0 | 0 | 0 | 124 | 123.4 | NA | 65.8 | 20.74 | 30 | 0.84 | NA | 1.298 | -4.4 | 8.40 | 0.066 | 120 | 46.0 | 146.2 | 6.54 | 5.38 | 1.44 |
| B | 5.320000 | 24.17333 | 0.2206667 | 67.6 | 141.4 | 0.154 | 0.34 | 0.04 | -100 | 124.2 | 46.8 | 0 | 0 | 0 | 132 | 118.6 | 1004 | 65.2 | 18.96 | 684 | 0.84 | NA | 1.298 | -4.4 | 8.38 | 0.046 | 120 | 46.0 | 146.4 | 6.52 | 5.34 | 1.44 |
## Brand.Code Carb.Volume Fill.Ounces PC.Volume
## Length:2571 Min. :5.040 Min. :23.63 Min. :0.07933
## Class :character 1st Qu.:5.293 1st Qu.:23.92 1st Qu.:0.23917
## Mode :character Median :5.347 Median :23.97 Median :0.27133
## Mean :5.370 Mean :23.97 Mean :0.27712
## 3rd Qu.:5.453 3rd Qu.:24.03 3rd Qu.:0.31200
## Max. :5.700 Max. :24.32 Max. :0.47800
## NA's :10 NA's :38 NA's :39
## Carb.Pressure Carb.Temp PSC PSC.Fill
## Min. :57.00 Min. :128.6 Min. :0.00200 Min. :0.0000
## 1st Qu.:65.60 1st Qu.:138.4 1st Qu.:0.04800 1st Qu.:0.1000
## Median :68.20 Median :140.8 Median :0.07600 Median :0.1800
## Mean :68.19 Mean :141.1 Mean :0.08457 Mean :0.1954
## 3rd Qu.:70.60 3rd Qu.:143.8 3rd Qu.:0.11200 3rd Qu.:0.2600
## Max. :79.40 Max. :154.0 Max. :0.27000 Max. :0.6200
## NA's :27 NA's :26 NA's :33 NA's :23
## PSC.CO2 Mnf.Flow Carb.Pressure1 Fill.Pressure
## Min. :0.00000 Min. :-100.20 Min. :105.6 Min. :34.60
## 1st Qu.:0.02000 1st Qu.:-100.00 1st Qu.:119.0 1st Qu.:46.00
## Median :0.04000 Median : 65.20 Median :123.2 Median :46.40
## Mean :0.05641 Mean : 24.57 Mean :122.6 Mean :47.92
## 3rd Qu.:0.08000 3rd Qu.: 140.80 3rd Qu.:125.4 3rd Qu.:50.00
## Max. :0.24000 Max. : 229.40 Max. :140.2 Max. :60.40
## NA's :39 NA's :2 NA's :32 NA's :22
## Hyd.Pressure1 Hyd.Pressure2 Hyd.Pressure3 Hyd.Pressure4
## Min. :-0.80 Min. : 0.00 Min. :-1.20 Min. : 52.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 86.00
## Median :11.40 Median :28.60 Median :27.60 Median : 96.00
## Mean :12.44 Mean :20.96 Mean :20.46 Mean : 96.29
## 3rd Qu.:20.20 3rd Qu.:34.60 3rd Qu.:33.40 3rd Qu.:102.00
## Max. :58.00 Max. :59.40 Max. :50.00 Max. :142.00
## NA's :11 NA's :15 NA's :15 NA's :30
## Filler.Level Filler.Speed Temperature Usage.cont Carb.Flow
## Min. : 55.8 Min. : 998 Min. :63.60 Min. :12.08 Min. : 26
## 1st Qu.: 98.3 1st Qu.:3888 1st Qu.:65.20 1st Qu.:18.36 1st Qu.:1144
## Median :118.4 Median :3982 Median :65.60 Median :21.79 Median :3028
## Mean :109.3 Mean :3687 Mean :65.97 Mean :20.99 Mean :2468
## 3rd Qu.:120.0 3rd Qu.:3998 3rd Qu.:66.40 3rd Qu.:23.75 3rd Qu.:3186
## Max. :161.2 Max. :4030 Max. :76.20 Max. :25.90 Max. :5104
## NA's :20 NA's :57 NA's :14 NA's :5 NA's :2
## Density MFR Balling Pressure.Vacuum
## Min. :0.240 Min. : 31.4 Min. :-0.170 Min. :-6.600
## 1st Qu.:0.900 1st Qu.:706.3 1st Qu.: 1.496 1st Qu.:-5.600
## Median :0.980 Median :724.0 Median : 1.648 Median :-5.400
## Mean :1.174 Mean :704.0 Mean : 2.198 Mean :-5.216
## 3rd Qu.:1.620 3rd Qu.:731.0 3rd Qu.: 3.292 3rd Qu.:-5.000
## Max. :1.920 Max. :868.6 Max. : 4.012 Max. :-3.600
## NA's :1 NA's :212 NA's :1
## PH Oxygen.Filler Bowl.Setpoint Pressure.Setpoint
## Min. :7.880 Min. :0.00240 Min. : 70.0 Min. :44.00
## 1st Qu.:8.440 1st Qu.:0.02200 1st Qu.:100.0 1st Qu.:46.00
## Median :8.540 Median :0.03340 Median :120.0 Median :46.00
## Mean :8.546 Mean :0.04684 Mean :109.3 Mean :47.62
## 3rd Qu.:8.680 3rd Qu.:0.06000 3rd Qu.:120.0 3rd Qu.:50.00
## Max. :9.360 Max. :0.40000 Max. :140.0 Max. :52.00
## NA's :4 NA's :12 NA's :2 NA's :12
## Air.Pressurer Alch.Rel Carb.Rel Balling.Lvl
## Min. :140.8 Min. :5.280 Min. :4.960 Min. :0.00
## 1st Qu.:142.2 1st Qu.:6.540 1st Qu.:5.340 1st Qu.:1.38
## Median :142.6 Median :6.560 Median :5.400 Median :1.48
## Mean :142.8 Mean :6.897 Mean :5.437 Mean :2.05
## 3rd Qu.:143.0 3rd Qu.:7.240 3rd Qu.:5.540 3rd Qu.:3.14
## Max. :148.2 Max. :8.620 Max. :6.060 Max. :3.66
## NA's :9 NA's :10 NA's :1We observed the dataset has 33 variables and 2571 observations. All the entire data is numerical except the variable Brand.Code and some random missing values. Amount all the manufacturing processes at ABC Beverage, there is response variable (PH) which we will find the predictive model.
Data Preparation
Checking for Missing Values
## The dataset contains missing values for a total record of : 724##
## The test dataset contains missing values for a total record of : 366##
## The percentage of the overall missing values in the dataframe is: 0.85## %The actual dataset has missing values which represents about .85% of the total record. The first variable Brand.code has empty values, we will fill those with NA and evaluate again. Thus, we want to visualize these missing values to see how we can treat them.
## Warning: package 'VIM' was built under R version 4.0.5## Loading required package: colorspace## Loading required package: grid## VIM is ready to use.## Suggestions and bug-reports can be submitted at: https://github.com/statistikat/VIM/issues##
## Attaching package: 'VIM'## The following object is masked from 'package:datasets':
##
## sleep
## `summarise()` has grouped output by 'variables'. You can override using the `.groups` argument.| variables | number.missing |
|---|---|
| MFR | 212 |
| Brand.Code | 120 |
| Filler.Speed | 57 |
| PC.Volume | 39 |
| PSC.CO2 | 39 |
| Fill.Ounces | 38 |
| PSC | 33 |
| Carb.Pressure1 | 32 |
| Hyd.Pressure4 | 30 |
| Carb.Pressure | 27 |
| Carb.Temp | 26 |
| PSC.Fill | 23 |
| Fill.Pressure | 22 |
| Filler.Level | 20 |
| Hyd.Pressure2 | 15 |
| Hyd.Pressure3 | 15 |
| Temperature | 14 |
| Oxygen.Filler | 12 |
| Pressure.Setpoint | 12 |
| Hyd.Pressure1 | 11 |
| Carb.Rel | 10 |
| Carb.Volume | 10 |
| Alch.Rel | 9 |
| Usage.cont | 5 |
| PH | 4 |
| Bowl.Setpoint | 2 |
| Carb.Flow | 2 |
| Mnf.Flow | 2 |
| Balling | 1 |
| Balling.Lvl | 1 |
| Density | 1 |
## `summarise()` has grouped output by 'variables'. You can override using the `.groups` argument.
After carefully inspected the data, we observed that the variable Brand.Code has 120 missing values. The variable Brand.Code is a categorical datatype and we have no clue how each character is attributed. Therefore, it makes sense to delete these observations as there are no pertinence and would be hard to impute.
The response variable PH only have 4 missing values which represents (4/2571)*100 = 0.156% of the total observations. In addition, variable MFR appears to have the most missing values(212) or 8.24%. Therefore, it is safe to impute these missing values rather deleting them with potential to introduce biasing in the overall report. These missing values are not stack in a row neither in column which add more support toward imputation Vs. deletion. However, We attempt to delete any row where more than 50% of values are missing. This is to detect if the missing variables are at random or in a stack. Before we apply the imputation method, we would like to visualize the distribution of PH and MFR.
Imputation Method
## [1] 2451 33## `summarise()` has grouped output by 'variables'. You can override using the `.groups` argument.| variables | number.missing |
|---|---|
| MFR | 199 |
| Filler.Speed | 54 |
| PSC.CO2 | 37 |
| PC.Volume | 35 |
| Fill.Ounces | 34 |
| Carb.Pressure1 | 31 |
| PSC | 30 |
| Carb.Pressure | 26 |
| Hyd.Pressure4 | 26 |
| Carb.Temp | 23 |
| Fill.Pressure | 19 |
| PSC.Fill | 19 |
| Filler.Level | 18 |
| Hyd.Pressure2 | 15 |
| Hyd.Pressure3 | 15 |
| Temperature | 13 |
| Hyd.Pressure1 | 11 |
| Oxygen.Filler | 11 |
| Pressure.Setpoint | 11 |
| Carb.Volume | 10 |
| Alch.Rel | 8 |
| Carb.Rel | 8 |
| Usage.cont | 5 |
| PH | 4 |
| Bowl.Setpoint | 2 |
| Carb.Flow | 2 |
| Mnf.Flow | 2 |
| Balling | 1 |
| Density | 1 |
Let’s impute and train the dataset.
## We clearly see that there is no row ith more than 50% missing valuesNow we have imputed and trained the data, let’s visualize the data distribution and correlation.
## Warning: package 'ggthemes' was built under R version 4.0.5
From data distribution, we see that the the response variable PH and PC.Volume, Carb.Temp, Carb.Pressure, Fill.Ounces, Carb.Temp have a nearly normal distribution. Air.Pressurer, Mnf.Flow, Oxygen.Filler seem to carry out some outliers. But at this time, we don’t have much information about this ABC Beverage production, we cannot make up the reality of each data.
Modeling
Random Forest model is taking forever to output the result. So, we decided to skip it and try other model.
Partial Least Square
plsTune_model <- train(trainX, trainY,
method = "pls",
## The default tuning grid evaluates
## components 1... tuneLength
tuneLength = 20,
trControl = trainControl(method = 'cv'),
preProc = c("center", "scale"))
plsTune_model## Partial Least Squares
##
## 1962 samples
## 24 predictor
##
## Pre-processing: centered (24), scaled (24)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 1765, 1766, 1766, 1767, 1765, 1766, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 0.8944526 0.2084566 0.7096512
## 2 0.8500287 0.2848535 0.6674477
## 3 0.8415433 0.2995823 0.6552234
## 4 0.8345556 0.3111808 0.6510362
## 5 0.8316803 0.3162315 0.6471487
## 6 0.8301915 0.3187882 0.6448294
## 7 0.8298546 0.3194020 0.6434899
## 8 0.8299076 0.3193567 0.6436537
## 9 0.8299011 0.3194576 0.6433087
## 10 0.8299954 0.3192963 0.6433714
## 11 0.8299935 0.3192892 0.6434168
## 12 0.8300420 0.3192256 0.6434630
## 13 0.8300951 0.3191415 0.6435261
## 14 0.8301257 0.3190925 0.6435518
## 15 0.8302130 0.3189633 0.6436104
## 16 0.8302699 0.3188697 0.6436422
## 17 0.8302671 0.3188746 0.6436371
## 18 0.8302627 0.3188821 0.6436305
## 19 0.8302645 0.3188790 0.6436318
## 20 0.8302658 0.3188772 0.6436327
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was ncomp = 7.plot(plsTune_model)
Cubist Model
cubist_model <- train(x = trainX,
y = trainY,
method = 'cubist')
cubist_model## Cubist
##
## 1962 samples
## 24 predictor
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 1962, 1962, 1962, 1962, 1962, 1962, ...
## Resampling results across tuning parameters:
##
## committees neighbors RMSE Rsquared MAE
## 1 0 0.9606675 0.2997340 0.6579803
## 1 5 0.9524572 0.3284958 0.6523413
## 1 9 0.9490128 0.3250238 0.6490548
## 10 0 0.6987576 0.5229419 0.5053949
## 10 5 0.6837112 0.5463524 0.4944870
## 10 9 0.6842059 0.5442682 0.4952738
## 20 0 0.6701765 0.5604086 0.4858149
## 20 5 0.6542271 0.5809799 0.4739299
## 20 9 0.6550634 0.5794689 0.4752895
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were committees = 20 and neighbors = 5.Boosted Trees Model
gbmGrid <- expand.grid(.interaction.depth = seq(1, 7, by = 2),
.n.trees = seq(100, 1000, by = 50),
.shrinkage = c(0.01, 0.1, 0.5),
.n.minobsinnode=c(5,10,15))
set.seed(100)
boostedTrees_model <- train(x = trainX,
y = trainY,
method = "gbm",
tuneGrid = gbmGrid,
## The gbm() function produces copious amounts
## of output, so pass in the verbose option
## to avoid printing a lot to the screen.
verbose = FALSE)
boostedTrees_model ## Stochastic Gradient Boosting
##
## 1962 samples
## 24 predictor
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 1962, 1962, 1962, 1962, 1962, 1962, ...
## Resampling results across tuning parameters:
##
## shrinkage interaction.depth n.minobsinnode n.trees RMSE Rsquared
## 0.01 1 5 100 0.9027671 0.2502947
## 0.01 1 5 150 0.8815385 0.2756013
## 0.01 1 5 200 0.8666240 0.2916629
## 0.01 1 5 250 0.8560026 0.3034460
## 0.01 1 5 300 0.8479230 0.3119501
## 0.01 1 5 350 0.8416749 0.3187636
## 0.01 1 5 400 0.8365414 0.3241339
## 0.01 1 5 450 0.8322917 0.3287534
## 0.01 1 5 500 0.8288068 0.3327444
## 0.01 1 5 550 0.8257497 0.3362609
## 0.01 1 5 600 0.8231628 0.3392515
## 0.01 1 5 650 0.8209173 0.3419249
## 0.01 1 5 700 0.8188495 0.3443666
## 0.01 1 5 750 0.8170694 0.3464877
## 0.01 1 5 800 0.8155779 0.3481619
## 0.01 1 5 850 0.8140004 0.3500223
## 0.01 1 5 900 0.8126801 0.3516072
## 0.01 1 5 950 0.8113651 0.3531645
## 0.01 1 5 1000 0.8102601 0.3545122
## 0.01 1 10 100 0.9024451 0.2502413
## 0.01 1 10 150 0.8815489 0.2748070
## 0.01 1 10 200 0.8664225 0.2915997
## 0.01 1 10 250 0.8559163 0.3028739
## 0.01 1 10 300 0.8477081 0.3115384
## 0.01 1 10 350 0.8412165 0.3187059
## 0.01 1 10 400 0.8360950 0.3240338
## 0.01 1 10 450 0.8320385 0.3285838
## 0.01 1 10 500 0.8282869 0.3329763
## 0.01 1 10 550 0.8255219 0.3362783
## 0.01 1 10 600 0.8229146 0.3392254
## 0.01 1 10 650 0.8206803 0.3416794
## 0.01 1 10 700 0.8187129 0.3440697
## 0.01 1 10 750 0.8168601 0.3462422
## 0.01 1 10 800 0.8151603 0.3483854
## 0.01 1 10 850 0.8135789 0.3502210
## 0.01 1 10 900 0.8123004 0.3516902
## 0.01 1 10 950 0.8110097 0.3533543
## 0.01 1 10 1000 0.8097855 0.3548235
## 0.01 1 15 100 0.9024960 0.2514522
## 0.01 1 15 150 0.8815048 0.2753039
## 0.01 1 15 200 0.8662897 0.2919083
## 0.01 1 15 250 0.8553841 0.3034022
## 0.01 1 15 300 0.8471240 0.3130230
## 0.01 1 15 350 0.8405611 0.3201025
## 0.01 1 15 400 0.8354190 0.3256030
## 0.01 1 15 450 0.8311603 0.3300512
## 0.01 1 15 500 0.8275274 0.3343211
## 0.01 1 15 550 0.8244565 0.3376167
## 0.01 1 15 600 0.8218576 0.3407923
## 0.01 1 15 650 0.8195754 0.3434856
## 0.01 1 15 700 0.8175824 0.3457152
## 0.01 1 15 750 0.8157892 0.3479945
## 0.01 1 15 800 0.8142122 0.3498783
## 0.01 1 15 850 0.8127814 0.3516448
## 0.01 1 15 900 0.8113430 0.3534111
## 0.01 1 15 950 0.8101490 0.3547820
## 0.01 1 15 1000 0.8088807 0.3562373
## 0.01 3 5 100 0.8555142 0.3519710
## 0.01 3 5 150 0.8262012 0.3716789
## 0.01 3 5 200 0.8086755 0.3847245
## 0.01 3 5 250 0.7976414 0.3938499
## 0.01 3 5 300 0.7898598 0.4008618
## 0.01 3 5 350 0.7839291 0.4069497
## 0.01 3 5 400 0.7789721 0.4120751
## 0.01 3 5 450 0.7747340 0.4167354
## 0.01 3 5 500 0.7712358 0.4206367
## 0.01 3 5 550 0.7679987 0.4243096
## 0.01 3 5 600 0.7652624 0.4274786
## 0.01 3 5 650 0.7627651 0.4303772
## 0.01 3 5 700 0.7606055 0.4327767
## 0.01 3 5 750 0.7585261 0.4353192
## 0.01 3 5 800 0.7567266 0.4374163
## 0.01 3 5 850 0.7550021 0.4395014
## 0.01 3 5 900 0.7532885 0.4415504
## 0.01 3 5 950 0.7518498 0.4433222
## 0.01 3 5 1000 0.7505270 0.4449478
## 0.01 3 10 100 0.8545496 0.3545292
## 0.01 3 10 150 0.8254726 0.3732090
## 0.01 3 10 200 0.8077311 0.3859062
## 0.01 3 10 250 0.7964670 0.3950914
## 0.01 3 10 300 0.7886586 0.4023268
## 0.01 3 10 350 0.7827179 0.4082658
## 0.01 3 10 400 0.7775886 0.4138511
## 0.01 3 10 450 0.7735223 0.4182805
## 0.01 3 10 500 0.7699901 0.4223111
## 0.01 3 10 550 0.7670937 0.4253377
## 0.01 3 10 600 0.7645356 0.4282445
## 0.01 3 10 650 0.7619647 0.4312929
## 0.01 3 10 700 0.7596374 0.4340060
## 0.01 3 10 750 0.7578581 0.4360215
## 0.01 3 10 800 0.7561868 0.4378967
## 0.01 3 10 850 0.7547150 0.4395191
## 0.01 3 10 900 0.7533277 0.4410516
## 0.01 3 10 950 0.7519528 0.4427347
## 0.01 3 10 1000 0.7507514 0.4441559
## 0.01 3 15 100 0.8544778 0.3549477
## 0.01 3 15 150 0.8245308 0.3744610
## 0.01 3 15 200 0.8066716 0.3872027
## 0.01 3 15 250 0.7955440 0.3964313
## 0.01 3 15 300 0.7875589 0.4038156
## 0.01 3 15 350 0.7812853 0.4102765
## 0.01 3 15 400 0.7765724 0.4151654
## 0.01 3 15 450 0.7724145 0.4198120
## 0.01 3 15 500 0.7690770 0.4232892
## 0.01 3 15 550 0.7660649 0.4266313
## 0.01 3 15 600 0.7635632 0.4294646
## 0.01 3 15 650 0.7612590 0.4319540
## 0.01 3 15 700 0.7593158 0.4340742
## 0.01 3 15 750 0.7575283 0.4360555
## 0.01 3 15 800 0.7558236 0.4380592
## 0.01 3 15 850 0.7543579 0.4398040
## 0.01 3 15 900 0.7529737 0.4413530
## 0.01 3 15 950 0.7518567 0.4425805
## 0.01 3 15 1000 0.7507306 0.4438734
## 0.01 5 5 100 0.8358282 0.3912097
## 0.01 5 5 150 0.8043342 0.4078942
## 0.01 5 5 200 0.7858836 0.4196588
## 0.01 5 5 250 0.7737868 0.4293560
## 0.01 5 5 300 0.7656006 0.4365528
## 0.01 5 5 350 0.7591330 0.4428930
## 0.01 5 5 400 0.7541990 0.4476640
## 0.01 5 5 450 0.7500267 0.4521338
## 0.01 5 5 500 0.7463090 0.4561466
## 0.01 5 5 550 0.7432599 0.4595804
## 0.01 5 5 600 0.7405068 0.4627111
## 0.01 5 5 650 0.7381097 0.4653630
## 0.01 5 5 700 0.7359694 0.4678506
## 0.01 5 5 750 0.7338192 0.4704391
## 0.01 5 5 800 0.7320142 0.4725385
## 0.01 5 5 850 0.7303108 0.4745682
## 0.01 5 5 900 0.7288214 0.4762678
## 0.01 5 5 950 0.7273795 0.4780001
## 0.01 5 5 1000 0.7260450 0.4795973
## 0.01 5 10 100 0.8355243 0.3912746
## 0.01 5 10 150 0.8036535 0.4083769
## 0.01 5 10 200 0.7846877 0.4208908
## 0.01 5 10 250 0.7728169 0.4299885
## 0.01 5 10 300 0.7645951 0.4375976
## 0.01 5 10 350 0.7581178 0.4438740
## 0.01 5 10 400 0.7532771 0.4485964
## 0.01 5 10 450 0.7494803 0.4523875
## 0.01 5 10 500 0.7460237 0.4560315
## 0.01 5 10 550 0.7430784 0.4592822
## 0.01 5 10 600 0.7406058 0.4619384
## 0.01 5 10 650 0.7382983 0.4645207
## 0.01 5 10 700 0.7362674 0.4668649
## 0.01 5 10 750 0.7344093 0.4689140
## 0.01 5 10 800 0.7326811 0.4709881
## 0.01 5 10 850 0.7312508 0.4725762
## 0.01 5 10 900 0.7298714 0.4742309
## 0.01 5 10 950 0.7286537 0.4756507
## 0.01 5 10 1000 0.7275466 0.4769854
## 0.01 5 15 100 0.8349695 0.3927294
## 0.01 5 15 150 0.8027217 0.4095341
## 0.01 5 15 200 0.7842334 0.4213725
## 0.01 5 15 250 0.7723330 0.4308354
## 0.01 5 15 300 0.7640408 0.4382072
## 0.01 5 15 350 0.7576391 0.4442793
## 0.01 5 15 400 0.7528115 0.4489488
## 0.01 5 15 450 0.7487833 0.4531094
## 0.01 5 15 500 0.7454506 0.4565508
## 0.01 5 15 550 0.7426294 0.4595644
## 0.01 5 15 600 0.7403451 0.4620977
## 0.01 5 15 650 0.7384301 0.4640509
## 0.01 5 15 700 0.7365012 0.4661844
## 0.01 5 15 750 0.7346917 0.4682866
## 0.01 5 15 800 0.7329535 0.4703334
## 0.01 5 15 850 0.7315192 0.4719599
## 0.01 5 15 900 0.7302569 0.4733923
## 0.01 5 15 950 0.7289481 0.4749821
## 0.01 5 15 1000 0.7279076 0.4761958
## 0.01 7 5 100 0.8238805 0.4150075
## 0.01 7 5 150 0.7905616 0.4308842
## 0.01 7 5 200 0.7706340 0.4434165
## 0.01 7 5 250 0.7580872 0.4527427
## 0.01 7 5 300 0.7494473 0.4601728
## 0.01 7 5 350 0.7429788 0.4661906
## 0.01 7 5 400 0.7376600 0.4715507
## 0.01 7 5 450 0.7334188 0.4758186
## 0.01 7 5 500 0.7298358 0.4795314
## 0.01 7 5 550 0.7267613 0.4828920
## 0.01 7 5 600 0.7240402 0.4859766
## 0.01 7 5 650 0.7215861 0.4887380
## 0.01 7 5 700 0.7194663 0.4910795
## 0.01 7 5 750 0.7177064 0.4930762
## 0.01 7 5 800 0.7160316 0.4949800
## 0.01 7 5 850 0.7145732 0.4966015
## 0.01 7 5 900 0.7131405 0.4982568
## 0.01 7 5 950 0.7119393 0.4996425
## 0.01 7 5 1000 0.7107692 0.5010478
## 0.01 7 10 100 0.8227179 0.4157569
## 0.01 7 10 150 0.7891811 0.4320987
## 0.01 7 10 200 0.7694886 0.4444190
## 0.01 7 10 250 0.7570935 0.4534086
## 0.01 7 10 300 0.7483162 0.4612163
## 0.01 7 10 350 0.7416065 0.4675517
## 0.01 7 10 400 0.7368393 0.4720784
## 0.01 7 10 450 0.7324423 0.4766580
## 0.01 7 10 500 0.7288858 0.4803558
## 0.01 7 10 550 0.7261132 0.4832123
## 0.01 7 10 600 0.7236701 0.4858341
## 0.01 7 10 650 0.7215393 0.4881196
## 0.01 7 10 700 0.7195608 0.4903521
## 0.01 7 10 750 0.7176336 0.4925868
## 0.01 7 10 800 0.7160881 0.4943331
## 0.01 7 10 850 0.7145952 0.4960522
## 0.01 7 10 900 0.7132756 0.4976391
## 0.01 7 10 950 0.7122504 0.4987965
## 0.01 7 10 1000 0.7112355 0.4999683
## 0.01 7 15 100 0.8224930 0.4161225
## 0.01 7 15 150 0.7887043 0.4325848
## 0.01 7 15 200 0.7687527 0.4450733
## 0.01 7 15 250 0.7562679 0.4542501
## 0.01 7 15 300 0.7474978 0.4618884
## 0.01 7 15 350 0.7408831 0.4682301
## 0.01 7 15 400 0.7357730 0.4732812
## 0.01 7 15 450 0.7320648 0.4767104
## 0.01 7 15 500 0.7286523 0.4802026
## 0.01 7 15 550 0.7258382 0.4831476
## 0.01 7 15 600 0.7235908 0.4853986
## 0.01 7 15 650 0.7212496 0.4880174
## 0.01 7 15 700 0.7195224 0.4898705
## 0.01 7 15 750 0.7180864 0.4914259
## 0.01 7 15 800 0.7167232 0.4929726
## 0.01 7 15 850 0.7154455 0.4944563
## 0.01 7 15 900 0.7141713 0.4959910
## 0.01 7 15 950 0.7132654 0.4969828
## 0.01 7 15 1000 0.7123372 0.4980368
## 0.10 1 5 100 0.8112588 0.3515058
## 0.10 1 5 150 0.8040465 0.3602463
## 0.10 1 5 200 0.7993697 0.3663881
## 0.10 1 5 250 0.7980254 0.3678428
## 0.10 1 5 300 0.7971964 0.3692517
## 0.10 1 5 350 0.7963904 0.3706122
## 0.10 1 5 400 0.7965299 0.3706981
## 0.10 1 5 450 0.7959076 0.3717838
## 0.10 1 5 500 0.7971226 0.3706399
## 0.10 1 5 550 0.7978471 0.3698693
## 0.10 1 5 600 0.7981815 0.3701316
## 0.10 1 5 650 0.7983727 0.3699341
## 0.10 1 5 700 0.7987420 0.3699112
## 0.10 1 5 750 0.7992481 0.3697536
## 0.10 1 5 800 0.7998780 0.3691365
## 0.10 1 5 850 0.8007361 0.3681273
## 0.10 1 5 900 0.8018715 0.3671511
## 0.10 1 5 950 0.8026531 0.3664625
## 0.10 1 5 1000 0.8032905 0.3657363
## 0.10 1 10 100 0.8107716 0.3525870
## 0.10 1 10 150 0.8035668 0.3608138
## 0.10 1 10 200 0.8006496 0.3642544
## 0.10 1 10 250 0.7990834 0.3662778
## 0.10 1 10 300 0.7975165 0.3686819
## 0.10 1 10 350 0.7971470 0.3695231
## 0.10 1 10 400 0.7974609 0.3692953
## 0.10 1 10 450 0.7976625 0.3696692
## 0.10 1 10 500 0.7977919 0.3696538
## 0.10 1 10 550 0.7977366 0.3701725
## 0.10 1 10 600 0.7984458 0.3695995
## 0.10 1 10 650 0.7986790 0.3694401
## 0.10 1 10 700 0.7998073 0.3684138
## 0.10 1 10 750 0.8007689 0.3675597
## 0.10 1 10 800 0.8009586 0.3677854
## 0.10 1 10 850 0.8020075 0.3667478
## 0.10 1 10 900 0.8023987 0.3663600
## 0.10 1 10 950 0.8031337 0.3657337
## 0.10 1 10 1000 0.8036076 0.3656234
## 0.10 1 15 100 0.8101899 0.3531851
## 0.10 1 15 150 0.8016768 0.3639267
## 0.10 1 15 200 0.7985774 0.3674681
## 0.10 1 15 250 0.7964984 0.3702395
## 0.10 1 15 300 0.7960392 0.3709973
## 0.10 1 15 350 0.7957270 0.3716878
## 0.10 1 15 400 0.7957921 0.3719468
## 0.10 1 15 450 0.7963083 0.3714386
## 0.10 1 15 500 0.7966666 0.3713756
## 0.10 1 15 550 0.7969764 0.3713142
## 0.10 1 15 600 0.7975056 0.3711609
## 0.10 1 15 650 0.7982081 0.3705943
## 0.10 1 15 700 0.7984827 0.3703562
## 0.10 1 15 750 0.7988578 0.3704084
## 0.10 1 15 800 0.7994539 0.3700207
## 0.10 1 15 850 0.7996774 0.3700637
## 0.10 1 15 900 0.8008559 0.3685960
## 0.10 1 15 950 0.8010875 0.3686577
## 0.10 1 15 1000 0.8022279 0.3675526
## 0.10 3 5 100 0.7555901 0.4354095
## 0.10 3 5 150 0.7481190 0.4444274
## 0.10 3 5 200 0.7445625 0.4491732
## 0.10 3 5 250 0.7410394 0.4543711
## 0.10 3 5 300 0.7394350 0.4569992
## 0.10 3 5 350 0.7377529 0.4597695
## 0.10 3 5 400 0.7364678 0.4621092
## 0.10 3 5 450 0.7349594 0.4645127
## 0.10 3 5 500 0.7338912 0.4664436
## 0.10 3 5 550 0.7333741 0.4675530
## 0.10 3 5 600 0.7328053 0.4685641
## 0.10 3 5 650 0.7329162 0.4688659
## 0.10 3 5 700 0.7328768 0.4692122
## 0.10 3 5 750 0.7332230 0.4690354
## 0.10 3 5 800 0.7333792 0.4692508
## 0.10 3 5 850 0.7332650 0.4697718
## 0.10 3 5 900 0.7330931 0.4702930
## 0.10 3 5 950 0.7332424 0.4702686
## 0.10 3 5 1000 0.7329998 0.4709350
## 0.10 3 10 100 0.7568676 0.4328851
## 0.10 3 10 150 0.7500663 0.4416002
## 0.10 3 10 200 0.7467577 0.4461213
## 0.10 3 10 250 0.7434131 0.4511608
## 0.10 3 10 300 0.7413177 0.4544264
## 0.10 3 10 350 0.7401238 0.4565153
## 0.10 3 10 400 0.7383416 0.4595258
## 0.10 3 10 450 0.7378177 0.4606103
## 0.10 3 10 500 0.7376372 0.4612353
## 0.10 3 10 550 0.7373065 0.4620408
## 0.10 3 10 600 0.7376378 0.4620826
## 0.10 3 10 650 0.7378998 0.4621307
## 0.10 3 10 700 0.7379989 0.4623657
## 0.10 3 10 750 0.7376856 0.4631547
## 0.10 3 10 800 0.7378352 0.4632925
## 0.10 3 10 850 0.7378711 0.4635913
## 0.10 3 10 900 0.7381368 0.4634891
## 0.10 3 10 950 0.7379457 0.4640441
## 0.10 3 10 1000 0.7382079 0.4640268
## 0.10 3 15 100 0.7557882 0.4345089
## 0.10 3 15 150 0.7495388 0.4422570
## 0.10 3 15 200 0.7452435 0.4483760
## 0.10 3 15 250 0.7430042 0.4517632
## 0.10 3 15 300 0.7412229 0.4544964
## 0.10 3 15 350 0.7396444 0.4570332
## 0.10 3 15 400 0.7397018 0.4574871
## 0.10 3 15 450 0.7394826 0.4580923
## 0.10 3 15 500 0.7391679 0.4590423
## 0.10 3 15 550 0.7390278 0.4597181
## 0.10 3 15 600 0.7390187 0.4600707
## 0.10 3 15 650 0.7390962 0.4603995
## 0.10 3 15 700 0.7386837 0.4612917
## 0.10 3 15 750 0.7391790 0.4610697
## 0.10 3 15 800 0.7389922 0.4616885
## 0.10 3 15 850 0.7392808 0.4616941
## 0.10 3 15 900 0.7392533 0.4620530
## 0.10 3 15 950 0.7392122 0.4624829
## 0.10 3 15 1000 0.7394658 0.4624996
## 0.10 5 5 100 0.7362709 0.4626804
## 0.10 5 5 150 0.7301807 0.4705809
## 0.10 5 5 200 0.7266291 0.4756483
## 0.10 5 5 250 0.7246079 0.4788072
## 0.10 5 5 300 0.7237179 0.4804787
## 0.10 5 5 350 0.7229059 0.4820340
## 0.10 5 5 400 0.7229003 0.4824524
## 0.10 5 5 450 0.7223303 0.4835508
## 0.10 5 5 500 0.7218949 0.4845304
## 0.10 5 5 550 0.7211347 0.4858849
## 0.10 5 5 600 0.7213289 0.4858986
## 0.10 5 5 650 0.7214198 0.4861209
## 0.10 5 5 700 0.7208408 0.4869973
## 0.10 5 5 750 0.7207277 0.4874372
## 0.10 5 5 800 0.7208796 0.4874461
## 0.10 5 5 850 0.7205821 0.4879508
## 0.10 5 5 900 0.7204459 0.4883385
## 0.10 5 5 950 0.7206220 0.4883006
## 0.10 5 5 1000 0.7205012 0.4886044
## 0.10 5 10 100 0.7356597 0.4633844
## 0.10 5 10 150 0.7291443 0.4720249
## 0.10 5 10 200 0.7271574 0.4750940
## 0.10 5 10 250 0.7260502 0.4768252
## 0.10 5 10 300 0.7246916 0.4790878
## 0.10 5 10 350 0.7240519 0.4805588
## 0.10 5 10 400 0.7235385 0.4816196
## 0.10 5 10 450 0.7227065 0.4830327
## 0.10 5 10 500 0.7224803 0.4838434
## 0.10 5 10 550 0.7224667 0.4842086
## 0.10 5 10 600 0.7221528 0.4848872
## 0.10 5 10 650 0.7219081 0.4855292
## 0.10 5 10 700 0.7217965 0.4858717
## 0.10 5 10 750 0.7219567 0.4859240
## 0.10 5 10 800 0.7220143 0.4860561
## 0.10 5 10 850 0.7223475 0.4858827
## 0.10 5 10 900 0.7224687 0.4858673
## 0.10 5 10 950 0.7224909 0.4860810
## 0.10 5 10 1000 0.7226302 0.4860551
## 0.10 5 15 100 0.7350345 0.4643460
## 0.10 5 15 150 0.7295487 0.4714437
## 0.10 5 15 200 0.7270981 0.4751918
## 0.10 5 15 250 0.7251423 0.4782838
## 0.10 5 15 300 0.7237194 0.4805407
## 0.10 5 15 350 0.7229083 0.4821578
## 0.10 5 15 400 0.7227463 0.4828301
## 0.10 5 15 450 0.7226331 0.4833655
## 0.10 5 15 500 0.7225154 0.4840332
## 0.10 5 15 550 0.7225639 0.4842236
## 0.10 5 15 600 0.7220245 0.4854115
## 0.10 5 15 650 0.7225033 0.4850714
## 0.10 5 15 700 0.7226956 0.4851669
## 0.10 5 15 750 0.7231415 0.4848797
## 0.10 5 15 800 0.7229614 0.4853294
## 0.10 5 15 850 0.7231293 0.4854095
## 0.10 5 15 900 0.7234255 0.4852351
## 0.10 5 15 950 0.7238738 0.4848497
## 0.10 5 15 1000 0.7241675 0.4846651
## 0.10 7 5 100 0.7223310 0.4823206
## 0.10 7 5 150 0.7171421 0.4892966
## 0.10 7 5 200 0.7143861 0.4932923
## 0.10 7 5 250 0.7122205 0.4966068
## 0.10 7 5 300 0.7114626 0.4979458
## 0.10 7 5 350 0.7102122 0.4999633
## 0.10 7 5 400 0.7094835 0.5013095
## 0.10 7 5 450 0.7089838 0.5022806
## 0.10 7 5 500 0.7085873 0.5030294
## 0.10 7 5 550 0.7082374 0.5037410
## 0.10 7 5 600 0.7084055 0.5037271
## 0.10 7 5 650 0.7085002 0.5037275
## 0.10 7 5 700 0.7085411 0.5038271
## 0.10 7 5 750 0.7084580 0.5040296
## 0.10 7 5 800 0.7087398 0.5038580
## 0.10 7 5 850 0.7086284 0.5040770
## 0.10 7 5 900 0.7087874 0.5039586
## 0.10 7 5 950 0.7087830 0.5040781
## 0.10 7 5 1000 0.7088418 0.5040429
## 0.10 7 10 100 0.7246512 0.4788129
## 0.10 7 10 150 0.7195343 0.4858621
## 0.10 7 10 200 0.7173694 0.4891368
## 0.10 7 10 250 0.7162628 0.4911886
## 0.10 7 10 300 0.7151130 0.4931989
## 0.10 7 10 350 0.7146553 0.4942004
## 0.10 7 10 400 0.7144476 0.4947133
## 0.10 7 10 450 0.7141286 0.4954680
## 0.10 7 10 500 0.7140670 0.4958560
## 0.10 7 10 550 0.7146888 0.4953029
## 0.10 7 10 600 0.7147805 0.4954205
## 0.10 7 10 650 0.7145153 0.4959674
## 0.10 7 10 700 0.7147572 0.4958428
## 0.10 7 10 750 0.7146624 0.4961339
## 0.10 7 10 800 0.7148909 0.4959649
## 0.10 7 10 850 0.7150541 0.4959153
## 0.10 7 10 900 0.7152709 0.4957213
## 0.10 7 10 950 0.7154659 0.4955612
## 0.10 7 10 1000 0.7155349 0.4955282
## 0.10 7 15 100 0.7225575 0.4818629
## 0.10 7 15 150 0.7194175 0.4860821
## 0.10 7 15 200 0.7170371 0.4897166
## 0.10 7 15 250 0.7157168 0.4919205
## 0.10 7 15 300 0.7153167 0.4929559
## 0.10 7 15 350 0.7146005 0.4943051
## 0.10 7 15 400 0.7146521 0.4946860
## 0.10 7 15 450 0.7150489 0.4945677
## 0.10 7 15 500 0.7149200 0.4950250
## 0.10 7 15 550 0.7146899 0.4956165
## 0.10 7 15 600 0.7149702 0.4954393
## 0.10 7 15 650 0.7148640 0.4958558
## 0.10 7 15 700 0.7152209 0.4955583
## 0.10 7 15 750 0.7153228 0.4956232
## 0.10 7 15 800 0.7152933 0.4957815
## 0.10 7 15 850 0.7153998 0.4958196
## 0.10 7 15 900 0.7154947 0.4958181
## 0.10 7 15 950 0.7153523 0.4961430
## 0.10 7 15 1000 0.7154829 0.4961029
## 0.50 1 5 100 0.8176303 0.3449692
## 0.50 1 5 150 0.8222078 0.3425312
## 0.50 1 5 200 0.8278153 0.3392491
## 0.50 1 5 250 0.8320259 0.3356701
## 0.50 1 5 300 0.8358577 0.3326873
## 0.50 1 5 350 0.8365760 0.3342871
## 0.50 1 5 400 0.8391532 0.3341995
## 0.50 1 5 450 0.8417877 0.3320557
## 0.50 1 5 500 0.8457234 0.3296505
## 0.50 1 5 550 0.8481537 0.3286733
## 0.50 1 5 600 0.8501551 0.3268854
## 0.50 1 5 650 0.8525556 0.3257078
## 0.50 1 5 700 0.8559217 0.3227333
## 0.50 1 5 750 0.8572627 0.3226848
## 0.50 1 5 800 0.8608790 0.3200202
## 0.50 1 5 850 0.8637417 0.3177198
## 0.50 1 5 900 0.8681353 0.3146784
## 0.50 1 5 950 0.8694706 0.3139158
## 0.50 1 5 1000 0.8741808 0.3107950
## 0.50 1 10 100 0.8202601 0.3407824
## 0.50 1 10 150 0.8227222 0.3409693
## 0.50 1 10 200 0.8250012 0.3422395
## 0.50 1 10 250 0.8295444 0.3390052
## 0.50 1 10 300 0.8331593 0.3355927
## 0.50 1 10 350 0.8362265 0.3345444
## 0.50 1 10 400 0.8407577 0.3318576
## 0.50 1 10 450 0.8424562 0.3310506
## 0.50 1 10 500 0.8439409 0.3306252
## 0.50 1 10 550 0.8475220 0.3278512
## 0.50 1 10 600 0.8518319 0.3237616
## 0.50 1 10 650 0.8525352 0.3239662
## 0.50 1 10 700 0.8542273 0.3234852
## 0.50 1 10 750 0.8576183 0.3209173
## 0.50 1 10 800 0.8600713 0.3195905
## 0.50 1 10 850 0.8608784 0.3199532
## 0.50 1 10 900 0.8637259 0.3171740
## 0.50 1 10 950 0.8667616 0.3151186
## 0.50 1 10 1000 0.8673087 0.3151314
## 0.50 1 15 100 0.8139831 0.3492622
## 0.50 1 15 150 0.8189168 0.3460760
## 0.50 1 15 200 0.8220634 0.3456333
## 0.50 1 15 250 0.8257388 0.3429013
## 0.50 1 15 300 0.8282468 0.3414054
## 0.50 1 15 350 0.8334574 0.3379423
## 0.50 1 15 400 0.8349513 0.3376702
## 0.50 1 15 450 0.8384973 0.3349734
## 0.50 1 15 500 0.8408198 0.3335690
## 0.50 1 15 550 0.8461108 0.3284268
## 0.50 1 15 600 0.8490912 0.3266017
## 0.50 1 15 650 0.8530246 0.3247079
## 0.50 1 15 700 0.8561877 0.3216749
## 0.50 1 15 750 0.8584988 0.3202490
## 0.50 1 15 800 0.8592671 0.3207756
## 0.50 1 15 850 0.8610934 0.3195935
## 0.50 1 15 900 0.8638287 0.3168791
## 0.50 1 15 950 0.8657812 0.3167908
## 0.50 1 15 1000 0.8676599 0.3149820
## 0.50 3 5 100 0.8169701 0.3748757
## 0.50 3 5 150 0.8278618 0.3713804
## 0.50 3 5 200 0.8350191 0.3683560
## 0.50 3 5 250 0.8399383 0.3664533
## 0.50 3 5 300 0.8454946 0.3643383
## 0.50 3 5 350 0.8494067 0.3628236
## 0.50 3 5 400 0.8518094 0.3615678
## 0.50 3 5 450 0.8534660 0.3610482
## 0.50 3 5 500 0.8564701 0.3594146
## 0.50 3 5 550 0.8578068 0.3589602
## 0.50 3 5 600 0.8597885 0.3576223
## 0.50 3 5 650 0.8614178 0.3566090
## 0.50 3 5 700 0.8620204 0.3566222
## 0.50 3 5 750 0.8629840 0.3561857
## 0.50 3 5 800 0.8637936 0.3556904
## 0.50 3 5 850 0.8637512 0.3561181
## 0.50 3 5 900 0.8639283 0.3562959
## 0.50 3 5 950 0.8645526 0.3560619
## 0.50 3 5 1000 0.8649354 0.3557448
## 0.50 3 10 100 0.8187213 0.3724422
## 0.50 3 10 150 0.8267827 0.3712176
## 0.50 3 10 200 0.8351275 0.3676575
## 0.50 3 10 250 0.8399528 0.3668985
## 0.50 3 10 300 0.8439514 0.3661348
## 0.50 3 10 350 0.8470783 0.3657056
## 0.50 3 10 400 0.8504964 0.3637031
## 0.50 3 10 450 0.8538524 0.3617916
## 0.50 3 10 500 0.8549434 0.3619113
## 0.50 3 10 550 0.8562977 0.3616281
## 0.50 3 10 600 0.8579373 0.3610797
## 0.50 3 10 650 0.8598724 0.3602370
## 0.50 3 10 700 0.8611792 0.3595756
## 0.50 3 10 750 0.8624028 0.3591043
## 0.50 3 10 800 0.8631285 0.3588362
## 0.50 3 10 850 0.8643816 0.3583345
## 0.50 3 10 900 0.8646980 0.3583371
## 0.50 3 10 950 0.8656266 0.3578205
## 0.50 3 10 1000 0.8660916 0.3577421
## 0.50 3 15 100 0.8089695 0.3824340
## 0.50 3 15 150 0.8190651 0.3786007
## 0.50 3 15 200 0.8265648 0.3752293
## 0.50 3 15 250 0.8336033 0.3714889
## 0.50 3 15 300 0.8374661 0.3705100
## 0.50 3 15 350 0.8426723 0.3672375
## 0.50 3 15 400 0.8474531 0.3645703
## 0.50 3 15 450 0.8500113 0.3632378
## 0.50 3 15 500 0.8512297 0.3633056
## 0.50 3 15 550 0.8534907 0.3624648
## 0.50 3 15 600 0.8548682 0.3620510
## 0.50 3 15 650 0.8558115 0.3617024
## 0.50 3 15 700 0.8571146 0.3611267
## 0.50 3 15 750 0.8584259 0.3601942
## 0.50 3 15 800 0.8586041 0.3607017
## 0.50 3 15 850 0.8591575 0.3608395
## 0.50 3 15 900 0.8598483 0.3605310
## 0.50 3 15 950 0.8602077 0.3605484
## 0.50 3 15 1000 0.8608371 0.3601079
## 0.50 5 5 100 0.8349982 0.3668906
## 0.50 5 5 150 0.8478012 0.3608975
## 0.50 5 5 200 0.8560201 0.3562409
## 0.50 5 5 250 0.8596289 0.3547893
## 0.50 5 5 300 0.8617900 0.3547948
## 0.50 5 5 350 0.8637241 0.3538381
## 0.50 5 5 400 0.8655461 0.3527776
## 0.50 5 5 450 0.8660617 0.3528407
## 0.50 5 5 500 0.8666410 0.3526851
## 0.50 5 5 550 0.8669885 0.3524389
## 0.50 5 5 600 0.8674799 0.3521839
## 0.50 5 5 650 0.8679594 0.3519046
## 0.50 5 5 700 0.8681891 0.3517779
## 0.50 5 5 750 0.8682349 0.3517125
## 0.50 5 5 800 0.8683843 0.3516454
## 0.50 5 5 850 0.8685350 0.3515714
## 0.50 5 5 900 0.8685447 0.3515694
## 0.50 5 5 950 0.8686538 0.3515171
## 0.50 5 5 1000 0.8687706 0.3514333
## 0.50 5 10 100 0.8256026 0.3800482
## 0.50 5 10 150 0.8352510 0.3756216
## 0.50 5 10 200 0.8424767 0.3715713
## 0.50 5 10 250 0.8477803 0.3692073
## 0.50 5 10 300 0.8506780 0.3675026
## 0.50 5 10 350 0.8522349 0.3671004
## 0.50 5 10 400 0.8536781 0.3669274
## 0.50 5 10 450 0.8554897 0.3655368
## 0.50 5 10 500 0.8565912 0.3649105
## 0.50 5 10 550 0.8571724 0.3648001
## 0.50 5 10 600 0.8574771 0.3646807
## 0.50 5 10 650 0.8576623 0.3646440
## 0.50 5 10 700 0.8579649 0.3644880
## 0.50 5 10 750 0.8581629 0.3644009
## 0.50 5 10 800 0.8583310 0.3642678
## 0.50 5 10 850 0.8583358 0.3642694
## 0.50 5 10 900 0.8584524 0.3642302
## 0.50 5 10 950 0.8585401 0.3641953
## 0.50 5 10 1000 0.8586252 0.3641468
## 0.50 5 15 100 0.8274457 0.3734340
## 0.50 5 15 150 0.8364601 0.3699155
## 0.50 5 15 200 0.8421899 0.3682294
## 0.50 5 15 250 0.8462806 0.3673979
## 0.50 5 15 300 0.8481417 0.3674281
## 0.50 5 15 350 0.8496919 0.3667489
## 0.50 5 15 400 0.8505659 0.3669917
## 0.50 5 15 450 0.8526049 0.3653987
## 0.50 5 15 500 0.8535959 0.3647882
## 0.50 5 15 550 0.8540640 0.3646834
## 0.50 5 15 600 0.8546776 0.3644946
## 0.50 5 15 650 0.8548379 0.3645667
## 0.50 5 15 700 0.8552026 0.3645260
## 0.50 5 15 750 0.8556478 0.3641796
## 0.50 5 15 800 0.8558384 0.3641310
## 0.50 5 15 850 0.8559835 0.3640481
## 0.50 5 15 900 0.8560631 0.3640370
## 0.50 5 15 950 0.8560661 0.3640669
## 0.50 5 15 1000 0.8560888 0.3640574
## 0.50 7 5 100 0.8376036 0.3740224
## 0.50 7 5 150 0.8465795 0.3703086
## 0.50 7 5 200 0.8515756 0.3682676
## 0.50 7 5 250 0.8550854 0.3661843
## 0.50 7 5 300 0.8559963 0.3663080
## 0.50 7 5 350 0.8563145 0.3664926
## 0.50 7 5 400 0.8569158 0.3662261
## 0.50 7 5 450 0.8571897 0.3659800
## 0.50 7 5 500 0.8573873 0.3658053
## 0.50 7 5 550 0.8575390 0.3657033
## 0.50 7 5 600 0.8575539 0.3657905
## 0.50 7 5 650 0.8575791 0.3657542
## 0.50 7 5 700 0.8575980 0.3657712
## 0.50 7 5 750 0.8575755 0.3658003
## 0.50 7 5 800 0.8575808 0.3658096
## 0.50 7 5 850 0.8575746 0.3658195
## 0.50 7 5 900 0.8575685 0.3658314
## 0.50 7 5 950 0.8575836 0.3658215
## 0.50 7 5 1000 0.8575877 0.3658207
## 0.50 7 10 100 0.8417455 0.3669289
## 0.50 7 10 150 0.8521711 0.3619691
## 0.50 7 10 200 0.8585968 0.3579793
## 0.50 7 10 250 0.8608282 0.3576599
## 0.50 7 10 300 0.8628400 0.3561518
## 0.50 7 10 350 0.8642935 0.3552700
## 0.50 7 10 400 0.8647922 0.3550053
## 0.50 7 10 450 0.8650306 0.3548433
## 0.50 7 10 500 0.8652901 0.3546592
## 0.50 7 10 550 0.8653929 0.3546340
## 0.50 7 10 600 0.8655495 0.3545234
## 0.50 7 10 650 0.8656847 0.3544076
## 0.50 7 10 700 0.8657230 0.3543912
## 0.50 7 10 750 0.8657555 0.3543703
## 0.50 7 10 800 0.8657963 0.3543324
## 0.50 7 10 850 0.8658359 0.3543079
## 0.50 7 10 900 0.8658523 0.3543001
## 0.50 7 10 950 0.8658614 0.3542994
## 0.50 7 10 1000 0.8658736 0.3542849
## 0.50 7 15 100 0.8339788 0.3756222
## 0.50 7 15 150 0.8431838 0.3713549
## 0.50 7 15 200 0.8468878 0.3701715
## 0.50 7 15 250 0.8489773 0.3692509
## 0.50 7 15 300 0.8503006 0.3690962
## 0.50 7 15 350 0.8512013 0.3686063
## 0.50 7 15 400 0.8515248 0.3686450
## 0.50 7 15 450 0.8517966 0.3686039
## 0.50 7 15 500 0.8519906 0.3687330
## 0.50 7 15 550 0.8524276 0.3684632
## 0.50 7 15 600 0.8525433 0.3684123
## 0.50 7 15 650 0.8526159 0.3684103
## 0.50 7 15 700 0.8526565 0.3683382
## 0.50 7 15 750 0.8527200 0.3683108
## 0.50 7 15 800 0.8527421 0.3683246
## 0.50 7 15 850 0.8527415 0.3683354
## 0.50 7 15 900 0.8527484 0.3683415
## 0.50 7 15 950 0.8527325 0.3683574
## 0.50 7 15 1000 0.8527385 0.3683571
## MAE
## 0.7165315
## 0.6975660
## 0.6841743
## 0.6748375
## 0.6676504
## 0.6622258
## 0.6577789
## 0.6539546
## 0.6508250
## 0.6480024
## 0.6456692
## 0.6436589
## 0.6417023
## 0.6399914
## 0.6384869
## 0.6369867
## 0.6356226
## 0.6342019
## 0.6330082
## 0.7162144
## 0.6975259
## 0.6839439
## 0.6746790
## 0.6673944
## 0.6615995
## 0.6570732
## 0.6534615
## 0.6500632
## 0.6475555
## 0.6451602
## 0.6430084
## 0.6410935
## 0.6393440
## 0.6377073
## 0.6361592
## 0.6348133
## 0.6334423
## 0.6322510
## 0.7163093
## 0.6975345
## 0.6837853
## 0.6741328
## 0.6668582
## 0.6610170
## 0.6564126
## 0.6526000
## 0.6492432
## 0.6464573
## 0.6439760
## 0.6417217
## 0.6398843
## 0.6381200
## 0.6364977
## 0.6350338
## 0.6336012
## 0.6323754
## 0.6310613
## 0.6765912
## 0.6502049
## 0.6343078
## 0.6239918
## 0.6165461
## 0.6107892
## 0.6059297
## 0.6016977
## 0.5981683
## 0.5948455
## 0.5919841
## 0.5893136
## 0.5870634
## 0.5848444
## 0.5828021
## 0.5809951
## 0.5791753
## 0.5776019
## 0.5762593
## 0.6757975
## 0.6495594
## 0.6334269
## 0.6228452
## 0.6152953
## 0.6094036
## 0.6042428
## 0.6002399
## 0.5967496
## 0.5936952
## 0.5909447
## 0.5882710
## 0.5858524
## 0.5839414
## 0.5820938
## 0.5803227
## 0.5787526
## 0.5772853
## 0.5758558
## 0.6755589
## 0.6483998
## 0.6319978
## 0.6216343
## 0.6138838
## 0.6077817
## 0.6029289
## 0.5986817
## 0.5951581
## 0.5920869
## 0.5894264
## 0.5869088
## 0.5847644
## 0.5827627
## 0.5808148
## 0.5791984
## 0.5775122
## 0.5762349
## 0.5749228
## 0.6593188
## 0.6310622
## 0.6137969
## 0.6021733
## 0.5938218
## 0.5871862
## 0.5821303
## 0.5778698
## 0.5740129
## 0.5707424
## 0.5677350
## 0.5650887
## 0.5627780
## 0.5605689
## 0.5586706
## 0.5567906
## 0.5550834
## 0.5536008
## 0.5521563
## 0.6589417
## 0.6299909
## 0.6123891
## 0.6009217
## 0.5925828
## 0.5859364
## 0.5808750
## 0.5768023
## 0.5732230
## 0.5701653
## 0.5676284
## 0.5651980
## 0.5629880
## 0.5610399
## 0.5590714
## 0.5574073
## 0.5558226
## 0.5544616
## 0.5532506
## 0.6582440
## 0.6290561
## 0.6117039
## 0.5999710
## 0.5915460
## 0.5847539
## 0.5796612
## 0.5753731
## 0.5718351
## 0.5687385
## 0.5662931
## 0.5641819
## 0.5621210
## 0.5602128
## 0.5583694
## 0.5568374
## 0.5554444
## 0.5540086
## 0.5528894
## 0.6489661
## 0.6188574
## 0.5999789
## 0.5874214
## 0.5786461
## 0.5718496
## 0.5664970
## 0.5621937
## 0.5584042
## 0.5552829
## 0.5524121
## 0.5497180
## 0.5474387
## 0.5454842
## 0.5435555
## 0.5418539
## 0.5403112
## 0.5390711
## 0.5377413
## 0.6477449
## 0.6171644
## 0.5984513
## 0.5859862
## 0.5769776
## 0.5701639
## 0.5652227
## 0.5607311
## 0.5570053
## 0.5539996
## 0.5514124
## 0.5490557
## 0.5469568
## 0.5448523
## 0.5431199
## 0.5414919
## 0.5400502
## 0.5389095
## 0.5376930
## 0.6472953
## 0.6162655
## 0.5972711
## 0.5845591
## 0.5756202
## 0.5687095
## 0.5636337
## 0.5596480
## 0.5559817
## 0.5528919
## 0.5503771
## 0.5479375
## 0.5460466
## 0.5444431
## 0.5429910
## 0.5416274
## 0.5401765
## 0.5391730
## 0.5381863
## 0.6334881
## 0.6251932
## 0.6194331
## 0.6168148
## 0.6145443
## 0.6126791
## 0.6117815
## 0.6110570
## 0.6112315
## 0.6117214
## 0.6114012
## 0.6112952
## 0.6111255
## 0.6114282
## 0.6117075
## 0.6118566
## 0.6123983
## 0.6127479
## 0.6129743
## 0.6327411
## 0.6241191
## 0.6195357
## 0.6164880
## 0.6135105
## 0.6122608
## 0.6115027
## 0.6112961
## 0.6112668
## 0.6107208
## 0.6108438
## 0.6109242
## 0.6114232
## 0.6118078
## 0.6116273
## 0.6125162
## 0.6122888
## 0.6129892
## 0.6132705
## 0.6322511
## 0.6222765
## 0.6175423
## 0.6144465
## 0.6127889
## 0.6116735
## 0.6111090
## 0.6108402
## 0.6107647
## 0.6107585
## 0.6106368
## 0.6109038
## 0.6111140
## 0.6111734
## 0.6114638
## 0.6114500
## 0.6120840
## 0.6120759
## 0.6127480
## 0.5803268
## 0.5703849
## 0.5654008
## 0.5615104
## 0.5588305
## 0.5571209
## 0.5553206
## 0.5537180
## 0.5525465
## 0.5519524
## 0.5514127
## 0.5514925
## 0.5511896
## 0.5515028
## 0.5516358
## 0.5514404
## 0.5512182
## 0.5511875
## 0.5508421
## 0.5800310
## 0.5721351
## 0.5665524
## 0.5634161
## 0.5605608
## 0.5593934
## 0.5571463
## 0.5560858
## 0.5557044
## 0.5555012
## 0.5555283
## 0.5554358
## 0.5557282
## 0.5551323
## 0.5550752
## 0.5550495
## 0.5552624
## 0.5551347
## 0.5552139
## 0.5786593
## 0.5707894
## 0.5655867
## 0.5629156
## 0.5608477
## 0.5588636
## 0.5582527
## 0.5581207
## 0.5572684
## 0.5572148
## 0.5570240
## 0.5568113
## 0.5564403
## 0.5566337
## 0.5566143
## 0.5567394
## 0.5568093
## 0.5567271
## 0.5569657
## 0.5606517
## 0.5531296
## 0.5489322
## 0.5463914
## 0.5454999
## 0.5443973
## 0.5437687
## 0.5431236
## 0.5422876
## 0.5415927
## 0.5414275
## 0.5412260
## 0.5406929
## 0.5405397
## 0.5407101
## 0.5403520
## 0.5401070
## 0.5402533
## 0.5401865
## 0.5596808
## 0.5516231
## 0.5487006
## 0.5467639
## 0.5449674
## 0.5435442
## 0.5430781
## 0.5421399
## 0.5423804
## 0.5420202
## 0.5416766
## 0.5414589
## 0.5413813
## 0.5413742
## 0.5415347
## 0.5416864
## 0.5415390
## 0.5415262
## 0.5415651
## 0.5583515
## 0.5517047
## 0.5485361
## 0.5464440
## 0.5453053
## 0.5446155
## 0.5443130
## 0.5441529
## 0.5439032
## 0.5440750
## 0.5433451
## 0.5438579
## 0.5437435
## 0.5440202
## 0.5437675
## 0.5438695
## 0.5440567
## 0.5442538
## 0.5445689
## 0.5470475
## 0.5402487
## 0.5369799
## 0.5343050
## 0.5334068
## 0.5320705
## 0.5311612
## 0.5306730
## 0.5306985
## 0.5303867
## 0.5305935
## 0.5304338
## 0.5303045
## 0.5302368
## 0.5303459
## 0.5301100
## 0.5301676
## 0.5302094
## 0.5302515
## 0.5473985
## 0.5413064
## 0.5388137
## 0.5370478
## 0.5359613
## 0.5353158
## 0.5351351
## 0.5347533
## 0.5347018
## 0.5352318
## 0.5348023
## 0.5346489
## 0.5350058
## 0.5349556
## 0.5351404
## 0.5352827
## 0.5354246
## 0.5354241
## 0.5354123
## 0.5467643
## 0.5420682
## 0.5394987
## 0.5378951
## 0.5371288
## 0.5368251
## 0.5367547
## 0.5367503
## 0.5366427
## 0.5364246
## 0.5367191
## 0.5365577
## 0.5366976
## 0.5367411
## 0.5367078
## 0.5367019
## 0.5367877
## 0.5366288
## 0.5366619
## 0.6260326
## 0.6289692
## 0.6334462
## 0.6360899
## 0.6383825
## 0.6383862
## 0.6407107
## 0.6431510
## 0.6461598
## 0.6479065
## 0.6504941
## 0.6523834
## 0.6552015
## 0.6557152
## 0.6583923
## 0.6613319
## 0.6645882
## 0.6657268
## 0.6696734
## 0.6273135
## 0.6281726
## 0.6297823
## 0.6326301
## 0.6348561
## 0.6371556
## 0.6406945
## 0.6432524
## 0.6451704
## 0.6484172
## 0.6518426
## 0.6528874
## 0.6534926
## 0.6567112
## 0.6597282
## 0.6604048
## 0.6625273
## 0.6653238
## 0.6663581
## 0.6228063
## 0.6260780
## 0.6275443
## 0.6310560
## 0.6325061
## 0.6372159
## 0.6397056
## 0.6422473
## 0.6440801
## 0.6483576
## 0.6509055
## 0.6533993
## 0.6571208
## 0.6586361
## 0.6586387
## 0.6603918
## 0.6634114
## 0.6654443
## 0.6672391
## 0.6202514
## 0.6300776
## 0.6357268
## 0.6409373
## 0.6448536
## 0.6482943
## 0.6499999
## 0.6515684
## 0.6541810
## 0.6553118
## 0.6570807
## 0.6583959
## 0.6590922
## 0.6600639
## 0.6601703
## 0.6602427
## 0.6603036
## 0.6610487
## 0.6612666
## 0.6237798
## 0.6307963
## 0.6389619
## 0.6436699
## 0.6472054
## 0.6499762
## 0.6524875
## 0.6550149
## 0.6566790
## 0.6579443
## 0.6591369
## 0.6608484
## 0.6625006
## 0.6631973
## 0.6638231
## 0.6648965
## 0.6652394
## 0.6657093
## 0.6660295
## 0.6158480
## 0.6233988
## 0.6303367
## 0.6358160
## 0.6403353
## 0.6448085
## 0.6491641
## 0.6515796
## 0.6523641
## 0.6542456
## 0.6555397
## 0.6566364
## 0.6576917
## 0.6589834
## 0.6591224
## 0.6599401
## 0.6604026
## 0.6607633
## 0.6611006
## 0.6347825
## 0.6468156
## 0.6527199
## 0.6557980
## 0.6576273
## 0.6591766
## 0.6604945
## 0.6610023
## 0.6615806
## 0.6618291
## 0.6621945
## 0.6625792
## 0.6626816
## 0.6627145
## 0.6628480
## 0.6629759
## 0.6630489
## 0.6631781
## 0.6632356
## 0.6302742
## 0.6378987
## 0.6442935
## 0.6497724
## 0.6521314
## 0.6537054
## 0.6550074
## 0.6568319
## 0.6573422
## 0.6581533
## 0.6582525
## 0.6585348
## 0.6587717
## 0.6589447
## 0.6590978
## 0.6590511
## 0.6591729
## 0.6592121
## 0.6593415
## 0.6331473
## 0.6404490
## 0.6450796
## 0.6492386
## 0.6500474
## 0.6515146
## 0.6524453
## 0.6543188
## 0.6548772
## 0.6553785
## 0.6558582
## 0.6558340
## 0.6562471
## 0.6565654
## 0.6567849
## 0.6568068
## 0.6568449
## 0.6569303
## 0.6569348
## 0.6366651
## 0.6443008
## 0.6482057
## 0.6511808
## 0.6518098
## 0.6521180
## 0.6524906
## 0.6527077
## 0.6527903
## 0.6528299
## 0.6528622
## 0.6528428
## 0.6528354
## 0.6528419
## 0.6528399
## 0.6528312
## 0.6528238
## 0.6528329
## 0.6528428
## 0.6429706
## 0.6527712
## 0.6584631
## 0.6604800
## 0.6621063
## 0.6631601
## 0.6635105
## 0.6636100
## 0.6638352
## 0.6639087
## 0.6640519
## 0.6641147
## 0.6641240
## 0.6641711
## 0.6642133
## 0.6642440
## 0.6642572
## 0.6642590
## 0.6642746
## 0.6384031
## 0.6446733
## 0.6477012
## 0.6497108
## 0.6507464
## 0.6516043
## 0.6518820
## 0.6523114
## 0.6524641
## 0.6528270
## 0.6529354
## 0.6529912
## 0.6530285
## 0.6530624
## 0.6530775
## 0.6530883
## 0.6530950
## 0.6530742
## 0.6530885
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were n.trees = 550, interaction.depth =
## 7, shrinkage = 0.1 and n.minobsinnode = 5.plot(boostedTrees_model)
K-nearest Neighbors Model
## k-Nearest Neighbors
##
## 1962 samples
## 24 predictor
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 1962, 1962, 1962, 1962, 1962, 1962, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 5 0.8278116 0.3628391 0.6154042
## 7 0.8077098 0.3786993 0.6047007
## 9 0.8020305 0.3822446 0.6038914
## 11 0.8007580 0.3819450 0.6037865
## 13 0.8005034 0.3812098 0.6050144
## 15 0.7991664 0.3823557 0.6061000
## 17 0.7992378 0.3815188 0.6077787
## 19 0.8002526 0.3797092 0.6097327
## 21 0.8017696 0.3771813 0.6121655
## 23 0.8026414 0.3757101 0.6136102
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 15.
By curiosity, we want to check multilinear regression even we didn’t use it during the semester
## Linear Regression
##
## 1962 samples
## 24 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 1766, 1768, 1765, 1766, 1765, 1765, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 0.8294038 0.3207959 0.6428673
##
## Tuning parameter 'intercept' was held constant at a value of TRUEModel Selection
Looking at the models to find which gives the optimal resampling and test set performance.
library(kableExtra)## Warning: package 'kableExtra' was built under R version 4.0.5##
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##
## group_rowsPartial_Least_Squares <- postResample(pred = predict(plsTune_model, newdata=testX), obs = testY)
Cubist <- postResample(pred = predict(cubist_model, newdata=testX), obs = testY)
Boost_Trees <- postResample(pred = predict(boostedTrees_model, newdata=testX), obs = testY)
MultiLinear <- postResample(pred = predict(linear_model, newdata=testX), obs = testY)
KNN <- postResample(pred = predict(knn_model, newdata=testX), obs = testY)
models_performance <- rbind( "Partial Least Squares Model" = Partial_Least_Squares, "Cubist Model" = Cubist, "Boost Trees" = Boost_Trees, "KNN Model"= KNN, "Multilinear Model" = MultiLinear
)
models_performance %>%
kable() %>%
kable_material_dark() # kable_styling(bootstrap_options=c("hover", "striped", "condensed"))| RMSE | Rsquared | MAE | |
|---|---|---|---|
| Partial Least Squares Model | 0.8031337 | 0.3302809 | 0.6197529 |
| Cubist Model | 0.5989889 | 0.6265360 | 0.4305935 |
| Boost Trees | 0.6458077 | 0.5675270 | 0.4743690 |
| KNN Model | 0.7323568 | 0.4464454 | 0.5448429 |
| Multilinear Model | 0.8045229 | 0.3280464 | 0.6212196 |
The best model is Cubist Model based on the test set performance with the following results: RMSE Rsquared MAE 0.5989889 0.6265360 0.4305935
Importance of the predictors on the response variable, PH.
## cubist variable importance
##
## only 20 most important variables shown (out of 24)
##
## Overall
## Mnf.Flow 100.00
## Density 81.16
## Temperature 75.36
## Carb.Rel 75.36
## Air.Pressurer 63.77
## Pressure.Vacuum 61.59
## Carb.Pressure1 52.17
## Filler.Level 51.45
## Oxygen.Filler 50.00
## Usage.cont 44.93
## Hyd.Pressure2 44.20
## Carb.Flow 39.86
## Pressure.Setpoint 32.61
## Carb.Temp 28.99
## Carb.Volume 28.26
## Carb.Pressure 26.81
## Hyd.Pressure4 22.46
## Fill.Pressure 22.46
## PC.Volume 21.74
## MFR 12.32Evaluation Data
## [1] 9.02 8.99 9.03 9.27 9.03 9.05Let’s compare the predicted pH and the trained pH
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## renameReport
We given 02 dataset in the form of excel files. These datasets contain the actual data generated from ABC Beverage production and the evaluation data. Our was to use the actual data to predict the response variable ‘PH’. This variable called PH is a measure of how acidic or basic a liquid is. Our study shows that the drink made by the ABC company is of type basic. After the prediction the pH remains basic. We observed that the component ‘Mnf.Flow’ appears to have the most influence on the pH. Therefore, for a negative value of ‘Mnf.Flow’ , the predicted is more basic than the actual/current pH and for positive value of ‘Mnf.Flow’, the predicted pH remain less basic than the actual pH.
Recommendation:
Our study shows that the components below have greater influence on the pH of the drink being made. In other words, by controlling the variation of these components, the process engineers are likely to achieve a better pH. The attached excel file(New_Student_Evaluation) contains the predicted pH.
Components values
Mnf.Flow 100.00000
Density 81.15942
Temperature 75.36232
Carb.Rel 75.36232
Air.Pressurer 63.76812
Pressure.Vacuum 61.59420