IPL Pricing: Case Study to identify the best regression model to determine the independent variables that contribute to the dependent variable (Price of IPL Player)
IIMK ADSM 2020-21 Batch-2, Group 6: Ramana, Venugopal, Siju, Vikesh, Abdul
Load required packages
library(caret)## Warning: package 'caret' was built under R version 4.0.4## Loading required package: lattice## Loading required package: ggplot2library(glmnet)## Warning: package 'glmnet' was built under R version 4.0.4## Loading required package: Matrix## Loaded glmnet 4.1-1library(psych)## Warning: package 'psych' was built under R version 4.0.4##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
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## %+%, alphalibrary(readxl)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
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## recode## The following object is masked from 'package:psych':
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## logitLoad the data
setwd("C:/_MyData_/IIMK/Assignment 3_IPL Players Pricing")
iplData <- read_excel ("Pricing of players IMB381-XLS-ENG.xls", sheet = "Modified Data")
names(iplData)## [1] "Sl.NO." "PLAYER NAME" "L25" "B25-35"
## [5] "A35" "Country" "Team" "PLAYING ROLE"
## [9] "BAT" "BOW" "ALL" "BAT*SR"
## [13] "BOW*ECO" "BOW*SR-BL" "BAT*RUN-S" "BOW*WK-I"
## [17] "BAT*T-RUNS" "BAT*ODI-RUNS" "BOW*WK-O" "T-RUNS"
## [21] "T-WKTS" "ODI-RUNS" "ODI-SR-B" "ODI-WKTS"
## [25] "ODI-SR-BL" "CAPTAINCY EXP" "INDIA" "AUSTRALIA"
## [29] "OTHERS" "MTS" "ALL*SR-B" "ALL*SR-BL"
## [33] "ALL*ECON" "RUNS-S" "HS" "AVE"
## [37] "SR -B" "SIXERS" "RUNS-C" "WKTS"
## [41] "AVE-BL" "ECON" "SR -BL" "Year"
## [45] "Base Price(US$)" "Sold Price(US$)" "S_B Price" "SQRT(S-B)"# Create another data frame with only the required columns as mentioned in the case study's PDF
attach(iplData)
analysisData <- data.frame(L25, `B25-35`, A35, `RUNS-S`, `RUNS-C`, HS, AVE, `AVE-BL`, `SR -B`,
`SR -BL`, SIXERS, WKTS, ECON, `CAPTAINCY EXP`, `ODI-SR-B`, `ODI-SR-BL`,
`ODI-RUNS`, `ODI-WKTS`, `T-RUNS`, `T-WKTS`, BAT, BOW, ALL,
INDIA, AUSTRALIA, OTHERS, Year, `SQRT(S-B)`)
detach(iplData)
names (analysisData)## [1] "L25" "B25.35" "A35" "RUNS.S"
## [5] "RUNS.C" "HS" "AVE" "AVE.BL"
## [9] "SR..B" "SR..BL" "SIXERS" "WKTS"
## [13] "ECON" "CAPTAINCY.EXP" "ODI.SR.B" "ODI.SR.BL"
## [17] "ODI.RUNS" "ODI.WKTS" "T.RUNS" "T.WKTS"
## [21] "BAT" "BOW" "ALL" "INDIA"
## [25] "AUSTRALIA" "OTHERS" "Year" "SQRT.S.B."Check Linear Regression and VIF for multi-collinearity
lnModel <- lm (SQRT.S.B.~., data = analysisData)
summary(lnModel)##
## Call:
## lm(formula = SQRT.S.B. ~ ., data = analysisData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -660.21 -180.79 -20.17 172.48 653.92
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.466e+04 3.939e+04 -1.388 0.16810
## L25 1.977e+02 1.300e+02 1.521 0.13124
## B25.35 5.671e+01 7.657e+01 0.741 0.46055
## A35 NA NA NA NA
## RUNS.S 1.689e-01 1.135e-01 1.488 0.13980
## RUNS.C 1.251e-01 7.861e-02 1.592 0.11443
## HS -1.267e+00 1.773e+00 -0.714 0.47658
## AVE 3.742e+00 5.089e+00 0.735 0.46373
## AVE.BL 6.326e+00 7.159e+00 0.884 0.37896
## SR..B -8.626e-01 8.834e-01 -0.976 0.33107
## SR..BL -8.107e+00 9.862e+00 -0.822 0.41290
## SIXERS 1.558e+00 2.279e+00 0.684 0.49573
## WKTS 1.097e+00 9.992e-01 1.098 0.27483
## ECON -1.547e+00 7.452e+00 -0.208 0.83597
## CAPTAINCY.EXP 1.481e+02 8.290e+01 1.787 0.07685 .
## ODI.SR.B 5.022e-01 1.159e+00 0.433 0.66562
## ODI.SR.BL -2.326e+00 1.130e+00 -2.058 0.04204 *
## ODI.RUNS 2.777e-02 2.097e-02 1.324 0.18842
## ODI.WKTS 8.926e-01 5.197e-01 1.718 0.08880 .
## T.RUNS -3.139e-02 2.004e-02 -1.566 0.12030
## T.WKTS -3.327e-01 3.969e-01 -0.838 0.40389
## BAT -3.860e+01 9.942e+01 -0.388 0.69864
## BOW -5.220e+01 8.093e+01 -0.645 0.52031
## ALL NA NA NA NA
## INDIA 2.092e+02 7.290e+01 2.869 0.00498 **
## AUSTRALIA 8.518e+01 7.869e+01 1.083 0.28148
## OTHERS NA NA NA NA
## Year 2.730e+01 1.960e+01 1.393 0.16658
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 265.1 on 105 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.518, Adjusted R-squared: 0.4078
## F-statistic: 4.702 on 24 and 105 DF, p-value: 1.375e-08anova(lnModel)## Analysis of Variance Table
##
## Response: SQRT.S.B.
## Df Sum Sq Mean Sq F value Pr(>F)
## L25 1 591152 591152 8.4107 0.004544 **
## B25.35 1 145411 145411 2.0689 0.153307
## RUNS.S 1 3460455 3460455 49.2344 2.306e-10 ***
## RUNS.C 1 1319905 1319905 18.7792 3.372e-05 ***
## HS 1 68240 68240 0.9709 0.326720
## AVE 1 20144 20144 0.2866 0.593535
## AVE.BL 1 32983 32983 0.4693 0.494833
## SR..B 1 2604 2604 0.0371 0.847732
## SR..BL 1 121628 121628 1.7305 0.191214
## SIXERS 1 58337 58337 0.8300 0.364360
## WKTS 1 52152 52152 0.7420 0.390983
## ECON 1 10560 10560 0.1502 0.699091
## CAPTAINCY.EXP 1 155703 155703 2.2153 0.139646
## ODI.SR.B 1 21092 21092 0.3001 0.584984
## ODI.SR.BL 1 308208 308208 4.3851 0.038662 *
## ODI.RUNS 1 18984 18984 0.2701 0.604362
## ODI.WKTS 1 113317 113317 1.6122 0.206983
## T.RUNS 1 459410 459410 6.5364 0.011999 *
## T.WKTS 1 130339 130339 1.8544 0.176184
## BAT 1 19459 19459 0.2769 0.599878
## BOW 1 137 137 0.0019 0.964886
## INDIA 1 565628 565628 8.0476 0.005469 **
## AUSTRALIA 1 118686 118686 1.6886 0.196627
## Year 1 136373 136373 1.9403 0.166581
## Residuals 105 7379964 70285
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# vif (lnModel)
# This function results in error and blocks generating the HTML. The error is "there are aliased coefficients in the model". This means that there are few perfectly correlated variables.Findings
Linear regression results show that there are no highly significant IVs that contribute to the Pricing.
Shows India, but that is significant but that is at 90% confidence interval.
VIF shows that there seem to be perfectly correlated variables. So, check the correlation between all the numerical predictors.
As there are 28 IVs, we can plot all in one graph, but can’t read them. Hence plot them into two graphs.
pairs.panels(analysisData[c(-15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28)])
pairs.panels(analysisData[c(-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14)])
Findings
- This shows that the below variables are correlated:
- A35 and B25.35 - -0.83
- HS and RUNS.S - 0.83
- AVE and HS, RUN.S - 0.88, 0.77
- SR..BL and AVE.BL - 0.98
- SIXERS and HS, RUNS.S - 0.79, 0.87
- ECON and SR.BL, AVE.BL - 0.69, 0.69
- T.RUNS and ODI.RUNS - 0.89
- T.WKTS and ODI.WKTS - 0.82
- OTHERS and INDIA - -0.71
- As there are too many correlated variables, we can ignore Linear Regression and go with Lasso, Ridge and Elastic-Net Regression models.
# PARTITION THE DATA INTO TRAINING AND TEST
set.seed (1234)
index <- sample (2, nrow(analysisData), replace = TRUE, p = c(.70,.30))
trainData <- analysisData[index == 1,]
testData <- analysisData[index == 2,]
# Custom control parameters
# Use 10 fold cross validation and repeat it for 5 times
customControl <- trainControl(method = "repeatedcv", number = 10, repeats = 5)Run Linear Regression Model
set.seed (1234)
linearModel <- train (SQRT.S.B.~., trainData, method = "lm", trControl = customControl)## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
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## may be misleadinglinearModel$results## intercept RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 TRUE 336.4882 0.2917763 275.102 91.55101 0.2285392 70.13945linearModel## Linear Regression
##
## 99 samples
## 27 predictors
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times)
## Summary of sample sizes: 89, 90, 88, 88, 89, 90, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 336.4882 0.2917763 275.102
##
## Tuning parameter 'intercept' was held constant at a value of TRUEsummary(linearModel)##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -545.05 -151.59 -28.63 163.15 665.80
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.174e+04 4.704e+04 -0.887 0.37776
## L25 1.404e+02 1.626e+02 0.864 0.39057
## B25.35 -4.947e+01 9.922e+01 -0.499 0.61955
## A35 NA NA NA NA
## RUNS.S 1.363e-01 1.325e-01 1.029 0.30671
## RUNS.C 1.635e-01 8.985e-02 1.820 0.07288 .
## HS -1.747e+00 2.649e+00 -0.659 0.51163
## AVE 3.581e+00 6.381e+00 0.561 0.57632
## AVE.BL 7.864e+00 1.011e+01 0.778 0.43922
## SR..B -4.067e-01 1.037e+00 -0.392 0.69607
## SR..BL -1.016e+01 1.329e+01 -0.765 0.44697
## SIXERS 2.141e+00 2.641e+00 0.811 0.42001
## WKTS 5.883e-01 1.164e+00 0.505 0.61476
## ECON -3.427e+00 8.566e+00 -0.400 0.69024
## CAPTAINCY.EXP 2.005e+02 9.952e+01 2.014 0.04762 *
## ODI.SR.B 1.988e-01 1.426e+00 0.139 0.88945
## ODI.SR.BL -1.193e+00 1.521e+00 -0.784 0.43547
## ODI.RUNS 3.942e-02 2.503e-02 1.575 0.11953
## ODI.WKTS 5.995e-01 6.462e-01 0.928 0.35657
## T.RUNS -4.411e-02 2.377e-02 -1.856 0.06749 .
## T.WKTS -7.290e-02 5.186e-01 -0.141 0.88859
## BAT -3.827e+01 1.241e+02 -0.308 0.75869
## BOW -1.477e+01 9.679e+01 -0.153 0.87915
## ALL NA NA NA NA
## INDIA 2.504e+02 8.558e+01 2.926 0.00456 **
## AUSTRALIA 1.624e+02 9.338e+01 1.739 0.08616 .
## OTHERS NA NA NA NA
## Year 2.086e+01 2.341e+01 0.891 0.37571
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 277.3 on 74 degrees of freedom
## Multiple R-squared: 0.5413, Adjusted R-squared: 0.3925
## F-statistic: 3.638 on 24 and 74 DF, p-value: 1.038e-05Findings
- We can see that RMSE is 336.4882 and there are not many IVs that are highly significant to the dependent variable
- Player being from India is significant, but it is at 90% confidence interval.
Run Ridge Regression Model
set.seed (1234)
ridgeModel <- train (SQRT.S.B.~., trainData, method = "glmnet",
tuneGrid = expand.grid(alpha = 0, lambda = seq(0.0001, 1, length = 5)),
trControl = customControl)
ridgeModel## glmnet
##
## 99 samples
## 27 predictors
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times)
## Summary of sample sizes: 89, 90, 88, 88, 89, 90, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.000100 316.3624 0.3192681 259.4783
## 0.250075 316.3624 0.3192681 259.4783
## 0.500050 316.3624 0.3192681 259.4783
## 0.750025 316.3624 0.3192681 259.4783
## 1.000000 316.3624 0.3192681 259.4783
##
## Tuning parameter 'alpha' was held constant at a value of 0
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 0 and lambda = 1.plot(ridgeModel)
plot(ridgeModel$finalModel, xvar = "lambda", label = TRUE)
plot(ridgeModel$finalModel, xvar = "dev", label = TRUE)
plot(varImp(ridgeModel, scale = TRUE))
Findings of Ridge Regression
- We can see that RMSE is 316.3624 and the recommended alpha is 0 and lambda is 1.
- Also the Ridge Regression shows that below variables significantly contribute to the dependent variable SQRT.S.B.
- CAPTAINCY.EXP
- L25
- OTHERS
- INDIA
- B25.35
- AUSTRALIA
- BAT
- Year
- ALL
- A35
Run a Lasso Regression Model
#LASSO REGRESSION
set.seed(1234)
lassoModel <- train (SQRT.S.B.~., trainData, method = "glmnet",
tuneGrid = expand.grid(alpha = 1, lambda = seq(0.0001, 1, length = 5)),
trControl = customControl)
lassoModel## glmnet
##
## 99 samples
## 27 predictors
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times)
## Summary of sample sizes: 89, 90, 88, 88, 89, 90, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.000100 334.8978 0.2925710 273.9198
## 0.250075 333.1932 0.2933637 272.5206
## 0.500050 330.7415 0.2946883 270.4532
## 0.750025 328.5459 0.2956393 268.7194
## 1.000000 326.5725 0.2963811 267.4339
##
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 1.plot(lassoModel)
plot(lassoModel$finalModel, xvar = "lambda", label = TRUE)
plot(lassoModel$finalModel, xvar = "dev", label = TRUE)
plot(varImp(lassoModel, scale = TRUE))
Findings of Lasso Regression
- We can see that the least RMSE is 326.5725 and the recommended alpha is 1 and lambda is 1.
- Also the Lasso Regression shows that below variables significantly contribute to the dependent variable SQRT.S.B.
- CAPTAINCY.EXP
- OTHERS
- L25
- INDIA
- B25.35
- BAT
- Year
- ALL
Run Elastic-Net Regression Model
set.seed (1234)
elasticModel <- train (SQRT.S.B.~., trainData, method = "glmnet",
tuneGrid = expand.grid(alpha = seq(0,1, length = 10),
lambda = seq(0.0001, 1, length = 5)),
trControl = customControl)
elasticModel## glmnet
##
## 99 samples
## 27 predictors
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times)
## Summary of sample sizes: 89, 90, 88, 88, 89, 90, ...
## Resampling results across tuning parameters:
##
## alpha lambda RMSE Rsquared MAE
## 0.0000000 0.000100 316.3624 0.3192681 259.4783
## 0.0000000 0.250075 316.3624 0.3192681 259.4783
## 0.0000000 0.500050 316.3624 0.3192681 259.4783
## 0.0000000 0.750025 316.3624 0.3192681 259.4783
## 0.0000000 1.000000 316.3624 0.3192681 259.4783
## 0.1111111 0.000100 334.9100 0.2925636 273.9604
## 0.1111111 0.250075 334.3818 0.2928674 273.5494
## 0.1111111 0.500050 333.2412 0.2936938 272.6696
## 0.1111111 0.750025 332.1910 0.2944880 271.8173
## 0.1111111 1.000000 331.2245 0.2952417 271.0123
## 0.2222222 0.000100 334.9710 0.2925712 274.0026
## 0.2222222 0.250075 334.2067 0.2929751 273.4094
## 0.2222222 0.500050 332.8832 0.2938572 272.3630
## 0.2222222 0.750025 331.6641 0.2947287 271.3450
## 0.2222222 1.000000 330.5676 0.2955208 270.3934
## 0.3333333 0.000100 335.0047 0.2925156 274.0316
## 0.3333333 0.250075 334.0872 0.2929957 273.3073
## 0.3333333 0.500050 332.5908 0.2939777 272.0950
## 0.3333333 0.750025 331.2130 0.2948665 270.9078
## 0.3333333 1.000000 329.9909 0.2957272 269.8724
## 0.4444444 0.000100 334.9045 0.2926822 273.9539
## 0.4444444 0.250075 333.8838 0.2931465 273.1414
## 0.4444444 0.500050 332.2628 0.2941103 271.8068
## 0.4444444 0.750025 330.7539 0.2950362 270.4597
## 0.4444444 1.000000 329.4005 0.2959617 269.4271
## 0.5555556 0.000100 334.9206 0.2926477 273.9453
## 0.5555556 0.250075 333.7673 0.2932004 273.0255
## 0.5555556 0.500050 331.9730 0.2942200 271.5281
## 0.5555556 0.750025 330.3179 0.2952342 270.1220
## 0.5555556 1.000000 328.8457 0.2961641 268.9796
## 0.6666667 0.000100 334.9076 0.2926138 273.9296
## 0.6666667 0.250075 333.6333 0.2932368 272.9061
## 0.6666667 0.500050 331.6687 0.2943346 271.2313
## 0.6666667 0.750025 329.8882 0.2954054 269.8003
## 0.6666667 1.000000 328.2660 0.2962625 268.4927
## 0.7777778 0.000100 334.8844 0.2925911 273.9061
## 0.7777778 0.250075 333.4956 0.2932748 272.7869
## 0.7777778 0.500050 331.3579 0.2944575 270.9290
## 0.7777778 0.750025 329.4522 0.2955357 269.4618
## 0.7777778 1.000000 327.6948 0.2963300 268.1568
## 0.8888889 0.000100 334.9018 0.2925972 273.9160
## 0.8888889 0.250075 333.3437 0.2933123 272.6548
## 0.8888889 0.500050 331.0437 0.2945838 270.6667
## 0.8888889 0.750025 328.9870 0.2955903 269.0731
## 0.8888889 1.000000 327.1217 0.2963792 267.7821
## 1.0000000 0.000100 334.8978 0.2925710 273.9198
## 1.0000000 0.250075 333.1932 0.2933637 272.5206
## 1.0000000 0.500050 330.7415 0.2946883 270.4532
## 1.0000000 0.750025 328.5459 0.2956393 268.7194
## 1.0000000 1.000000 326.5725 0.2963811 267.4339
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 0 and lambda = 1.plot(elasticModel)
plot(varImp(elasticModel, scale = TRUE))
Findings of Elastic-Net Regression
- We can see that the least RMSE is 316.3624 and the recommended alpha is 0 and lambda is 1.
- Also the Elastic-Net Regression shows that the below variables significantly contribute to the dependent variable SQRT.S.B.
- CAPTAINCY.EXP
- L25
- OTHERS
- INDIA
- B25.35
- AUSTRALIA
- BAT
- Year
- ALL
- A35
Compare the 4 models
modelList <- list (linear = linearModel, lasso = lassoModel, ridge = ridgeModel, elastic = elasticModel)
modelComparison <- resamples(modelList)
summary (modelComparison)##
## Call:
## summary.resamples(object = modelComparison)
##
## Models: linear, lasso, ridge, elastic
## Number of resamples: 50
##
## MAE
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## linear 94.90724 232.0795 267.3368 275.1020 309.4318 445.5510 0
## lasso 99.61402 229.8958 259.2751 267.4339 303.2953 432.1984 0
## ridge 104.05325 223.4995 252.6031 259.4783 295.6658 425.4602 0
## elastic 104.05325 223.4995 252.6031 259.4783 295.6658 425.4602 0
##
## RMSE
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## linear 105.5140 271.2796 324.3533 336.4882 397.4152 577.1842 0
## lasso 113.3644 261.6002 315.3057 326.5725 386.4215 556.1973 0
## ridge 121.0110 258.4110 303.6545 316.3624 371.6800 546.0811 0
## elastic 121.0110 258.4110 303.6545 316.3624 371.6800 546.0811 0
##
## Rsquared
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## linear 2.511387e-05 0.1055304 0.2460802 0.2917763 0.4686587 0.9383782 0
## lasso 3.279814e-06 0.1050043 0.2593284 0.2963811 0.4651699 0.9350176 0
## ridge 5.674389e-05 0.1250421 0.2896259 0.3192681 0.4853880 0.9375848 0
## elastic 5.674389e-05 0.1250421 0.2896259 0.3192681 0.4853880 0.9375848 0Findings from comparing the models
- Ridge model has the least RMSE among the 4 models.
- We can see that the below variables are common across the 3 models (Ridge, Lasso and Elastic-Net) that are significantly contributing to the Pricing of the Player.
- Captaincy Experience (CAPTAINCY.EXP)
- Age of the player being up to 25 years or below 35 years (L25, B25.35)
- Player being from India, Australia and other countries (INDIA, AUSTRALIA, OTHERS)
- Player being a Batsman or All-Rounder (BAT, ALL)
- The year in which the player joined IPL (Year)
Find the Best Model
ridgeModel$bestTune## alpha lambda
## 5 0 1lassoModel$bestTune## alpha lambda
## 5 1 1elasticModel$bestTune## alpha lambda
## 5 0 1Findings
- There are 5 variables that are significantly contributing to the pricing with Alpha being 0 and Lambda being 1
- CAPTAINCY.EXP
- L25
- OTHERS
- INDIA
- B25.35
Examine the coefficients of Ridge Model
bestModel <- ridgeModel$finalModel
coef(bestModel, s = ridgeModel$bestTune$lambda)## 28 x 1 sparse Matrix of class "dgCMatrix"
## 1
## (Intercept) -4.325920e+04
## L25 1.437221e+02
## B25.35 -3.825291e+01
## A35 -1.318471e+01
## RUNS.S 1.047020e-01
## RUNS.C 1.228217e-01
## HS -7.727037e-01
## AVE 1.890611e+00
## AVE.BL 1.288837e+00
## SR..B -3.599746e-01
## SR..BL -1.261645e+00
## SIXERS 2.366044e+00
## WKTS 9.222959e-01
## ECON -1.844224e+00
## CAPTAINCY.EXP 1.751146e+02
## ODI.SR.B 2.992131e-01
## ODI.SR.BL -1.046566e+00
## ODI.RUNS 2.546127e-02
## ODI.WKTS 6.195488e-01
## T.RUNS -2.562485e-02
## T.WKTS -1.071907e-01
## BAT -2.404488e+01
## BOW 4.258354e+00
## ALL 2.140721e+01
## INDIA 1.204468e+02
## AUSTRALIA 3.344905e+01
## OTHERS -1.347188e+02
## Year 2.166016e+01Prediction comparing the Training Data and Testing Data
predictionOne <- predict(ridgeModel, trainData)
sqrt(mean((trainData$SQRT.S.B.-predictionOne)^2))## [1] 241.6788predictionTwo <- predict(ridgeModel, testData)
sqrt(mean((testData$SQRT.S.B..-predictionTwo)^2))## [1] NaNConclusions
- The RMSE with the Ridge Regression is 241.6788 which is the least.
- The most important variables that are contributing to the pricing and their coefficients are:
- Captaincy Experience = 0.0175
- Age being under 25 years = 0.0144
- Player being from countries other than India & Australia = -0.0135
- Player being from India = 0.0120
- Player being in the age of 25 to 35 = -0.382
- It is unclear for us how to interpret the NaN for RMSE of Test Data.