Pembentukan Model Terbaik - All Possible Regression dan Stepwise Regression Dengan RStudio
baalgainti
4/24/2020
Halo teman - teman, pada kesempatan kali ini gua akan berusaha memberikan tutorial alakadar tentang Pembentukan Model Regresi Terbaik dengan Metode All Possible Regression dan Stepwise Regression dengan menggunakan Rstudio. Tutorial ini khusus buat 2ST5 yang unch.
Sebagai contoh, kita disini menggunakan soal kuis Anareg kelas 2ST8, soalnya minta sendiri aja ya ke 2ST8 atogak 2ST3 atogak 2ST4
Ohiya jangan lupa install packagenya dulu install.packages(“olsrr”)
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversterakhir, karena gua gapaham cara import data kalo pas bikin rmarkdown (audah gabisa bisa), jadinya gua input dulu datanya
X1 <- c(185,600,372,142,432,290,346,328,354,266,320,197,266,173,190,239,190,241,189,358)
X2<- c(4,0.6,3.7,2.4,29.8,3.3,3.3,0.7,12.9,6.5,1.1,1,11.4,5.5,2.8,2.5,3.7,4.2,1.2,4.8)
X3 <- c(80,1,32,45,191,32,678,341,240,112,173,12,206,155,50,30,93,97,40,489)
X4 <- c(7.2,8.5,5.7,7.3,7.5,5,6.7,6.2,7.3,5,2.8,6.1,7.1,5.9,4.6,4.4,7.4,7.1,7.5,5.9)
Y <- c(521,367,443,365,614,385,286,397,764,427,153,231,524,328,240,286,285,569,96,498)
data <- data.frame(X1,X2,X3,X4,Y)All Possible Regression
Langsung aja gausah banyak cincong, scriptnya cuma gini ya gaes
model <- lm(Y~X1 + X2 + X3 + X4)
ols_step_all_possible(model)## Index N Predictors R-Square Adj. R-Square Mallow's Cp
## 2 1 1 X2 0.39055644 0.356698466 0.9930621
## 4 2 1 X4 0.15016950 0.102956693 7.6957504
## 1 3 1 X1 0.10039047 0.050412158 9.0837349
## 3 4 1 X3 0.03200334 -0.021774249 10.9905671
## 9 5 2 X2 X4 0.44207418 0.376435847 1.5565974
## 5 6 2 X1 X2 0.41427055 0.345361200 2.3318437
## 8 7 2 X2 X3 0.39890000 0.328182353 2.7604193
## 7 8 2 X1 X4 0.20943122 0.116423127 8.0433610
## 10 9 2 X3 X4 0.17839982 0.081740976 8.9086068
## 6 10 2 X1 X3 0.11154370 0.007019426 10.7727503
## 12 11 3 X1 X2 X4 0.45732619 0.355574853 3.1313269
## 14 12 3 X2 X3 X4 0.45086143 0.347897954 3.3115831
## 11 13 3 X1 X2 X3 0.41786224 0.308711414 4.2316968
## 13 14 3 X1 X3 X4 0.22215151 0.076304923 9.6886821
## 15 15 4 X1 X2 X3 X4 0.46203613 0.318579102 5.0000000plot(ols_step_all_possible(model))
ols_step_best_subset(model)## Best Subsets Regression
## --------------------------
## Model Index Predictors
## --------------------------
## 1 X2
## 2 X2 X4
## 3 X1 X2 X4
## 4 X1 X2 X3 X4
## --------------------------
##
## Subsets Regression Summary
## -------------------------------------------------------------------------------------------------------------------------------------------
## Adj. Pred
## Model R-Square R-Square R-Square C(p) AIC SBIC SBC MSEP FPE HSP APC
## -------------------------------------------------------------------------------------------------------------------------------------------
## 1 0.3906 0.3567 -0.5511 0.9931 255.4317 199.3194 258.4189 339554.6892 18664.5288 998.1031 0.7449
## 2 0.4421 0.3764 -0.515 1.5566 255.6653 200.4584 259.6483 330279.5170 18914.2332 1027.9475 0.7548
## 3 0.4573 0.3556 -0.85 3.1313 257.1110 202.7205 262.0896 342667.3801 20396.8679 1133.1593 0.8140
## 4 0.4620 0.3186 -1.1731 5.0000 258.9366 205.2902 264.9110 363957.1315 22466.4896 1283.7994 0.8966
## -------------------------------------------------------------------------------------------------------------------------------------------
## AIC: Akaike Information Criteria
## SBIC: Sawa's Bayesian Information Criteria
## SBC: Schwarz Bayesian Criteria
## MSEP: Estimated error of prediction, assuming multivariate normality
## FPE: Final Prediction Error
## HSP: Hocking's Sp
## APC: Amemiya Prediction Criteriaplot(ols_step_best_subset(model))
StepWise Regression
model <- lm(Y ~ ., data = data)
ols_step_both_p(model, details = TRUE)## Stepwise Selection Method
## ---------------------------
##
## Candidate Terms:
##
## 1. X1
## 2. X2
## 3. X3
## 4. X4
##
## We are selecting variables based on p value...
##
##
## Stepwise Selection: Step 1
##
## - X2 added
##
## Model Summary
## ------------------------------------------------------------------
## R 0.625 RMSE 130.260
## R-Squared 0.391 Coef. Var 33.490
## Adj. R-Squared 0.357 MSE 16967.753
## Pred R-Squared -0.551 MAE 103.478
## ------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ----------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ----------------------------------------------------------------------
## Regression 195725.388 1 195725.388 11.535 0.0032
## Residual 305419.562 18 16967.753
## Total 501144.950 19
## ----------------------------------------------------------------------
##
## Parameter Estimates
## ------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ------------------------------------------------------------------------------------------
## (Intercept) 308.103 37.617 8.191 0.000 229.072 387.133
## X2 15.341 4.517 0.625 3.396 0.003 5.851 24.831
## ------------------------------------------------------------------------------------------
##
##
##
## No more variables to be added/removed.
##
##
## Final Model Output
## ------------------
##
## Model Summary
## ------------------------------------------------------------------
## R 0.625 RMSE 130.260
## R-Squared 0.391 Coef. Var 33.490
## Adj. R-Squared 0.357 MSE 16967.753
## Pred R-Squared -0.551 MAE 103.478
## ------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ----------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ----------------------------------------------------------------------
## Regression 195725.388 1 195725.388 11.535 0.0032
## Residual 305419.562 18 16967.753
## Total 501144.950 19
## ----------------------------------------------------------------------
##
## Parameter Estimates
## ------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ------------------------------------------------------------------------------------------
## (Intercept) 308.103 37.617 8.191 0.000 229.072 387.133
## X2 15.341 4.517 0.625 3.396 0.003 5.851 24.831
## ------------------------------------------------------------------------------------------##
## Stepwise Selection Summary
## --------------------------------------------------------------------------------------
## Added/ Adj.
## Step Variable Removed R-Square R-Square C(p) AIC RMSE
## --------------------------------------------------------------------------------------
## 1 X2 addition 0.391 0.357 0.9930 255.4317 130.2603
## --------------------------------------------------------------------------------------dah begitu aja, selamat belajar