Load Package
library(readxl)
library(RcmdrMisc)
## Loading required package: car
## Warning: package 'car' was built under R version 4.0.4
## Loading required package: carData
## Loading required package: sandwich
library(olsrr)
## Warning: package 'olsrr' was built under R version 4.0.5
##
## Attaching package: 'olsrr'
## The following object is masked from 'package:datasets':
##
## rivers
library(dplyr)
##
## Attaching package: 'dplyr'
## The following object is masked from 'package:car':
##
## recode
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(DataExplorer)
## Warning: package 'DataExplorer' was built under R version 4.0.5
library(performance)
## Warning: package 'performance' was built under R version 4.0.5
library(sjPlot)
## Warning: package 'sjPlot' was built under R version 4.0.5
## Registered S3 methods overwritten by 'lme4':
## method from
## cooks.distance.influence.merMod car
## influence.merMod car
## dfbeta.influence.merMod car
## dfbetas.influence.merMod car
library(fBasics)
## Warning: package 'fBasics' was built under R version 4.0.5
## Loading required package: timeDate
## Loading required package: timeSeries
## Warning: package 'timeSeries' was built under R version 4.0.5
##
## Attaching package: 'fBasics'
## The following object is masked from 'package:car':
##
## densityPlot
library(qqplotr)
## Warning: package 'qqplotr' was built under R version 4.0.5
## Loading required package: ggplot2
##
## Attaching package: 'qqplotr'
## The following objects are masked from 'package:ggplot2':
##
## stat_qq_line, StatQqLine
library(ggstatsplot)
## Warning: package 'ggstatsplot' was built under R version 4.0.5
## You can cite this package as:
## Patil, I. (2021). Visualizations with statistical details: The 'ggstatsplot' approach.
## PsyArxiv. doi:10.31234/osf.io/p7mku
library(PerformanceAnalytics)
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following object is masked from 'package:timeSeries':
##
## time<-
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
## Attaching package: 'xts'
## The following objects are masked from 'package:dplyr':
##
## first, last
##
## Attaching package: 'PerformanceAnalytics'
## The following objects are masked from 'package:timeDate':
##
## kurtosis, skewness
## The following object is masked from 'package:graphics':
##
## legend
library(see)
## Warning: package 'see' was built under R version 4.0.5
Preparing Data
antar=read_excel("E:\\Praktikum13.xlsx",sheet="Sheet1")
## New names:
## * `` -> ...1
antar
## # A tibble: 13 x 6
## ...1 x1 x2 x3 x4 y
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1999 379558. 3.31 7100 210611000 24003.
## 2 2000 1389770. 10.3 9595 213395000 33515.
## 3 2001 1440406. 11.8 20266 216203000 30962.
## 4 2002 1505216. 9 9261 219026000 31289.
## 5 2003 1577171. 5.92 8571 221839000 32551.
## 6 2004 1656517. 6.35 9030 224607000 46525.
## 7 2005 1750815. 15.6 9751 227303000 57701.
## 8 2006 1847127. 5.66 9141 229919000 61066.
## 9 2007 1964327. 6.48 9142 232462000 74473.
## 10 2008 2082456. 4.15 9772 234951000 129197.
## 11 2009 2177742. 3.45 10356 237414000 96856.
## 12 2010 2310690. 5.96 9078 239871000 135606.
## 13 2011 1838058. 4.23 8731 242326000 156130.
Eksplorasi
plot_scatterplot(data = antar[,-1], by="y",geom_point_args= list(color="steelblue") )
ggcorrmat(data = antar %>% select(-1,-y))
#melihat matriks korelasi
chart.Correlation(antar[,-1], histogram=FALSE, pch=19)
model regresi berganda
regresi=lm(y~x1+x2+x3+x4,data=antar) #full model
regresi
##
## Call:
## lm(formula = y ~ x1 + x2 + x3 + x4, data = antar)
##
## Coefficients:
## (Intercept) x1 x2 x3 x4
## -1.082e+06 -3.088e-02 -5.043e+02 1.252e+00 5.267e-03
summary(regresi)
##
## Call:
## lm(formula = y ~ x1 + x2 + x3 + x4, data = antar)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19428.4 -12879.7 -858.6 9803.5 27917.0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.082e+06 2.747e+05 -3.939 0.00430 **
## x1 -3.088e-02 2.639e-02 -1.170 0.27567
## x2 -5.043e+02 2.038e+03 -0.247 0.81081
## x3 1.252e+00 2.078e+00 0.602 0.56356
## x4 5.267e-03 1.328e-03 3.966 0.00414 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19850 on 8 degrees of freedom
## Multiple R-squared: 0.872, Adjusted R-squared: 0.8079
## F-statistic: 13.62 on 4 and 8 DF, p-value: 0.001206
Model Checking
check_normality(regresi,effects="random")
## OK: residuals appear as normally distributed (p = 0.063).
plot(check_normality(regresi,effects="random"))
## OK: residuals appear as normally distributed (p = 0.063).
check_model(regresi,panel=T)
check_distribution(regresi)
## # Distribution of Model Family
##
## Predicted Distribution of Residuals
##
## Distribution Probability
## lognormal 34%
## normal 34%
## weibull 12%
##
## Predicted Distribution of Response
##
## Distribution Probability
## lognormal 81%
## exponential 6%
## uniform 6%
plot(check_distribution(regresi))
## Warning: Removed 4 rows containing missing values (geom_segment).
## Warning: Removed 4 rows containing missing values (geom_point).
m1<-lm(y~x1+x2+x3+x4,data=antar) #full model
m2<-lm(y~x1+x3+x4,data=antar)
m3<-lm(y~x1+x4,data=antar)
m4<-lm(y~x4,data=antar)
compare_performance(m1,m2,m3,m4)
## # Comparison of Model Performance Indices
##
## Name | Model | AIC | BIC | R2 | R2 (adj.) | RMSE | Sigma
## ----------------------------------------------------------------------------
## m1 | lm | 299.878 | 303.267 | 0.872 | 0.808 | 15572.818 | 19851.525
## m2 | lm | 297.977 | 300.802 | 0.871 | 0.828 | 15632.287 | 18787.671
## m3 | lm | 296.465 | 298.725 | 0.866 | 0.839 | 15928.702 | 18161.515
## m4 | lm | 296.762 | 298.457 | 0.840 | 0.826 | 17400.008 | 18915.803
plot(compare_performance(m1,m2,m3,m4))
#corelation partial
a=data.frame(antar$x1,antar$x2,antar$y)
partial.cor(a)
##
## Partial correlations:
## antar.x1 antar.x2 antar.y
## antar.x1 0.00000 0.34596 0.73343
## antar.x2 0.34596 0.00000 -0.52061
## antar.y 0.73343 -0.52061 0.00000
##
## Number of observations: 13
backward Elimination
bkward=ols_step_backward_p(regresi, prem = 0.1,details = TRUE)
## Backward Elimination Method
## ---------------------------
##
## Candidate Terms:
##
## 1 . x1
## 2 . x2
## 3 . x3
## 4 . x4
##
## We are eliminating variables based on p value...
##
## - x2
##
## Backward Elimination: Step 1
##
## Variable x2 Removed
##
## Model Summary
## ---------------------------------------------------------------------
## R 0.933 RMSE 18787.671
## R-Squared 0.871 Coef. Var 26.843
## Adj. R-Squared 0.828 MSE 352976562.982
## Pred R-Squared 0.735 MAE 13030.421
## ---------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------------
## Regression 21445330488.166 3 7148443496.055 20.252 2e-04
## Residual 3176789066.834 9 352976562.982
## Total 24622119555.000 12
## ------------------------------------------------------------------------------
##
## Parameter Estimates
## ---------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ---------------------------------------------------------------------------------------------------------
## (Intercept) -1116203.978 224622.029 -4.969 0.001 -1624334.309 -608073.647
## x1 -0.034 0.023 -0.359 -1.466 0.177 -0.085 0.018
## x3 1.109 1.888 0.078 0.587 0.572 -3.164 5.381
## x4 0.005 0.001 1.236 4.953 0.001 0.003 0.008
## ---------------------------------------------------------------------------------------------------------
##
##
## - x3
##
## Backward Elimination: Step 2
##
## Variable x3 Removed
##
## Model Summary
## ---------------------------------------------------------------------
## R 0.931 RMSE 18161.515
## R-Squared 0.866 Coef. Var 25.949
## Adj. R-Squared 0.839 MSE 329840623.858
## Pred R-Squared 0.787 MAE 14111.311
## ---------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## -------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -------------------------------------------------------------------------------
## Regression 21323713316.418 2 10661856658.209 32.324 0.0000
## Residual 3298406238.582 10 329840623.858
## Total 24622119555.000 12
## -------------------------------------------------------------------------------
##
## Parameter Estimates
## ---------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ---------------------------------------------------------------------------------------------------------
## (Intercept) -1051096.141 188815.248 -5.567 0.000 -1471802.731 -630389.551
## x1 -0.028 0.020 -0.303 -1.390 0.195 -0.074 0.017
## x4 0.005 0.001 1.173 5.388 0.000 0.003 0.007
## ---------------------------------------------------------------------------------------------------------
##
##
## - x1
##
## Backward Elimination: Step 3
##
## Variable x1 Removed
##
## Model Summary
## ---------------------------------------------------------------------
## R 0.917 RMSE 18915.803
## R-Squared 0.840 Coef. Var 27.026
## Adj. R-Squared 0.826 MSE 357807598.508
## Pred R-Squared 0.766 MAE 16333.415
## ---------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## -------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -------------------------------------------------------------------------------
## Regression 20686235971.408 1 20686235971.408 57.814 0.0000
## Residual 3935883583.592 11 357807598.508
## Total 24622119555.000 12
## -------------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------------------
## (Intercept) -843383.027 120239.219 -7.014 0.000 -1108027.763 -578738.291
## x4 0.004 0.001 0.917 7.604 0.000 0.003 0.005
## --------------------------------------------------------------------------------------------------------
##
##
##
## No more variables satisfy the condition of p value = 0.1
##
##
## Variables Removed:
##
## - x2
## - x3
## - x1
##
##
## Final Model Output
## ------------------
##
## Model Summary
## ---------------------------------------------------------------------
## R 0.917 RMSE 18915.803
## R-Squared 0.840 Coef. Var 27.026
## Adj. R-Squared 0.826 MSE 357807598.508
## Pred R-Squared 0.766 MAE 16333.415
## ---------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## -------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -------------------------------------------------------------------------------
## Regression 20686235971.408 1 20686235971.408 57.814 0.0000
## Residual 3935883583.592 11 357807598.508
## Total 24622119555.000 12
## -------------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------------------
## (Intercept) -843383.027 120239.219 -7.014 0.000 -1108027.763 -578738.291
## x4 0.004 0.001 0.917 7.604 0.000 0.003 0.005
## --------------------------------------------------------------------------------------------------------
forward Selection
forward=ols_step_forward_p(regresi, penter = 0.1,details = TRUE)
## Forward Selection Method
## ---------------------------
##
## Candidate Terms:
##
## 1. x1
## 2. x2
## 3. x3
## 4. x4
##
## We are selecting variables based on p value...
##
##
## Forward Selection: Step 1
##
## - x4
##
## Model Summary
## ---------------------------------------------------------------------
## R 0.917 RMSE 18915.803
## R-Squared 0.840 Coef. Var 27.026
## Adj. R-Squared 0.826 MSE 357807598.508
## Pred R-Squared 0.766 MAE 16333.415
## ---------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## -------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -------------------------------------------------------------------------------
## Regression 20686235971.408 1 20686235971.408 57.814 0.0000
## Residual 3935883583.592 11 357807598.508
## Total 24622119555.000 12
## -------------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------------------
## (Intercept) -843383.027 120239.219 -7.014 0.000 -1108027.763 -578738.291
## x4 0.004 0.001 0.917 7.604 0.000 0.003 0.005
## --------------------------------------------------------------------------------------------------------
##
##
##
## No more variables to be added.
##
## Variables Entered:
##
## + x4
##
##
## Final Model Output
## ------------------
##
## Model Summary
## ---------------------------------------------------------------------
## R 0.917 RMSE 18915.803
## R-Squared 0.840 Coef. Var 27.026
## Adj. R-Squared 0.826 MSE 357807598.508
## Pred R-Squared 0.766 MAE 16333.415
## ---------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## -------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -------------------------------------------------------------------------------
## Regression 20686235971.408 1 20686235971.408 57.814 0.0000
## Residual 3935883583.592 11 357807598.508
## Total 24622119555.000 12
## -------------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------------------
## (Intercept) -843383.027 120239.219 -7.014 0.000 -1108027.763 -578738.291
## x4 0.004 0.001 0.917 7.604 0.000 0.003 0.005
## --------------------------------------------------------------------------------------------------------
stepwise regression
stepw=ols_step_both_p(regresi, penter = 0.15, prem = 0.15,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
##
## - x4 added
##
## Model Summary
## ---------------------------------------------------------------------
## R 0.917 RMSE 18915.803
## R-Squared 0.840 Coef. Var 27.026
## Adj. R-Squared 0.826 MSE 357807598.508
## Pred R-Squared 0.766 MAE 16333.415
## ---------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## -------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -------------------------------------------------------------------------------
## Regression 20686235971.408 1 20686235971.408 57.814 0.0000
## Residual 3935883583.592 11 357807598.508
## Total 24622119555.000 12
## -------------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------------------
## (Intercept) -843383.027 120239.219 -7.014 0.000 -1108027.763 -578738.291
## x4 0.004 0.001 0.917 7.604 0.000 0.003 0.005
## --------------------------------------------------------------------------------------------------------
##
##
##
## No more variables to be added/removed.
##
##
## Final Model Output
## ------------------
##
## Model Summary
## ---------------------------------------------------------------------
## R 0.917 RMSE 18915.803
## R-Squared 0.840 Coef. Var 27.026
## Adj. R-Squared 0.826 MSE 357807598.508
## Pred R-Squared 0.766 MAE 16333.415
## ---------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## -------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -------------------------------------------------------------------------------
## Regression 20686235971.408 1 20686235971.408 57.814 0.0000
## Residual 3935883583.592 11 357807598.508
## Total 24622119555.000 12
## -------------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------------------
## (Intercept) -843383.027 120239.219 -7.014 0.000 -1108027.763 -578738.291
## x4 0.004 0.001 0.917 7.604 0.000 0.003 0.005
## --------------------------------------------------------------------------------------------------------