3338230009_Studi Kasus Konsultasi Statistika
Zahra Mahendra Putri (3338230009)
2026-04-03
data asli
library(readxl)
datastudi <- read_excel("C:/Users/Zahra Mahendra Putri/OneDrive - untirta.ac.id/Documents/STATISTIKA UNTIRTA/MATA KULIAH/SEMESTER 6/Konsultasi Statistika/studikasus.xlsx")
datastudi## # A tibble: 24 × 6
## Perlakuan Waktu Warna Aroma Rasa Tekstur
## <chr> <chr> <dbl> <dbl> <dbl> <dbl>
## 1 A H7 2.67 2.58 2.76 2.56
## 2 A H7 2.69 2.71 2.73 2.84
## 3 A H7 2.62 2.71 2.62 2.8
## 4 A H14 2.69 2.78 2.93 2.76
## 5 A H14 2.67 2.64 2.58 2.4
## 6 A H14 2.76 2.87 2.73 2.51
## 7 B H7 2.69 2.71 2.69 2.78
## 8 B H7 2.71 2.78 2.78 2.64
## 9 B H7 2.96 2.91 2.69 2.93
## 10 B H14 2.84 2.78 3.04 2.98
## # ℹ 14 more rowslibrary(readxl)
data1 <- read_excel("C:/Users/Zahra Mahendra Putri/OneDrive - untirta.ac.id/Documents/STATISTIKA UNTIRTA/MATA KULIAH/SEMESTER 6/Konsultasi Statistika/studikasus.xlsx",
sheet = "data1")
data2 <- read_excel("C:/Users/Zahra Mahendra Putri/OneDrive - untirta.ac.id/Documents/STATISTIKA UNTIRTA/MATA KULIAH/SEMESTER 6/Konsultasi Statistika/studikasus.xlsx",
sheet = "data2")
data3 <- read_excel("C:/Users/Zahra Mahendra Putri/OneDrive - untirta.ac.id/Documents/STATISTIKA UNTIRTA/MATA KULIAH/SEMESTER 6/Konsultasi Statistika/studikasus.xlsx",
sheet = "data3")DATA 1
karakteristik data
summary(data1)## Perlakuan Waktu Warna Aroma
## Length:24 Length:24 Min. :2.620 Min. :2.580
## Class :character Class :character 1st Qu.:2.705 1st Qu.:2.763
## Mode :character Mode :character Median :2.925 Median :2.945
## Mean :3.015 Mean :3.031
## 3rd Qu.:3.248 3rd Qu.:3.295
## Max. :3.690 Max. :3.670
## Rasa Tekstur
## Min. :2.580 Min. :2.400
## 1st Qu.:2.730 1st Qu.:2.775
## Median :3.065 Median :3.065
## Mean :3.033 Mean :3.051
## 3rd Qu.:3.290 3rd Qu.:3.315
## Max. :3.640 Max. :3.710Uji Asumsi : Uji Normalitas
- Cek outlier menggunakan boxplot
boxplot(data1$Warna, main="Boxplot Warna")
boxplot(data1$Aroma, main="Boxplot Aroma")
boxplot(data1$Rasa, main="Boxplot Rasa")
boxplot(data1$Tekstur, main="Boxplot Tekstur")
par(mfrow = c(2,2))
boxplot(data1$Warna, main="Warna", col="lightblue")
boxplot(data1$Aroma, main="Aroma", col="lightgreen")
boxplot(data1$Rasa, main="Rasa", col="lightpink")
boxplot(data1$Tekstur, main="Tekstur", col="lightyellow")
2. Model Anova 2.1 Warna
model_warna <- aov(Warna ~ Perlakuan * Waktu, data = data1)
shapiro.test(residuals(model_warna))##
## Shapiro-Wilk normality test
##
## data: residuals(model_warna)
## W = 0.86843, p-value = 0.004902dikarenakan uji normalitas variabel warna tidak normal maka :
data1$Warna_ln <- log(data1$Warna)
model_warna_ln <- aov(Warna_ln ~ Perlakuan * Waktu, data = data1)
shapiro.test(residuals(model_warna_ln))##
## Shapiro-Wilk normality test
##
## data: residuals(model_warna_ln)
## W = 0.88607, p-value = 0.011042.2 Aroma
model_aroma <- aov(Aroma ~ Perlakuan * Waktu, data = data1)
shapiro.test(residuals(model_aroma))##
## Shapiro-Wilk normality test
##
## data: residuals(model_aroma)
## W = 0.96479, p-value = 0.54182.3 Rasa
model_rasa <- aov(Rasa ~ Perlakuan * Waktu, data = data1)
shapiro.test(residuals(model_rasa))##
## Shapiro-Wilk normality test
##
## data: residuals(model_rasa)
## W = 0.95572, p-value = 0.35862.4 Tekstur
model_tekstur <- aov(Tekstur ~ Perlakuan * Waktu, data = data1)
shapiro.test(residuals(model_tekstur))##
## Shapiro-Wilk normality test
##
## data: residuals(model_tekstur)
## W = 0.97694, p-value = 0.8335Homogenitas
library(car)## Loading required package: carDataleveneTest(Warna ~ Perlakuan * Waktu, data = data1)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 7 1.5156 0.2315
## 16leveneTest(Aroma ~ Perlakuan * Waktu, data = data1)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 7 0.5773 0.7644
## 16leveneTest(Rasa ~ Perlakuan * Waktu, data = data1)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 7 0.7804 0.6129
## 16leveneTest(Tekstur ~ Perlakuan * Waktu, data = data1)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 7 0.4227 0.8741
## 16Anova dua arah
- Warna
summary(model_warna)## Df Sum Sq Mean Sq F value Pr(>F)
## Perlakuan 3 1.9578 0.6526 23.071 4.71e-06 ***
## Waktu 1 0.0852 0.0852 3.012 0.102
## Perlakuan:Waktu 3 0.0545 0.0182 0.643 0.599
## Residuals 16 0.4526 0.0283
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Aroma
summary(model_aroma)## Df Sum Sq Mean Sq F value Pr(>F)
## Perlakuan 3 1.9388 0.6463 16.838 3.32e-05 ***
## Waktu 1 0.0400 0.0400 1.043 0.322
## Perlakuan:Waktu 3 0.0126 0.0042 0.109 0.953
## Residuals 16 0.6141 0.0384
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Rasa
summary(model_rasa)## Df Sum Sq Mean Sq F value Pr(>F)
## Perlakuan 3 1.7342 0.5781 19.532 1.35e-05 ***
## Waktu 1 0.0840 0.0840 2.839 0.111
## Perlakuan:Waktu 3 0.0258 0.0086 0.290 0.832
## Residuals 16 0.4735 0.0296
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Tekstur
summary(model_tekstur)## Df Sum Sq Mean Sq F value Pr(>F)
## Perlakuan 3 2.3145 0.7715 20.831 9e-06 ***
## Waktu 1 0.0353 0.0353 0.952 0.344
## Perlakuan:Waktu 3 0.1548 0.0516 1.393 0.281
## Residuals 16 0.5926 0.0370
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Uji Lanjut (Post-Hoc)
- Pada Warna
TukeyHSD(model_warna)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Warna ~ Perlakuan * Waktu, data = data1)
##
## $Perlakuan
## diff lwr upr p adj
## B-A 0.1083333 -0.1694828 0.3861495 0.6854623
## C-A 0.5266667 0.2488505 0.8044828 0.0002970
## D-A 0.6900000 0.4121838 0.9678162 0.0000136
## C-B 0.4183333 0.1405172 0.6961495 0.0027373
## D-B 0.5816667 0.3038505 0.8594828 0.0001009
## D-C 0.1633333 -0.1144828 0.4411495 0.3644715
##
## $Waktu
## diff lwr upr p adj
## H7-H14 -0.1191667 -0.2647253 0.02639201 0.1018615
##
## $`Perlakuan:Waktu`
## diff lwr upr p adj
## B:H14-A:H14 0.09000000 -0.38544208 0.56544208 0.9971723
## C:H14-A:H14 0.59000000 0.11455792 1.06544208 0.0100463
## D:H14-A:H14 0.79000000 0.31455792 1.26544208 0.0006113
## A:H7-A:H14 -0.04666667 -0.52210875 0.42877542 0.9999610
## B:H7-A:H14 0.08000000 -0.39544208 0.55544208 0.9986462
## C:H7-A:H14 0.41666667 -0.05877542 0.89210875 0.1089870
## D:H7-A:H14 0.54333333 0.06789125 1.01877542 0.0194561
## C:H14-B:H14 0.50000000 0.02455792 0.97544208 0.0356729
## D:H14-B:H14 0.70000000 0.22455792 1.17544208 0.0021192
## A:H7-B:H14 -0.13666667 -0.61210875 0.33877542 0.9686069
## B:H7-B:H14 -0.01000000 -0.48544208 0.46544208 1.0000000
## C:H7-B:H14 0.32666667 -0.14877542 0.80210875 0.3134991
## D:H7-B:H14 0.45333333 -0.02210875 0.92877542 0.0674032
## D:H14-C:H14 0.20000000 -0.27544208 0.67544208 0.8184975
## A:H7-C:H14 -0.63666667 -1.11210875 -0.16122458 0.0051783
## B:H7-C:H14 -0.51000000 -0.98544208 -0.03455792 0.0310467
## C:H7-C:H14 -0.17333333 -0.64877542 0.30210875 0.8999836
## D:H7-C:H14 -0.04666667 -0.52210875 0.42877542 0.9999610
## A:H7-D:H14 -0.83666667 -1.31210875 -0.36122458 0.0003262
## B:H7-D:H14 -0.71000000 -1.18544208 -0.23455792 0.0018425
## C:H7-D:H14 -0.37333333 -0.84877542 0.10210875 0.1861504
## D:H7-D:H14 -0.24666667 -0.72210875 0.22877542 0.6310042
## B:H7-A:H7 0.12666667 -0.34877542 0.60210875 0.9791194
## C:H7-A:H7 0.46333333 -0.01210875 0.93877542 0.0589276
## D:H7-A:H7 0.59000000 0.11455792 1.06544208 0.0100463
## C:H7-B:H7 0.33666667 -0.13877542 0.81210875 0.2820001
## D:H7-B:H7 0.46333333 -0.01210875 0.93877542 0.0589276
## D:H7-C:H7 0.12666667 -0.34877542 0.60210875 0.9791194- Pada Aroma
TukeyHSD(model_aroma)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Aroma ~ Perlakuan * Waktu, data = data1)
##
## $Perlakuan
## diff lwr upr p adj
## B-A 0.0900000 -0.23361719 0.4136172 0.8553683
## C-A 0.4733333 0.14971614 0.7969505 0.0035180
## D-A 0.7000000 0.37638281 1.0236172 0.0000698
## C-B 0.3833333 0.05971614 0.7069505 0.0176851
## D-B 0.6100000 0.28638281 0.9336172 0.0003153
## D-C 0.2266667 -0.09695052 0.5502839 0.2274506
##
## $Waktu
## diff lwr upr p adj
## H7-H14 -0.08166667 -0.2512223 0.08788895 0.3224198
##
## $`Perlakuan:Waktu`
## diff lwr upr p adj
## B:H14-A:H14 0.04666667 -0.507157218 0.600490551 0.9999862
## C:H14-A:H14 0.46666667 -0.087157218 1.020490551 0.1335141
## D:H14-A:H14 0.72000000 0.166176116 1.273823884 0.0067397
## A:H7-A:H14 -0.09666667 -0.650490551 0.457157218 0.9982941
## B:H7-A:H14 0.03666667 -0.517157218 0.590490551 0.9999974
## C:H7-A:H14 0.38333333 -0.170490551 0.937157218 0.3056843
## D:H7-A:H14 0.58333333 0.029509449 1.137157218 0.0352918
## C:H14-B:H14 0.42000000 -0.133823884 0.973823884 0.2160996
## D:H14-B:H14 0.67333333 0.119509449 1.227157218 0.0119060
## A:H7-B:H14 -0.14333333 -0.697157218 0.410490551 0.9822003
## B:H7-B:H14 -0.01000000 -0.563823884 0.543823884 1.0000000
## C:H7-B:H14 0.33666667 -0.217157218 0.890490551 0.4514648
## D:H7-B:H14 0.53666667 -0.017157218 1.090490551 0.0610467
## D:H14-C:H14 0.25333333 -0.300490551 0.807157218 0.7530354
## A:H7-C:H14 -0.56333333 -1.117157218 -0.009509449 0.0447189
## B:H7-C:H14 -0.43000000 -0.983823884 0.123823884 0.1955816
## C:H7-C:H14 -0.08333333 -0.637157218 0.470490551 0.9993379
## D:H7-C:H14 0.11666667 -0.437157218 0.670490551 0.9945823
## A:H7-D:H14 -0.81666667 -1.370490551 -0.262842782 0.0020872
## B:H7-D:H14 -0.68333333 -1.237157218 -0.129509449 0.0105400
## C:H7-D:H14 -0.33666667 -0.890490551 0.217157218 0.4514648
## D:H7-D:H14 -0.13666667 -0.690490551 0.417157218 0.9863692
## B:H7-A:H7 0.13333333 -0.420490551 0.687157218 0.9881554
## C:H7-A:H7 0.48000000 -0.073823884 1.033823884 0.1155764
## D:H7-A:H7 0.68000000 0.126176116 1.233823884 0.0109771
## C:H7-B:H7 0.34666667 -0.207157218 0.900490551 0.4175588
## D:H7-B:H7 0.54666667 -0.007157218 1.100490551 0.0543578
## D:H7-C:H7 0.20000000 -0.353823884 0.753823884 0.9041441- Pada Rasa
TukeyHSD(model_rasa)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Rasa ~ Perlakuan * Waktu, data = data1)
##
## $Perlakuan
## diff lwr upr p adj
## B-A 0.0900000 -0.1941682 0.3741682 0.8018426
## C-A 0.5100000 0.2258318 0.7941682 0.0005224
## D-A 0.6333333 0.3491651 0.9175016 0.0000495
## C-B 0.4200000 0.1358318 0.7041682 0.0032172
## D-B 0.5433333 0.2591651 0.8275016 0.0002714
## D-C 0.1233333 -0.1608349 0.4075016 0.6107115
##
## $Waktu
## diff lwr upr p adj
## H7-H14 -0.1183333 -0.2672201 0.03055344 0.1114149
##
## $`Perlakuan:Waktu`
## diff lwr upr p adj
## B:H14-A:H14 0.163333333 -0.322979381 0.6496460 0.9314643
## C:H14-A:H14 0.576666667 0.090353953 1.0629794 0.0145738
## D:H14-A:H14 0.643333333 0.157020619 1.1296460 0.0057772
## A:H7-A:H14 -0.043333333 -0.529646047 0.4429794 0.9999798
## B:H7-A:H14 -0.026666667 -0.512979381 0.4596460 0.9999993
## C:H7-A:H14 0.400000000 -0.086312714 0.8863127 0.1502989
## D:H7-A:H14 0.580000000 0.093687286 1.0663127 0.0139163
## C:H14-B:H14 0.413333333 -0.072979381 0.8996460 0.1278296
## D:H14-B:H14 0.480000000 -0.006312714 0.9663127 0.0543780
## A:H7-B:H14 -0.206666667 -0.692979381 0.2796460 0.8112589
## B:H7-B:H14 -0.190000000 -0.676312714 0.2963127 0.8651620
## C:H7-B:H14 0.236666667 -0.249646047 0.7229794 0.6962619
## D:H7-B:H14 0.416666667 -0.069646047 0.9029794 0.1226899
## D:H14-C:H14 0.066666667 -0.419646047 0.5529794 0.9996387
## A:H7-C:H14 -0.620000000 -1.106312714 -0.1336873 0.0079876
## B:H7-C:H14 -0.603333333 -1.089646047 -0.1170206 0.0100682
## C:H7-C:H14 -0.176666667 -0.662979381 0.3096460 0.9015587
## D:H7-C:H14 0.003333333 -0.482979381 0.4896460 1.0000000
## A:H7-D:H14 -0.686666667 -1.172979381 -0.2003540 0.0031717
## B:H7-D:H14 -0.670000000 -1.156312714 -0.1836873 0.0039926
## C:H7-D:H14 -0.243333333 -0.729646047 0.2429794 0.6686854
## D:H7-D:H14 -0.063333333 -0.549646047 0.4229794 0.9997421
## B:H7-A:H7 0.016666667 -0.469646047 0.5029794 1.0000000
## C:H7-A:H7 0.443333333 -0.042979381 0.9296460 0.0877274
## D:H7-A:H7 0.623333333 0.137020619 1.1096460 0.0076262
## C:H7-B:H7 0.426666667 -0.059646047 0.9129794 0.1083432
## D:H7-B:H7 0.606666667 0.120353953 1.0929794 0.0096128
## D:H7-C:H7 0.180000000 -0.306312714 0.6663127 0.8930576- Pada Tekstur
TukeyHSD(model_tekstur)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Tekstur ~ Perlakuan * Waktu, data = data1)
##
## $Perlakuan
## diff lwr upr p adj
## B-A 0.2133333 -0.1045597 0.5312264 0.2588962
## C-A 0.7550000 0.4371069 1.0728931 0.0000233
## D-A 0.6550000 0.3371069 0.9728931 0.0001207
## C-B 0.5416667 0.2237736 0.8595597 0.0008740
## D-B 0.4416667 0.1237736 0.7595597 0.0053908
## D-C -0.1000000 -0.4178931 0.2178931 0.8049873
##
## $Waktu
## diff lwr upr p adj
## H7-H14 -0.07666667 -0.2432232 0.08988986 0.3436867
##
## $`Perlakuan:Waktu`
## diff lwr upr p adj
## B:H14-A:H14 0.376666667 -0.16736123 0.9206946 0.3053655
## C:H14-A:H14 0.880000000 0.33597210 1.4240279 0.0008135
## D:H14-A:H14 0.873333333 0.32930544 1.4173612 0.0008812
## A:H7-A:H14 0.176666667 -0.36736123 0.7206946 0.9417258
## B:H7-A:H14 0.226666667 -0.31736123 0.7706946 0.8251348
## C:H7-A:H14 0.806666667 0.26263877 1.3506946 0.0019767
## D:H7-A:H14 0.613333333 0.06930544 1.1573612 0.0215700
## C:H14-B:H14 0.503333333 -0.04069456 1.0473612 0.0805945
## D:H14-B:H14 0.496666667 -0.04736123 1.0406946 0.0870087
## A:H7-B:H14 -0.200000000 -0.74402790 0.3440279 0.8962102
## B:H7-B:H14 -0.150000000 -0.69402790 0.3940279 0.9748471
## C:H7-B:H14 0.430000000 -0.11402790 0.9740279 0.1807964
## D:H7-B:H14 0.236666667 -0.30736123 0.7806946 0.7938733
## D:H14-C:H14 -0.006666667 -0.55069456 0.5373612 1.0000000
## A:H7-C:H14 -0.703333333 -1.24736123 -0.1593054 0.0070767
## B:H7-C:H14 -0.653333333 -1.19736123 -0.1093054 0.0131619
## C:H7-C:H14 -0.073333333 -0.61736123 0.4706946 0.9996765
## D:H7-C:H14 -0.266666667 -0.81069456 0.2773612 0.6892349
## A:H7-D:H14 -0.696666667 -1.24069456 -0.1526388 0.0076874
## B:H7-D:H14 -0.646666667 -1.19069456 -0.1026388 0.0142948
## C:H7-D:H14 -0.066666667 -0.61069456 0.4773612 0.9998275
## D:H7-D:H14 -0.260000000 -0.80402790 0.2840279 0.7135677
## B:H7-A:H7 0.050000000 -0.49402790 0.5940279 0.9999751
## C:H7-A:H7 0.630000000 0.08597210 1.1740279 0.0175658
## D:H7-A:H7 0.436666667 -0.10736123 0.9806946 0.1686024
## C:H7-B:H7 0.580000000 0.03597210 1.1240279 0.0324246
## D:H7-B:H7 0.386666667 -0.15736123 0.9306946 0.2782169
## D:H7-C:H7 -0.193333333 -0.73736123 0.3506946 0.9108552Data 2
Karakteristik Data
data2 <- read_excel("C:/Users/Zahra Mahendra Putri/OneDrive - untirta.ac.id/Documents/STATISTIKA UNTIRTA/MATA KULIAH/SEMESTER 6/Konsultasi Statistika/studikasus.xlsx",
sheet = "data2")
summary(data2)## X1.1 X1.2 X1.3 X1.4 X2.1
## Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.00 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :3.00 Median :2.000 Median :1.000 Median :2.000 Median :1.000
## Mean :2.51 Mean :2.059 Mean :1.647 Mean :2.196 Mean :1.294
## 3rd Qu.:3.00 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:1.000
## Max. :4.00 Max. :4.000 Max. :4.000 Max. :4.000 Max. :3.000
## X2.2 X2.3 X2.4 X2.5
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :2.000 Median :1.000
## Mean :1.196 Mean :1.725 Mean :1.961 Mean :1.647
## 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :3.000 Max. :4.000 Max. :4.000 Max. :4.000
## Y1.1 Y1.2 Y1.3 Z1.1
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :2.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:4.000 1st Qu.:2.000
## Median :1.000 Median :1.000 Median :4.000 Median :3.000
## Mean :1.471 Mean :1.373 Mean :3.686 Mean :2.941
## 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :3.000 Max. :3.000 Max. :4.000 Max. :4.000
## Z1.2 Z1.3
## Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:1.000
## Median :3.000 Median :1.000
## Mean :2.941 Mean :1.824
## 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :3.000# X1 (Disiplin Kerja)
data2$X1<- rowMeans(data2[, c("X1.1","X1.2","X1.3","X1.4")])
# X2 (Emotional Quotient)
data2$X2 <- rowMeans(data2[, c("X2.1","X2.2","X2.3","X2.4","X2.5")])
# X3 (Kepuasan Kerja)
data2$X3 <- rowMeans(data2[, c("Z1.1","Z1.2","Z1.3")])
# Y (Kinerja)
data2$Y <- rowMeans(data2[, c("Y1.1","Y1.2","Y1.3")])Model Regresi
model_reg <- lm(Y ~ X1 + X2 + X3, data = data2)
summary(model_reg)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3, data = data2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.49480 -0.23221 -0.00473 0.21474 1.00696
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.8712 0.5325 3.514 0.000987 ***
## X1 0.1284 0.1121 1.146 0.257650
## X2 0.1987 0.1449 1.371 0.176753
## X3 -0.1073 0.1516 -0.708 0.482429
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5036 on 47 degrees of freedom
## Multiple R-squared: 0.1258, Adjusted R-squared: 0.06996
## F-statistic: 2.254 on 3 and 47 DF, p-value: 0.09439Cek outlier
par(mfrow = c(2,2))
boxplot(data2$Y, main = "Y")
boxplot(data2$X1, main = "X1")
boxplot(data2$X2, main = "X2")
boxplot(data2$X3, main = "X3")
## Model baru
cooksd <- cooks.distance(model_reg)
plot(cooksd, type="h")
abline(h = 4/length(cooksd), col="red")
which(cooksd > 4/length(cooksd))## 10 14 17 20 23 30
## 10 14 17 20 23 30data2[which(cooksd > 4/length(cooksd)), ]## # A tibble: 6 × 19
## X1.1 X1.2 X1.3 X1.4 X2.1 X2.2 X2.3 X2.4 X2.5 Y1.1 Y1.2 Y1.3 Z1.1
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 3 3 4 3 2 1 3 1 3 3 3 4 2
## 2 3 1 1 2 3 2 3 2 3 3 3 4 2
## 3 1 1 1 1 1 1 1 2 1 1 1 1 4
## 4 4 2 3 3 2 3 3 3 4 1 1 1 3
## 5 3 1 4 4 1 1 4 3 3 3 3 4 2
## 6 3 3 3 3 1 1 3 3 1 3 3 4 2
## # ℹ 6 more variables: Z1.2 <dbl>, Z1.3 <dbl>, X1 <dbl>, X2 <dbl>, X3 <dbl>,
## # Y <dbl>data_baru <- data2[-20, ]
model2 <- lm(Y ~ X1 + X2 + X3, data = data_baru)
summary(model2)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3, data = data_baru)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.80784 -0.22625 0.03737 0.15547 0.94145
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8469 0.5255 1.612 0.11389
## X1 0.1540 0.0973 1.582 0.12044
## X2 0.4602 0.1410 3.263 0.00208 **
## X3 0.1274 0.1434 0.888 0.37914
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4364 on 46 degrees of freedom
## Multiple R-squared: 0.2833, Adjusted R-squared: 0.2366
## F-statistic: 6.062 on 3 and 46 DF, p-value: 0.001446Uji Asumsi : Uji Normalitas – Shapiro Wilk
shapiro.test(residuals(model_reg))##
## Shapiro-Wilk normality test
##
## data: residuals(model_reg)
## W = 0.96256, p-value = 0.1072qqnorm(residuals(model_reg))
qqline(residuals(model_reg))
## Uji Asumsi : Auto Korelasi – Durbin Watson
durbinWatsonTest(model_reg)## lag Autocorrelation D-W Statistic p-value
## 1 0.1108094 1.696735 0.288
## Alternative hypothesis: rho != 0Uji heteroskedastisitas : Bp Test
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericbptest(model_reg)##
## studentized Breusch-Pagan test
##
## data: model_reg
## BP = 14.603, df = 3, p-value = 0.002189dikarenakan terjadi heteroskedastisitas maka :
data2$Y_log <- log(data2$Y)
model_reg_log <- lm(Y_log ~ X1 + X2 + X3, data = data2)
bptest(model_reg_log)##
## studentized Breusch-Pagan test
##
## data: model_reg_log
## BP = 8.3345, df = 3, p-value = 0.03958Uji Multikolinearitas
library(car)
vif(model_reg)## X1 X2 X3
## 1.127526 1.289677 1.153864data 3
data
data3 <- read_excel("C:/Users/Zahra Mahendra Putri/OneDrive - untirta.ac.id/Documents/STATISTIKA UNTIRTA/MATA KULIAH/SEMESTER 6/Konsultasi Statistika/studikasus.xlsx",
sheet = "data3")Karakteristik data
summary(data3)## Waktu Data Inflasi
## Min. :2026-01-03 00:00:00 Min. :0.01320
## 1st Qu.:2026-03-30 12:00:00 1st Qu.:0.03575
## Median :2026-06-26 12:00:00 Median :0.05620
## Mean :2026-06-27 00:00:00 Mean :0.06019
## 3rd Qu.:2026-09-23 06:00:00 3rd Qu.:0.07185
## Max. :2026-12-20 00:00:00 Max. :0.18380Identifikasi Pola Data
inflasi <- as.numeric(gsub("%", "", data3$`Data Inflasi`))
ts_inflasi <- ts(inflasi, start = c(2003,1), frequency = 12)
plot(ts_inflasi,
main = "Inflasi Bulanan 2003–2020",
ylab = "Inflasi (%)",
xlab = "Tahun",
col = "blue")
## cek stasioneritas
library(tseries)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zooadf.test(ts_inflasi)##
## Augmented Dickey-Fuller Test
##
## data: ts_inflasi
## Dickey-Fuller = -3.5936, Lag order = 5, p-value = 0.03499
## alternative hypothesis: stationarylibrary(forecast)
ndiffs(ts_inflasi) # tren## [1] 1nsdiffs(ts_inflasi) # musiman## [1] 0ARIMA
library(forecast)
model_arima <- auto.arima(ts_inflasi)
summary(model_arima)## Series: ts_inflasi
## ARIMA(2,1,0)(0,0,1)[12] with drift
##
## Coefficients:
## ar1 ar2 sma1 drift
## 0.1362 -0.1451 -0.8150 -3e-04
## s.e. 0.0678 0.0680 0.0548 2e-04
##
## sigma^2 = 6.291e-05: log likelihood = 730.31
## AIC=-1450.62 AICc=-1450.33 BIC=-1433.76
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.000142688 0.007839273 0.004000209 -1.026325 7.018252 0.1334602
## ACF1
## Training set 0.005910675check diagnotisc model
checkresiduals(model_arima)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,1,0)(0,0,1)[12] with drift
## Q* = 17.263, df = 21, p-value = 0.6951
##
## Model df: 3. Total lags used: 24Peramalan 12 bulan ke depan
forecast_12 <- forecast(model_arima, h = 12)
plot(forecast_12, main = "Forecast Inflasi selama 1 Tahun ke Depan")
forecast_12## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2021 0.01866747 0.0085016348 0.02883331 0.003120167 0.03421477
## Feb 2021 0.01632108 0.0009343061 0.03170785 -0.007210958 0.03985311
## Mar 2021 0.01500957 -0.0034861993 0.03350534 -0.013277269 0.04329641
## Apr 2021 0.01308146 -0.0078911978 0.03405412 -0.018993453 0.04515638
## May 2021 0.01268192 -0.0105626224 0.03592647 -0.022867542 0.04823139
## Jun 2021 0.01462941 -0.0107129541 0.03997177 -0.024128390 0.05338721
## Jul 2021 0.01879307 -0.0084826628 0.04606881 -0.022921565 0.06050771
## Aug 2021 0.01997370 -0.0091030219 0.04905042 -0.024495309 0.06444271
## Sep 2021 0.02068821 -0.0100841974 0.05146063 -0.026374128 0.06775056
## Oct 2021 0.02109605 -0.0112839027 0.05347599 -0.028424812 0.07061690
## Nov 2021 0.02026387 -0.0136475820 0.05417532 -0.031599220 0.07212696
## Dec 2021 0.02018462 -0.0151920547 0.05556130 -0.033919337 0.07428858Evaluasi Model
# Fitted value
fitted_val <- fitted(model_arima)
# MAE
MAE <- mean(abs(ts_inflasi - fitted_val), na.rm = TRUE)
# MAPE
MAPE <- mean(abs((ts_inflasi - fitted_val) / ts_inflasi), na.rm = TRUE) * 100# Output
MAE## [1] 0.004000209# Output
MAPE## [1] 7.018252