Eksplorasi
Lilis
2024-06-14
Nomor 1
library(readxl)
library(ggplot2)Nomor1 <- read_xlsx("D:/Cooliah/Semester 4/Analisis Eksplorasi Data/UAS/Data2.xlsx", sheet = 1)
Nomor1## # A tibble: 50 × 3
## Participant `Daily Sleep Duration (in hours)` `Productivity Score`
## <dbl> <dbl> <dbl>
## 1 1 7.5 85
## 2 2 6.2 72
## 3 3 8.1 91
## 4 4 6.8 78
## 5 5 7.9 87
## 6 6 5.6 63
## 7 7 6.9 76
## 8 8 7.2 81
## 9 9 6.5 70
## 10 10 8.3 93
## # ℹ 40 more rowsX=Nomor1$'Daily Sleep Duration (in hours)'
Y=Nomor1$'Productivity Score'Scatter Plot
plot(X,Y)
Interpretasi : Hubungan antara durasi tidur harian dan skor
produktivitas dapat dilihat dalam scatter plot berikut. Scatter plot
yang dibuat dengan Rstudio tersebut menunjukkan pola hubungan positif.
Artinya, semakin panjang durasi waktu tidur maka semakin besar pula skor
produktivitasnya
Korelasi
library(corrplot)## corrplot 0.92 loadedkorelasi <- cor(Nomor1)
korelasi## Participant Daily Sleep Duration (in hours)
## Participant 1.00000000 0.04573604
## Daily Sleep Duration (in hours) 0.04573604 1.00000000
## Productivity Score 0.03300362 0.97773838
## Productivity Score
## Participant 0.03300362
## Daily Sleep Duration (in hours) 0.97773838
## Productivity Score 1.00000000Dari nilai korelasi antara durasi tidur harian dan skor produktivitas yang didapatkan melalui Rstudio yaitu sebesar 0,978 menunjukkan pola hubungan positif yang sangat kuat di antara peubah tersebut.
Model Regresi
model = lm(Y~X)
anova(model)## Analysis of Variance Table
##
## Response: Y
## Df Sum Sq Mean Sq F value Pr(>F)
## X 1 4116.7 4116.7 1042.2 < 2.2e-16 ***
## Residuals 48 189.6 3.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model)##
## Call:
## lm(formula = Y ~ X)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.1105 -1.2229 -0.0134 1.6346 3.6144
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.8506 2.6297 -1.845 0.0713 .
## X 11.8123 0.3659 32.283 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.987 on 48 degrees of freedom
## Multiple R-squared: 0.956, Adjusted R-squared: 0.9551
## F-statistic: 1042 on 1 and 48 DF, p-value: < 2.2e-16Interpretasi : Nilai p-value < 0,05 maka tolak H0, maka peubah penjelas tersebut signifikan terhadap peubah respon. Dari serangkaian eksplorasi data yang dilakukan, didapatkan bahwa hubungan antara durasi tidur harian dan skor produktivitas terdapat hubungan yang signifikan. Hubungannya adalah positif dengan nilai korelasi 0,978
Nomor 2
library(readxl)
library(ggplot2)Nomor2 <- read_xlsx("D:/Cooliah/Semester 4/Analisis Eksplorasi Data/UAS/Data2.xlsx", sheet = 2)
Nomor2## # A tibble: 50 × 9
## No. Usia IMT Konsumsi Kalori Haria…¹ `Jumlah Langkah` `Kadar Kolesterol`
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 35 25 2000 8000 180
## 2 2 42 29 1800 6000 220
## 3 3 28 22 2200 9000 160
## 4 4 55 31 2500 5000 240
## 5 5 46 26 1900 7000 200
## 6 6 39 24 2100 8000 180
## 7 7 52 28 1800 4000 220
## 8 8 31 23 2300 9000 170
## 9 9 48 27 2200 6000 200
## 10 10 41 25 1900 7000 190
## # ℹ 40 more rows
## # ℹ abbreviated name: ¹​`Konsumsi Kalori Harian`
## # ℹ 3 more variables: `Tekanan Darah` <dbl>, Merokok <dbl>,
## # `Riwayat Penyakit Jantung` <dbl>Mengganti ya dan tidak ke numeric
Nomor2$Merokok <- as.numeric(Nomor2$Merokok)
Nomor2$`Riwayat Penyakit Jantung` <- as.numeric(Nomor2$`Riwayat Penyakit Jantung`)X1=Nomor2$Usia
X2=Nomor2$IMT
X3=Nomor2$`Konsumsi Kalori Harian`
X4=Nomor2$`Jumlah Langkah`
X5=Nomor2$`Kadar Kolesterol`
X6=Nomor2$`Tekanan Darah`
X7=Nomor2$Merokok
Y2=Nomor2$`Riwayat Penyakit Jantung`str(Nomor2)## tibble [50 × 9] (S3: tbl_df/tbl/data.frame)
## $ No. : num [1:50] 1 2 3 4 5 6 7 8 9 10 ...
## $ Usia : num [1:50] 35 42 28 55 46 39 52 31 48 41 ...
## $ IMT : num [1:50] 25 29 22 31 26 24 28 23 27 25 ...
## $ Konsumsi Kalori Harian : num [1:50] 2000 1800 2200 2500 1900 2100 1800 2300 2200 1900 ...
## $ Jumlah Langkah : num [1:50] 8000 6000 9000 5000 7000 8000 4000 9000 6000 7000 ...
## $ Kadar Kolesterol : num [1:50] 180 220 160 240 200 180 220 170 200 190 ...
## $ Tekanan Darah : num [1:50] 120 130 110 140 120 130 140 110 120 130 ...
## $ Merokok : num [1:50] 0 1 0 0 1 0 1 1 0 0 ...
## $ Riwayat Penyakit Jantung: num [1:50] 0 0 1 1 0 0 1 0 1 0 ...Korelasi
library(corrplot)
korelasi2 <- cor(Nomor2)
korelasi2## No. Usia IMT
## No. 1.000000000 0.07971784 -0.02455513
## Usia 0.079717843 1.00000000 0.60724087
## IMT -0.024555126 0.60724087 1.00000000
## Konsumsi Kalori Harian -0.043682751 0.10400083 0.12349421
## Jumlah Langkah -0.076415334 -0.44921765 -0.63870192
## Kadar Kolesterol -0.011089970 0.73619766 0.57121412
## Tekanan Darah -0.007072482 0.42952994 0.30455480
## Merokok -0.155915759 -0.32406802 0.11656310
## Riwayat Penyakit Jantung 0.029980519 0.34077119 0.07684638
## Konsumsi Kalori Harian Jumlah Langkah Kadar Kolesterol
## No. -0.04368275 -0.07641533 -0.01108997
## Usia 0.10400083 -0.44921765 0.73619766
## IMT 0.12349421 -0.63870192 0.57121412
## Konsumsi Kalori Harian 1.00000000 0.22045524 0.06910793
## Jumlah Langkah 0.22045524 1.00000000 -0.40353442
## Kadar Kolesterol 0.06910793 -0.40353442 1.00000000
## Tekanan Darah -0.24437588 -0.51170847 0.62631678
## Merokok -0.14214453 -0.14383562 -0.31179800
## Riwayat Penyakit Jantung -0.06591812 -0.33358535 0.56892437
## Tekanan Darah Merokok Riwayat Penyakit Jantung
## No. -0.007072482 -0.1559158 0.02998052
## Usia 0.429529945 -0.3240680 0.34077119
## IMT 0.304554795 0.1165631 0.07684638
## Konsumsi Kalori Harian -0.244375883 -0.1421445 -0.06591812
## Jumlah Langkah -0.511708474 -0.1438356 -0.33358535
## Kadar Kolesterol 0.626316780 -0.3117980 0.56892437
## Tekanan Darah 1.000000000 -0.3061862 0.56352285
## Merokok -0.306186218 1.0000000 -0.32963426
## Riwayat Penyakit Jantung 0.563522855 -0.3296343 1.00000000corrplot(korelasi2,
method = 'number',
bg = "white",
number.cex = 0.9,
tl.col = "black",
tl.cex = 0.6,
cl.cex = 0.6,
type = "upper")
Dari semua peubah yang dimiliki pada soal nomor 2 didapatkan matriks
korelasi sebagai berikut. Terlihat bahwa hubungan yang paling kuat
adalah hubungan antara usia dan kadar kolesterol yaitu sebesar 0,74.
Hal ini menunjukkan semakin tua usia seseorang maka kadar kolesterol juga akan semakin tinggi. Sedangkan, hubungan negatif yang paling kuat adalah antara jumlah langkah dan IMT yaitu sebesar -0,64. Artinya semakin besar jumlah langkah maka semakin kecil IMT seseorang.
Model regresi awal
model2 = lm(Y2~X1+X2+X3+X4+X5+X6+X7)
anova(model2)## Analysis of Variance Table
##
## Response: Y2
## Df Sum Sq Mean Sq F value Pr(>F)
## X1 1 1.3680 1.3680 10.7866 0.002067 **
## X2 1 0.3158 0.3158 2.4900 0.122076
## X3 1 0.0947 0.0947 0.7469 0.392370
## X4 1 1.2479 1.2479 9.8399 0.003117 **
## X5 1 3.2229 3.2229 25.4129 9.314e-06 ***
## X6 1 0.1275 0.1275 1.0052 0.321789
## X7 1 0.0769 0.0769 0.6062 0.440590
## Residuals 42 5.3264 0.1268
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model2)##
## Call:
## lm(formula = Y2 ~ X1 + X2 + X3 + X4 + X5 + X6 + X7)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.61096 -0.18114 0.02495 0.13878 0.97520
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.920e-01 1.546e+00 0.189 0.851118
## X1 -7.022e-03 1.116e-02 -0.629 0.532748
## X2 -1.259e-01 3.988e-02 -3.157 0.002945 **
## X3 1.993e-04 3.054e-04 0.653 0.517620
## X4 -1.447e-04 5.524e-05 -2.619 0.012213 *
## X5 1.822e-02 5.123e-03 3.557 0.000946 ***
## X6 5.886e-03 8.160e-03 0.721 0.474677
## X7 -1.048e-01 1.346e-01 -0.779 0.440590
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3561 on 42 degrees of freedom
## Multiple R-squared: 0.5478, Adjusted R-squared: 0.4725
## F-statistic: 7.27 on 7 and 42 DF, p-value: 1.045e-05Namun, dari hasil eksplorasi tersebut masih didapatkan nilai R-squared yang cenderung rendah yaitu sebesar 0,5478 sehingga perlu dilakukan analisis lebih lanjut
eksplorasi amatan berpengaruh
library(olsrr)## Warning: package 'olsrr' was built under R version 4.3.3##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversolsrr::ols_plot_resid_lev(model2)
influence.measures(model2)## Influence measures of
## lm(formula = Y2 ~ X1 + X2 + X3 + X4 + X5 + X6 + X7) :
##
## dfb.1_ dfb.X1 dfb.X2 dfb.X3 dfb.X4 dfb.X5 dfb.X6
## 1 -0.005856 5.17e-02 -0.056098 3.63e-02 -0.027875 0.02000 0.00408
## 2 0.242475 3.81e-01 -0.328282 4.39e-01 -0.235025 -0.48989 0.08141
## 3 0.507490 -4.88e-01 -0.166518 3.44e-01 -0.206710 -0.21399 -0.24516
## 4 -0.030631 -1.13e-02 0.011491 3.05e-02 -0.001923 0.01258 0.01051
## 5 -0.026350 -1.44e-01 0.088571 1.26e-01 -0.079363 -0.09199 0.06263
## 6 0.107645 -5.71e-02 -0.014900 -7.44e-02 -0.120098 0.19631 -0.23278
## 7 -0.002720 3.82e-02 -0.044015 -2.44e-02 -0.024792 0.02862 0.02571
## 8 -0.002920 -3.92e-04 -0.011166 1.74e-02 0.004397 0.00117 0.00223
## 9 0.187243 2.47e-02 -0.041981 1.05e-01 -0.242688 0.04156 -0.24893
## 10 -0.018718 9.80e-03 -0.043842 1.36e-01 -0.057878 0.10444 -0.11290
## 11 -0.009170 3.17e-02 -0.027627 -2.08e-02 0.039208 0.01983 0.00478
## 12 0.000339 -9.84e-05 -0.000297 -7.23e-05 -0.000312 0.00023 -0.00024
## 13 0.008439 -1.18e-01 0.013201 7.68e-02 -0.138935 0.03996 -0.01170
## 14 0.064573 -3.95e-02 0.018002 -5.17e-02 -0.037731 0.00867 -0.05856
## 15 0.234118 3.42e-01 -0.255931 -1.32e-01 -0.070233 -0.03078 -0.13843
## 16 -0.011685 5.40e-03 -0.021545 -5.13e-03 0.016115 0.01116 0.02389
## 17 -0.129632 2.80e-01 -0.151381 4.60e-01 -0.207588 0.24703 -0.23881
## 18 -0.175174 -1.88e-01 0.187911 -4.84e-02 0.135060 0.02308 0.12216
## 19 -0.091337 -1.46e-01 0.324917 -2.73e-01 0.195305 -0.20591 0.20462
## 20 -0.005497 5.84e-03 -0.002014 1.40e-03 0.011335 -0.01140 0.01363
## 21 0.007224 3.07e-01 -0.183168 -3.02e-02 -0.090619 -0.17536 0.24977
## 22 -0.090088 2.19e-01 0.056336 -1.17e-01 0.065620 -0.14453 0.15423
## 23 -0.133702 8.79e-02 -0.055069 -4.13e-02 0.200626 -0.19994 0.34348
## 24 0.038920 -5.01e-02 -0.023373 -1.26e-01 0.018725 0.05801 0.01425
## 25 0.044623 1.92e-02 -0.020460 -6.05e-03 -0.047501 -0.01418 -0.02038
## 26 -0.010537 -1.33e-02 0.028156 -5.90e-02 0.005174 0.03593 -0.00409
## 27 0.006089 8.20e-03 -0.000150 -7.57e-03 0.006007 -0.00319 -0.00683
## 28 -0.015235 -2.64e-02 0.028708 3.90e-02 -0.013337 -0.03781 0.02511
## 29 0.047146 -2.53e-02 -0.070895 -1.82e-02 -0.036169 0.05381 -0.01268
## 30 0.001427 1.38e-01 -0.206671 1.49e-01 -0.010389 0.15473 -0.09430
## 31 -0.253606 -1.83e-01 0.206516 -2.23e-01 0.429292 0.29696 -0.07518
## 32 0.103561 -8.08e-02 0.131584 -1.72e-01 -0.024669 0.02097 -0.15391
## 33 -0.327832 -1.26e-01 0.261909 7.08e-02 0.184354 -0.04186 0.20298
## 34 -0.114976 4.83e-02 0.063512 -1.82e-02 0.142155 -0.13381 0.17629
## 35 0.008166 8.22e-02 -0.072593 1.30e-01 -0.121047 -0.10846 0.09839
## 36 0.007965 4.00e-02 0.097419 -1.07e-01 -0.011443 -0.08574 0.02645
## 37 0.114750 -2.14e-01 0.085074 3.59e-02 -0.201844 0.24035 -0.32272
## 38 0.037825 -8.38e-02 -0.013720 -1.24e-01 0.011738 0.07366 0.00830
## 39 0.037278 1.40e-03 -0.013216 -5.11e-03 -0.042776 -0.00485 -0.01957
## 40 -0.072026 -1.30e-02 0.152327 -1.89e-01 0.065928 0.05296 0.01010
## 41 0.009144 1.45e-02 -0.000834 -1.13e-02 0.009428 -0.00586 -0.00985
## 42 -0.013924 -3.05e-02 0.027815 3.54e-02 -0.013373 -0.03120 0.02171
## 43 0.047146 -2.53e-02 -0.070895 -1.82e-02 -0.036169 0.05381 -0.01268
## 44 0.256917 6.83e-02 -0.230434 -1.02e-01 -0.208471 -0.14873 0.08653
## 45 -0.253606 -1.83e-01 0.206516 -2.23e-01 0.429292 0.29696 -0.07518
## 46 -0.072973 2.61e-02 0.002124 5.68e-02 0.041197 -0.03121 0.07533
## 47 -0.009895 -6.66e-02 -0.023676 3.15e-02 -0.025906 0.05254 0.00627
## 48 -0.117158 -1.84e-02 -0.063219 8.92e-02 0.086522 0.09839 0.07330
## 49 -0.091052 2.00e-01 0.108422 -2.52e-02 0.189050 -0.10694 -0.02400
## 50 0.008626 4.13e-02 0.032779 -4.74e-03 0.001275 -0.06388 0.00197
## dfb.X7 dffit cov.r cook.d hat inf
## 1 7.27e-02 -0.116234 1.299 1.72e-03 0.0910
## 2 -2.41e-01 -0.927307 0.945 1.03e-01 0.2378
## 3 -6.68e-01 1.502778 0.211 2.27e-01 0.1678 *
## 4 -1.56e-03 0.052739 1.706 3.56e-04 0.2901 *
## 5 -2.36e-01 -0.352260 1.179 1.56e-02 0.1273
## 6 2.59e-02 -0.325578 1.171 1.33e-02 0.1153
## 7 8.44e-02 0.142445 1.500 2.59e-03 0.2042
## 8 1.81e-02 0.033962 1.456 1.48e-04 0.1681
## 9 -2.23e-01 0.461221 0.832 2.57e-02 0.0805
## 10 1.34e-01 -0.336021 0.928 1.39e-02 0.0613
## 11 -6.23e-03 -0.095956 1.377 1.18e-03 0.1298
## 12 2.07e-05 -0.000442 1.665 2.50e-08 0.2716 *
## 13 2.97e-03 -0.234148 1.262 6.95e-03 0.1148
## 14 -1.38e-02 0.109028 1.468 1.52e-03 0.1825
## 15 2.13e-01 -0.510808 0.950 3.19e-02 0.1183
## 16 1.23e-02 0.051882 1.507 3.45e-04 0.1970
## 17 4.76e-01 1.007062 0.941 1.21e-01 0.2575
## 18 -1.34e-01 -0.324445 1.469 1.34e-02 0.2293
## 19 -3.03e-01 0.618086 0.613 4.44e-02 0.0844
## 20 1.79e-02 0.029269 1.363 1.10e-04 0.1117
## 21 3.31e-01 0.585749 1.298 4.28e-02 0.2413
## 22 1.51e-01 -0.389824 1.294 1.91e-02 0.1801
## 23 2.56e-01 -0.531516 0.838 3.41e-02 0.1010
## 24 -9.14e-02 0.264732 1.024 8.72e-03 0.0561
## 25 -5.32e-02 -0.089939 1.334 1.03e-03 0.1031
## 26 -2.41e-02 0.106344 1.425 1.45e-03 0.1586
## 27 -4.36e-03 0.018709 1.427 4.48e-05 0.1506
## 28 1.31e-02 0.090873 1.427 1.06e-03 0.1574
## 29 -1.61e-02 0.112574 1.356 1.62e-03 0.1215
## 30 8.02e-02 0.368831 1.492 1.72e-02 0.2495
## 31 2.10e-01 -0.709236 0.710 5.93e-02 0.1237
## 32 -3.67e-02 0.290715 1.443 1.07e-02 0.2101
## 33 1.38e-01 -0.453591 0.844 2.49e-02 0.0804
## 34 1.08e-01 0.230953 1.582 6.80e-03 0.2564 *
## 35 -1.37e-02 0.254905 1.522 8.28e-03 0.2355
## 36 -1.22e-01 -0.238256 1.434 7.23e-03 0.1929
## 37 -2.72e-01 0.505286 0.963 3.13e-02 0.1198
## 38 -1.02e-01 0.269365 1.036 9.04e-03 0.0599
## 39 -4.99e-02 -0.073833 1.332 6.97e-04 0.0984
## 40 -7.65e-02 0.329979 1.365 1.38e-02 0.1887
## 41 -5.72e-03 0.029057 1.446 1.08e-04 0.1623
## 42 9.59e-03 0.084611 1.443 9.16e-04 0.1656
## 43 -1.61e-02 0.112574 1.356 1.62e-03 0.1215
## 44 7.49e-02 -0.509021 1.237 3.24e-02 0.1987
## 45 2.10e-01 -0.709236 0.710 5.93e-02 0.1237
## 46 1.03e-03 -0.110074 1.449 1.55e-03 0.1725
## 47 2.08e-02 -0.097315 1.423 1.21e-03 0.1564
## 48 2.64e-02 0.268256 1.156 9.05e-03 0.0895
## 49 9.45e-02 -0.332352 1.594 1.40e-02 0.2803 *
## 50 -3.14e-02 0.086215 1.515 9.51e-04 0.2043Kemudian, dilakukan analisis terhadap amatan yang berpengaruh dan didapatkan bahwa ada outlier atau pencilan, yaitu pada amatan ke 3 dan 19.
Jarak cook
influence.measures(model2) #menghitung berbagai ukuran pengaruh atau pengaruh dari observasi dalam model regresi## Influence measures of
## lm(formula = Y2 ~ X1 + X2 + X3 + X4 + X5 + X6 + X7) :
##
## dfb.1_ dfb.X1 dfb.X2 dfb.X3 dfb.X4 dfb.X5 dfb.X6
## 1 -0.005856 5.17e-02 -0.056098 3.63e-02 -0.027875 0.02000 0.00408
## 2 0.242475 3.81e-01 -0.328282 4.39e-01 -0.235025 -0.48989 0.08141
## 3 0.507490 -4.88e-01 -0.166518 3.44e-01 -0.206710 -0.21399 -0.24516
## 4 -0.030631 -1.13e-02 0.011491 3.05e-02 -0.001923 0.01258 0.01051
## 5 -0.026350 -1.44e-01 0.088571 1.26e-01 -0.079363 -0.09199 0.06263
## 6 0.107645 -5.71e-02 -0.014900 -7.44e-02 -0.120098 0.19631 -0.23278
## 7 -0.002720 3.82e-02 -0.044015 -2.44e-02 -0.024792 0.02862 0.02571
## 8 -0.002920 -3.92e-04 -0.011166 1.74e-02 0.004397 0.00117 0.00223
## 9 0.187243 2.47e-02 -0.041981 1.05e-01 -0.242688 0.04156 -0.24893
## 10 -0.018718 9.80e-03 -0.043842 1.36e-01 -0.057878 0.10444 -0.11290
## 11 -0.009170 3.17e-02 -0.027627 -2.08e-02 0.039208 0.01983 0.00478
## 12 0.000339 -9.84e-05 -0.000297 -7.23e-05 -0.000312 0.00023 -0.00024
## 13 0.008439 -1.18e-01 0.013201 7.68e-02 -0.138935 0.03996 -0.01170
## 14 0.064573 -3.95e-02 0.018002 -5.17e-02 -0.037731 0.00867 -0.05856
## 15 0.234118 3.42e-01 -0.255931 -1.32e-01 -0.070233 -0.03078 -0.13843
## 16 -0.011685 5.40e-03 -0.021545 -5.13e-03 0.016115 0.01116 0.02389
## 17 -0.129632 2.80e-01 -0.151381 4.60e-01 -0.207588 0.24703 -0.23881
## 18 -0.175174 -1.88e-01 0.187911 -4.84e-02 0.135060 0.02308 0.12216
## 19 -0.091337 -1.46e-01 0.324917 -2.73e-01 0.195305 -0.20591 0.20462
## 20 -0.005497 5.84e-03 -0.002014 1.40e-03 0.011335 -0.01140 0.01363
## 21 0.007224 3.07e-01 -0.183168 -3.02e-02 -0.090619 -0.17536 0.24977
## 22 -0.090088 2.19e-01 0.056336 -1.17e-01 0.065620 -0.14453 0.15423
## 23 -0.133702 8.79e-02 -0.055069 -4.13e-02 0.200626 -0.19994 0.34348
## 24 0.038920 -5.01e-02 -0.023373 -1.26e-01 0.018725 0.05801 0.01425
## 25 0.044623 1.92e-02 -0.020460 -6.05e-03 -0.047501 -0.01418 -0.02038
## 26 -0.010537 -1.33e-02 0.028156 -5.90e-02 0.005174 0.03593 -0.00409
## 27 0.006089 8.20e-03 -0.000150 -7.57e-03 0.006007 -0.00319 -0.00683
## 28 -0.015235 -2.64e-02 0.028708 3.90e-02 -0.013337 -0.03781 0.02511
## 29 0.047146 -2.53e-02 -0.070895 -1.82e-02 -0.036169 0.05381 -0.01268
## 30 0.001427 1.38e-01 -0.206671 1.49e-01 -0.010389 0.15473 -0.09430
## 31 -0.253606 -1.83e-01 0.206516 -2.23e-01 0.429292 0.29696 -0.07518
## 32 0.103561 -8.08e-02 0.131584 -1.72e-01 -0.024669 0.02097 -0.15391
## 33 -0.327832 -1.26e-01 0.261909 7.08e-02 0.184354 -0.04186 0.20298
## 34 -0.114976 4.83e-02 0.063512 -1.82e-02 0.142155 -0.13381 0.17629
## 35 0.008166 8.22e-02 -0.072593 1.30e-01 -0.121047 -0.10846 0.09839
## 36 0.007965 4.00e-02 0.097419 -1.07e-01 -0.011443 -0.08574 0.02645
## 37 0.114750 -2.14e-01 0.085074 3.59e-02 -0.201844 0.24035 -0.32272
## 38 0.037825 -8.38e-02 -0.013720 -1.24e-01 0.011738 0.07366 0.00830
## 39 0.037278 1.40e-03 -0.013216 -5.11e-03 -0.042776 -0.00485 -0.01957
## 40 -0.072026 -1.30e-02 0.152327 -1.89e-01 0.065928 0.05296 0.01010
## 41 0.009144 1.45e-02 -0.000834 -1.13e-02 0.009428 -0.00586 -0.00985
## 42 -0.013924 -3.05e-02 0.027815 3.54e-02 -0.013373 -0.03120 0.02171
## 43 0.047146 -2.53e-02 -0.070895 -1.82e-02 -0.036169 0.05381 -0.01268
## 44 0.256917 6.83e-02 -0.230434 -1.02e-01 -0.208471 -0.14873 0.08653
## 45 -0.253606 -1.83e-01 0.206516 -2.23e-01 0.429292 0.29696 -0.07518
## 46 -0.072973 2.61e-02 0.002124 5.68e-02 0.041197 -0.03121 0.07533
## 47 -0.009895 -6.66e-02 -0.023676 3.15e-02 -0.025906 0.05254 0.00627
## 48 -0.117158 -1.84e-02 -0.063219 8.92e-02 0.086522 0.09839 0.07330
## 49 -0.091052 2.00e-01 0.108422 -2.52e-02 0.189050 -0.10694 -0.02400
## 50 0.008626 4.13e-02 0.032779 -4.74e-03 0.001275 -0.06388 0.00197
## dfb.X7 dffit cov.r cook.d hat inf
## 1 7.27e-02 -0.116234 1.299 1.72e-03 0.0910
## 2 -2.41e-01 -0.927307 0.945 1.03e-01 0.2378
## 3 -6.68e-01 1.502778 0.211 2.27e-01 0.1678 *
## 4 -1.56e-03 0.052739 1.706 3.56e-04 0.2901 *
## 5 -2.36e-01 -0.352260 1.179 1.56e-02 0.1273
## 6 2.59e-02 -0.325578 1.171 1.33e-02 0.1153
## 7 8.44e-02 0.142445 1.500 2.59e-03 0.2042
## 8 1.81e-02 0.033962 1.456 1.48e-04 0.1681
## 9 -2.23e-01 0.461221 0.832 2.57e-02 0.0805
## 10 1.34e-01 -0.336021 0.928 1.39e-02 0.0613
## 11 -6.23e-03 -0.095956 1.377 1.18e-03 0.1298
## 12 2.07e-05 -0.000442 1.665 2.50e-08 0.2716 *
## 13 2.97e-03 -0.234148 1.262 6.95e-03 0.1148
## 14 -1.38e-02 0.109028 1.468 1.52e-03 0.1825
## 15 2.13e-01 -0.510808 0.950 3.19e-02 0.1183
## 16 1.23e-02 0.051882 1.507 3.45e-04 0.1970
## 17 4.76e-01 1.007062 0.941 1.21e-01 0.2575
## 18 -1.34e-01 -0.324445 1.469 1.34e-02 0.2293
## 19 -3.03e-01 0.618086 0.613 4.44e-02 0.0844
## 20 1.79e-02 0.029269 1.363 1.10e-04 0.1117
## 21 3.31e-01 0.585749 1.298 4.28e-02 0.2413
## 22 1.51e-01 -0.389824 1.294 1.91e-02 0.1801
## 23 2.56e-01 -0.531516 0.838 3.41e-02 0.1010
## 24 -9.14e-02 0.264732 1.024 8.72e-03 0.0561
## 25 -5.32e-02 -0.089939 1.334 1.03e-03 0.1031
## 26 -2.41e-02 0.106344 1.425 1.45e-03 0.1586
## 27 -4.36e-03 0.018709 1.427 4.48e-05 0.1506
## 28 1.31e-02 0.090873 1.427 1.06e-03 0.1574
## 29 -1.61e-02 0.112574 1.356 1.62e-03 0.1215
## 30 8.02e-02 0.368831 1.492 1.72e-02 0.2495
## 31 2.10e-01 -0.709236 0.710 5.93e-02 0.1237
## 32 -3.67e-02 0.290715 1.443 1.07e-02 0.2101
## 33 1.38e-01 -0.453591 0.844 2.49e-02 0.0804
## 34 1.08e-01 0.230953 1.582 6.80e-03 0.2564 *
## 35 -1.37e-02 0.254905 1.522 8.28e-03 0.2355
## 36 -1.22e-01 -0.238256 1.434 7.23e-03 0.1929
## 37 -2.72e-01 0.505286 0.963 3.13e-02 0.1198
## 38 -1.02e-01 0.269365 1.036 9.04e-03 0.0599
## 39 -4.99e-02 -0.073833 1.332 6.97e-04 0.0984
## 40 -7.65e-02 0.329979 1.365 1.38e-02 0.1887
## 41 -5.72e-03 0.029057 1.446 1.08e-04 0.1623
## 42 9.59e-03 0.084611 1.443 9.16e-04 0.1656
## 43 -1.61e-02 0.112574 1.356 1.62e-03 0.1215
## 44 7.49e-02 -0.509021 1.237 3.24e-02 0.1987
## 45 2.10e-01 -0.709236 0.710 5.93e-02 0.1237
## 46 1.03e-03 -0.110074 1.449 1.55e-03 0.1725
## 47 2.08e-02 -0.097315 1.423 1.21e-03 0.1564
## 48 2.64e-02 0.268256 1.156 9.05e-03 0.0895
## 49 9.45e-02 -0.332352 1.594 1.40e-02 0.2803 *
## 50 -3.14e-02 0.086215 1.515 9.51e-04 0.2043f<-qf(0.05,6,43) #probabilitas, peubah-1, jmlh amatan-peubah
f## [1] 0.2654548di<-cooks.distance(model2) #di = jarak cook, di>f = apakah nilai jarak cook lbh besar dr nilai kuantil f
di## 1 2 3 4 5 6
## 1.724304e-03 1.031719e-01 2.271348e-01 3.560921e-04 1.556640e-02 1.330940e-02
## 7 8 9 10 11 12
## 2.593192e-03 1.476768e-04 2.571579e-02 1.387302e-02 1.177247e-03 2.502502e-08
## 13 14 15 16 17 18
## 6.948723e-03 1.520161e-03 3.189875e-02 3.445867e-04 1.212190e-01 1.336367e-02
## 19 20 21 22 23 24
## 4.442781e-02 1.096798e-04 4.280745e-02 1.913566e-02 3.408519e-02 8.723028e-03
## 25 26 27 28 29 30
## 1.034007e-03 1.445989e-03 4.481750e-05 1.056285e-03 1.619124e-03 1.724720e-02
## 31 32 33 34 35 36
## 5.925966e-02 1.073886e-02 2.491503e-02 6.804352e-03 8.277602e-03 7.226928e-03
## 37 38 39 40 41 42
## 3.126171e-02 9.039614e-03 6.971829e-04 1.378533e-02 1.081016e-04 9.159025e-04
## 43 44 45 46 47 48
## 1.619124e-03 3.235305e-02 5.925966e-02 1.549280e-03 1.211139e-03 9.052840e-03
## 49 50
## 1.404683e-02 9.511173e-04data.frame(di, di>f)## di di...f
## 1 1.724304e-03 FALSE
## 2 1.031719e-01 FALSE
## 3 2.271348e-01 FALSE
## 4 3.560921e-04 FALSE
## 5 1.556640e-02 FALSE
## 6 1.330940e-02 FALSE
## 7 2.593192e-03 FALSE
## 8 1.476768e-04 FALSE
## 9 2.571579e-02 FALSE
## 10 1.387302e-02 FALSE
## 11 1.177247e-03 FALSE
## 12 2.502502e-08 FALSE
## 13 6.948723e-03 FALSE
## 14 1.520161e-03 FALSE
## 15 3.189875e-02 FALSE
## 16 3.445867e-04 FALSE
## 17 1.212190e-01 FALSE
## 18 1.336367e-02 FALSE
## 19 4.442781e-02 FALSE
## 20 1.096798e-04 FALSE
## 21 4.280745e-02 FALSE
## 22 1.913566e-02 FALSE
## 23 3.408519e-02 FALSE
## 24 8.723028e-03 FALSE
## 25 1.034007e-03 FALSE
## 26 1.445989e-03 FALSE
## 27 4.481750e-05 FALSE
## 28 1.056285e-03 FALSE
## 29 1.619124e-03 FALSE
## 30 1.724720e-02 FALSE
## 31 5.925966e-02 FALSE
## 32 1.073886e-02 FALSE
## 33 2.491503e-02 FALSE
## 34 6.804352e-03 FALSE
## 35 8.277602e-03 FALSE
## 36 7.226928e-03 FALSE
## 37 3.126171e-02 FALSE
## 38 9.039614e-03 FALSE
## 39 6.971829e-04 FALSE
## 40 1.378533e-02 FALSE
## 41 1.081016e-04 FALSE
## 42 9.159025e-04 FALSE
## 43 1.619124e-03 FALSE
## 44 3.235305e-02 FALSE
## 45 5.925966e-02 FALSE
## 46 1.549280e-03 FALSE
## 47 1.211139e-03 FALSE
## 48 9.052840e-03 FALSE
## 49 1.404683e-02 FALSE
## 50 9.511173e-04 FALSESedangkan, pada jarak cook tidak ditemukan amatan berpengaruh, maka dilakukan terlebih dahulu kombinasi penghapusan untuk amatan 3 dan 19.
lakukan penghapusan thdp amatan ke-3 (model tanpa amatan ke-3)
model2_tanpa_3 = lm(Y2~X1+X2+X3+X4+X5+X6+X7, data=Nomor2[-3,])
anova(model2_tanpa_3)## Analysis of Variance Table
##
## Response: Y2
## Df Sum Sq Mean Sq F value Pr(>F)
## X1 1 1.3680 1.3680 10.7866 0.002067 **
## X2 1 0.3158 0.3158 2.4900 0.122076
## X3 1 0.0947 0.0947 0.7469 0.392370
## X4 1 1.2479 1.2479 9.8399 0.003117 **
## X5 1 3.2229 3.2229 25.4129 9.314e-06 ***
## X6 1 0.1275 0.1275 1.0052 0.321789
## X7 1 0.0769 0.0769 0.6062 0.440590
## Residuals 42 5.3264 0.1268
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model2_tanpa_3)##
## Call:
## lm(formula = Y2 ~ X1 + X2 + X3 + X4 + X5 + X6 + X7, data = Nomor2[-3,
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.61096 -0.18114 0.02495 0.13878 0.97520
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.920e-01 1.546e+00 0.189 0.851118
## X1 -7.022e-03 1.116e-02 -0.629 0.532748
## X2 -1.259e-01 3.988e-02 -3.157 0.002945 **
## X3 1.993e-04 3.054e-04 0.653 0.517620
## X4 -1.447e-04 5.524e-05 -2.619 0.012213 *
## X5 1.822e-02 5.123e-03 3.557 0.000946 ***
## X6 5.886e-03 8.160e-03 0.721 0.474677
## X7 -1.048e-01 1.346e-01 -0.779 0.440590
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3561 on 42 degrees of freedom
## Multiple R-squared: 0.5478, Adjusted R-squared: 0.4725
## F-statistic: 7.27 on 7 and 42 DF, p-value: 1.045e-05Interpretasi : Tanpa amatan ke-3 didapatkan nilai R-squared sebesar 0,5478
lakukan penghapusan thdp amatan ke-19 (model tanpa amatan ke-19)
model2_tanpa_19 = lm(Y2~X1+X2+X3+X4+X5+X6+X7, data=Nomor2[-19,])
anova(model2_tanpa_19)## Analysis of Variance Table
##
## Response: Y2
## Df Sum Sq Mean Sq F value Pr(>F)
## X1 1 1.3680 1.3680 10.7866 0.002067 **
## X2 1 0.3158 0.3158 2.4900 0.122076
## X3 1 0.0947 0.0947 0.7469 0.392370
## X4 1 1.2479 1.2479 9.8399 0.003117 **
## X5 1 3.2229 3.2229 25.4129 9.314e-06 ***
## X6 1 0.1275 0.1275 1.0052 0.321789
## X7 1 0.0769 0.0769 0.6062 0.440590
## Residuals 42 5.3264 0.1268
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model2_tanpa_19)##
## Call:
## lm(formula = Y2 ~ X1 + X2 + X3 + X4 + X5 + X6 + X7, data = Nomor2[-19,
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.61096 -0.18114 0.02495 0.13878 0.97520
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.920e-01 1.546e+00 0.189 0.851118
## X1 -7.022e-03 1.116e-02 -0.629 0.532748
## X2 -1.259e-01 3.988e-02 -3.157 0.002945 **
## X3 1.993e-04 3.054e-04 0.653 0.517620
## X4 -1.447e-04 5.524e-05 -2.619 0.012213 *
## X5 1.822e-02 5.123e-03 3.557 0.000946 ***
## X6 5.886e-03 8.160e-03 0.721 0.474677
## X7 -1.048e-01 1.346e-01 -0.779 0.440590
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3561 on 42 degrees of freedom
## Multiple R-squared: 0.5478, Adjusted R-squared: 0.4725
## F-statistic: 7.27 on 7 and 42 DF, p-value: 1.045e-05Interpretasi : Tanpa amatan ke-19 didapatkan nilai R-squared sebesar 0,5478
lakukan penghapusan thdp amatan ke-3 dan 19 (model tanpa amatan ke-3 dan 19)
model2_tanpa_3dan19 = lm(Y2~X1+X2+X3+X4+X5+X6+X7, data=Nomor2[c(-3,-19),])
anova(model2_tanpa_3dan19)## Analysis of Variance Table
##
## Response: Y2
## Df Sum Sq Mean Sq F value Pr(>F)
## X1 1 1.3680 1.3680 10.7866 0.002067 **
## X2 1 0.3158 0.3158 2.4900 0.122076
## X3 1 0.0947 0.0947 0.7469 0.392370
## X4 1 1.2479 1.2479 9.8399 0.003117 **
## X5 1 3.2229 3.2229 25.4129 9.314e-06 ***
## X6 1 0.1275 0.1275 1.0052 0.321789
## X7 1 0.0769 0.0769 0.6062 0.440590
## Residuals 42 5.3264 0.1268
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model2_tanpa_3dan19)##
## Call:
## lm(formula = Y2 ~ X1 + X2 + X3 + X4 + X5 + X6 + X7, data = Nomor2[c(-3,
## -19), ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.61096 -0.18114 0.02495 0.13878 0.97520
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.920e-01 1.546e+00 0.189 0.851118
## X1 -7.022e-03 1.116e-02 -0.629 0.532748
## X2 -1.259e-01 3.988e-02 -3.157 0.002945 **
## X3 1.993e-04 3.054e-04 0.653 0.517620
## X4 -1.447e-04 5.524e-05 -2.619 0.012213 *
## X5 1.822e-02 5.123e-03 3.557 0.000946 ***
## X6 5.886e-03 8.160e-03 0.721 0.474677
## X7 -1.048e-01 1.346e-01 -0.779 0.440590
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3561 on 42 degrees of freedom
## Multiple R-squared: 0.5478, Adjusted R-squared: 0.4725
## F-statistic: 7.27 on 7 and 42 DF, p-value: 1.045e-05Interpretasi : Tanpa amatan ke-3 dan 19 didapatkan nilai R-squared sebesar 0,5478
Maka, tidak ada penghapusan nilai amatan pada data ini karena nilai R-squared tertinggi pada model awal yaitu sebesar 0,5478.
Uji Asumsi
Nilai Harapan sisaan bernilai nol
t.test(resid(model2), mu = 0,)##
## One Sample t-test
##
## data: resid(model2)
## t = -7.2816e-17, df = 49, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.09369997 0.09369997
## sample estimates:
## mean of x
## -3.395179e-18Uji Normalitas
#Dengan eksplorasi
plot(model2,2); 
#Menggunakan Uji Saphiro Wilk
shapiro.test(residuals(model2))##
## Shapiro-Wilk normality test
##
## data: residuals(model2)
## W = 0.97191, p-value = 0.2764Ho : Sisaan menyebar normal H1 : Sisaan tidak menyebar normal Tolak H0 jika P-value < alpha
Uji Homoskedastisitas
#Dengan eksplorasi
plot(model2,1)
#Menggunakan uji Breusch-Pagan
lmtest::bptest(model2)##
## studentized Breusch-Pagan test
##
## data: model2
## BP = 7.7157, df = 7, p-value = 0.3583Keterangan HAsil Eksplorasi : 1. Sisaan di sekitar 0 → Nilai harapan galat sama dengan nol 2. Lebar pita sama untuk setiap nilai dugaan → ragam homogen
Hasil uji formal dengan Breusch Pagan : Ho : Ragam sisaan homogen H1 : Ragam sisaan tidak homogen Tolak H0 jika P-value < alpha
Uji Autokorelasi
#Dengan eksplorasi
plot(x = 1:dim(Nomor2)[1],
y = model2$residuals,
type = 'b',
ylab = "Residuals",
xlab = "Observation")
# Menggunakan uji Durbin-Watson
lmtest::dwtest(model2);##
## Durbin-Watson test
##
## data: model2
## DW = 2.4147, p-value = 0.9493
## alternative hypothesis: true autocorrelation is greater than 0# Menggunakan run test
randtests::runs.test(model2$residuals)##
## Runs Test
##
## data: model2$residuals
## statistic = 1.7146, runs = 32, n1 = 25, n2 = 25, n = 50, p-value =
## 0.08641
## alternative hypothesis: nonrandomnessHasil uji formal dengan Durbin-Watson:
Ho : Antar sisaan tidak terjadi autokorelasi H1 : Antar sisaan terjadi autokorelasi Tolak H0 jika P-value < alpha
Uji Multikolinearitas
car::vif(model2)## X1 X2 X3 X4 X5 X6 X7
## 2.861750 2.883731 1.310128 2.564437 3.397707 2.520059 1.646389Jika nilai VIF < 10, maka tidak terjadi multikolinearitas pada peubah bebasnya
Nomor 3
library(readxl)
library(ggplot2)Nomor3 <- read_xlsx("D:/Cooliah/Semester 4/Analisis Eksplorasi Data/UAS/Data2.xlsx", sheet = 3)
Nomor3## # A tibble: 15 × 2
## Hari `Penjualan (ribu Rupiah)`
## <dbl> <dbl>
## 1 1 20
## 2 2 25
## 3 3 18
## 4 4 22
## 5 5 30
## 6 6 35
## 7 7 28
## 8 8 19
## 9 9 24
## 10 10 29
## 11 11 32
## 12 12 26
## 13 13 21
## 14 14 27
## 15 15 23str(Nomor3)## tibble [15 × 2] (S3: tbl_df/tbl/data.frame)
## $ Hari : num [1:15] 1 2 3 4 5 6 7 8 9 10 ...
## $ Penjualan (ribu Rupiah): num [1:15] 20 25 18 22 30 35 28 19 24 29 ...Mengganti nama kolom
colnames(Nomor3) <- c("x","y")
Nomor3## # A tibble: 15 × 2
## x y
## <dbl> <dbl>
## 1 1 20
## 2 2 25
## 3 3 18
## 4 4 22
## 5 5 30
## 6 6 35
## 7 7 28
## 8 8 19
## 9 9 24
## 10 10 29
## 11 11 32
## 12 12 26
## 13 13 21
## 14 14 27
## 15 15 23#Mengurutkan data
Nomor3 <- Nomor3[order(Nomor3$x),]#Menghitung banyak titik anggota jendela
q <- 0.5
n <- 15
nq <- n*q
nq## [1] 7.5#banyak jendela jika desimal naik keatas maka
nq = 8Titik Focal 1
#Mencari nilai jarak(d), z, dan bobot(w) Jarak(d) xi-xp
d1 = Nomor3$x-Nomor3$x[1]
d1## [1] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14Nilai z
h1 = max(d1[1:5])
h1## [1] 4z1 = d1/h1
z1## [1] 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50Pemilihan h berdasarkan 1-5 titik terdekat bertujuan untuk menentukan jendela lokal yang menangkap struktur lokal data secara efektif. Ini membantu dalam menghasilkan estimasi yang lebih halus dan lebih responsif terhadap perubahan lokal, tanpa terlalu dipengaruhi oleh titik-titik yang jauh atau outlier
Nilai bobot
w1 = (1-abs(z1)^3)^3
w1## [1] 1.000000e+00 9.538536e-01 6.699219e-01 1.932259e-01 0.000000e+00
## [6] -8.658638e-01 -1.339648e+01 -8.284622e+01 -3.430000e+02 -1.121825e+03
## [11] -3.128150e+03 -7.758717e+03 -1.757600e+04 -3.701968e+04 -7.342847e+04wm1 <- diag(w1)
wm1## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [2,] 0 0.9538536 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [3,] 0 0.0000000 0.6699219 0.0000000 0 0.0000000 0.00000 0.00000
## [4,] 0 0.0000000 0.0000000 0.1932259 0 0.0000000 0.00000 0.00000
## [5,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [6,] 0 0.0000000 0.0000000 0.0000000 0 -0.8658638 0.00000 0.00000
## [7,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 -13.39648 0.00000
## [8,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 -82.84622
## [9,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [10,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [11,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [12,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [13,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [14,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [15,] 0 0.0000000 0.0000000 0.0000000 0 0.0000000 0.00000 0.00000
## [,9] [,10] [,11] [,12] [,13] [,14] [,15]
## [1,] 0 0.000 0.00 0.000 0 0.00 0.00
## [2,] 0 0.000 0.00 0.000 0 0.00 0.00
## [3,] 0 0.000 0.00 0.000 0 0.00 0.00
## [4,] 0 0.000 0.00 0.000 0 0.00 0.00
## [5,] 0 0.000 0.00 0.000 0 0.00 0.00
## [6,] 0 0.000 0.00 0.000 0 0.00 0.00
## [7,] 0 0.000 0.00 0.000 0 0.00 0.00
## [8,] 0 0.000 0.00 0.000 0 0.00 0.00
## [9,] -343 0.000 0.00 0.000 0 0.00 0.00
## [10,] 0 -1121.825 0.00 0.000 0 0.00 0.00
## [11,] 0 0.000 -3128.15 0.000 0 0.00 0.00
## [12,] 0 0.000 0.00 -7758.717 0 0.00 0.00
## [13,] 0 0.000 0.00 0.000 -17576 0.00 0.00
## [14,] 0 0.000 0.00 0.000 0 -37019.68 0.00
## [15,] 0 0.000 0.00 0.000 0 0.00 -73428.47#Menentukan nilai y duga Weighted Least Square Bduga = (X’ W X)^(-1) X’ W y
y <- as.matrix(Nomor3$y)
y## [,1]
## [1,] 20
## [2,] 25
## [3,] 18
## [4,] 22
## [5,] 30
## [6,] 35
## [7,] 28
## [8,] 19
## [9,] 24
## [10,] 29
## [11,] 32
## [12,] 26
## [13,] 21
## [14,] 27
## [15,] 23x <- matrix(c(rep(1,15),Nomor3$x), ncol=2, nrow=15, byrow=F)
x## [,1] [,2]
## [1,] 1 1
## [2,] 1 2
## [3,] 1 3
## [4,] 1 4
## [5,] 1 5
## [6,] 1 6
## [7,] 1 7
## [8,] 1 8
## [9,] 1 9
## [10,] 1 10
## [11,] 1 11
## [12,] 1 12
## [13,] 1 13
## [14,] 1 14
## [15,] 1 15#ncol=k+1, kolom pertama berisi 1, nfrow=banyak baris Mencari b1
b.1 <- solve(t(x)%*%wm1%*%x)%*%t(x)%*%wm1%*%y
b.1## [,1]
## [1,] 36.5168099
## [2,] -0.8677701yduga <- b0+b1x
yduga1 = b.1[1]+b.1[2]*Nomor3$x
y1 <- yduga1[1]
y1## [1] 35.64904perhitungan ini terus dilakukan hingga titik focal pint ke-15
Local Regression
plot(Nomor3$x, Nomor3$y,
main = 'Plot antara Hari dan Penjualan',
xlab = 'Hari',
ylab = 'Penjualan (Ribu Rupiah)')
Membuat LOESS dengan q = 0,5
loessmod15 <- loess(y~x, data = Nomor3, span = 0.5)Mendapatkan Smooth Output
smoothed15 <- predict(loessmod15)#Plot
ggplot(Nomor3, aes(x = x, y = y)) +
geom_point() +
geom_line(aes(y = smoothed15), color = 'green', size = 1) +
ggtitle("Plot") +
xlab("X") +
ylab("Y")## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
Diperolah output sebagai berikut. Dapat dilihat, dengan nilai q=0,5
didapatkan plot sangat fluktuatif untuk pola hubungan antara hari dan
penjualan
Membuat pemulusan dengan LOESS menggunakan semua q
Making Model Local Regresion for Dataset Cars
loess03 <- loess(y~x, data = Nomor3, span = 0.3, degree=1)
loess04 <- loess(y~x, data = Nomor3, span = 0.4, degree=1)
loess05 <- loess(y~x, data = Nomor3, span = 0.5, degree=1)
loess06 <- loess(y~x, data = Nomor3, span = 0.6, degree=1)
loess07 <- loess(y~x, data = Nomor3, span = 0.7, degree=1)
loess08 <- loess(y~x, data = Nomor3, span = 0.8, degree=1)
loess09 <- loess(y~x, data = Nomor3, span = 0.9, degree=1)#Get Smooth Output
smoothed03 <- predict(loess03)
smoothed04 <- predict(loess04)
smoothed05 <- predict(loess05)
smoothed06 <- predict(loess06)
smoothed07 <- predict(loess07)
smoothed08 <- predict(loess08)
smoothed09 <- predict(loess09)#Plot
# Menginisialisasi plot
plot(Nomor3$x, Nomor3$y, type = "p", main = "Plot Nomor3 dengan Garis Smoothed", xlab = "X", ylab = "Y")
# Menambahkan garis smoothed ke plot
lines(Nomor3$x, smoothed03, col = 'green', lwd = 3)
lines(Nomor3$x, smoothed04, col = 'blue', lwd = 3)
lines(Nomor3$x, smoothed05, col = 'green', lwd = 3)
lines(Nomor3$x, smoothed06, col = 'blue', lwd = 3)
lines(Nomor3$x, smoothed07, col = 'green', lwd = 3)
lines(Nomor3$x, smoothed08, col = 'blue', lwd = 3)
lines(Nomor3$x, smoothed09, col = 'green', lwd = 3)
Berikut adalah plot dengan nilai q = 0,8 maka didapatkan garis pemulusan
yang jauh lebih mulus dari sebelumnya. Semakin tinggi nilai q maka
semakin mulus garis pemulusan yang didapatkan. Ditunjukkan bahwa pada
hari 1-8 penjualan terus menaik setiap harinya. Sedangkan pada hari ke
8-15 penjualan terus menurun
plot(Nomor3$x, Nomor3$y, type = "p", main = "Plot Nomor3 dengan Garis Smoothed", xlab = "X", ylab = "Y")
lines(Nomor3$x, smoothed08, col = 'blue', lwd = 3)