Regresi Piecewise
Alfaridzi Nasaruddin
2026-05-29
Seorang mahasiswa ingin mengetahui pengaruh jam belajar terhadap nilai ujian. Dari hasil pengamatan, peningkatan nilai sangat cepat ketika jam belajar masih sedikit. Namun setelah melewati sekitar 5 jam belajar per hari, peningkatan nilai mulai melambat karena efek belajar tambahan semakin kecil. Oleh karena itu digunakan regresi piecewise untuk memodelkan dua pola hubungan yang berbeda.
data <- read.csv("D:/Youtube/Regresi/Piecedata.csv")
data## X jam_belajar nilai
## 1 1 1.000000 45.75810
## 2 2 1.060403 47.56251
## 3 3 1.120805 55.20128
## 4 4 1.181208 49.73170
## 5 5 1.241611 50.45004
## 6 6 1.302013 57.27637
## 7 7 1.362416 52.74299
## 8 8 1.422819 46.32231
## 9 9 1.483221 49.11836
## 10 10 1.543624 50.56635
## 11 11 1.604027 57.72854
## 12 12 1.664430 54.75469
## 13 13 1.724832 55.40174
## 14 14 1.785235 54.72461
## 15 15 1.845638 52.54174
## 16 16 1.906040 62.39597
## 17 17 1.966443 57.72295
## 18 18 2.026846 48.34830
## 19 19 2.087248 59.50341
## 20 20 2.147651 55.29004
## 21 21 2.208054 53.39313
## 22 22 2.268456 57.27575
## 23 23 2.328859 54.52685
## 24 24 2.389262 56.19853
## 25 25 2.449664 57.09716
## 26 26 2.510067 53.33376
## 27 27 2.570470 63.91491
## 28 28 2.630872 61.66047
## 29 29 2.691275 56.97765
## 30 30 2.751678 67.02868
## 31 31 2.812081 64.20250
## 32 32 2.872483 61.79958
## 33 33 2.932886 67.04359
## 34 34 2.993289 67.45884
## 35 35 3.053691 67.71585
## 36 36 3.114094 67.66731
## 37 37 3.174497 67.61164
## 38 38 3.234899 65.63155
## 39 39 3.295302 65.13857
## 40 40 3.355705 65.32375
## 41 41 3.416107 64.55003
## 42 42 3.476510 66.98041
## 43 43 3.536913 63.23372
## 44 44 3.597315 77.45435
## 45 45 3.657718 74.09359
## 46 46 3.718121 65.25253
## 47 47 3.778523 68.61665
## 48 48 3.838926 68.84479
## 49 49 3.899329 74.31449
## 50 50 3.959732 71.34438
## 51 51 4.020134 73.17435
## 52 52 4.080537 72.53011
## 53 53 4.140940 72.95603
## 54 54 4.201342 79.08515
## 55 55 4.261745 73.19088
## 56 56 4.322148 80.64306
## 57 57 4.382550 68.86539
## 58 58 4.442953 77.88208
## 59 59 4.503356 76.52226
## 60 60 4.563758 77.37383
## 61 61 4.624161 78.51185
## 62 62 4.684564 75.46722
## 63 63 4.744966 76.62690
## 64 64 4.805369 74.36865
## 65 65 4.865772 74.63901
## 66 66 4.926174 80.62351
## 67 67 4.986577 81.68546
## 68 68 5.046980 80.30598
## 69 69 5.107383 83.90383
## 70 70 5.167785 88.53591
## 71 71 5.228188 78.49225
## 72 72 5.288591 71.34051
## 73 73 5.348993 84.72094
## 74 74 5.409396 77.98199
## 75 75 5.469799 78.18756
## 76 76 5.530201 85.16269
## 77 77 5.590604 80.04212
## 78 78 5.651007 76.41914
## 79 79 5.711409 82.14803
## 80 80 5.771812 80.98806
## 81 81 5.832215 81.68749
## 82 82 5.892617 83.32636
## 83 83 5.953020 80.42340
## 84 84 6.013423 84.60435
## 85 85 6.073826 81.26570
## 86 86 6.134228 83.59558
## 87 87 6.194631 86.77662
## 88 88 6.255034 84.25079
## 89 89 6.315436 81.32715
## 90 90 6.375839 87.34691
## 91 91 6.436242 86.84650
## 92 92 6.496644 85.18688
## 93 93 6.557047 84.06902
## 94 94 6.617450 80.72328
## 95 95 6.677852 88.79831
## 96 96 6.738255 81.07547
## 97 97 6.798658 92.34665
## 98 98 6.859060 89.84856
## 99 99 6.919463 82.89612
## 100 100 6.979866 79.85405
## 101 101 7.040268 81.23891
## 102 102 7.100671 85.22888
## 103 103 7.161074 83.33538
## 104 104 7.221477 83.05278
## 105 105 7.281879 80.75728
## 106 106 7.342282 84.50445
## 107 107 7.402685 81.66575
## 108 108 7.463087 78.25441
## 109 109 7.523490 83.52607
## 110 110 7.583893 88.84377
## 111 111 7.644295 82.98720
## 112 112 7.704698 87.84125
## 113 113 7.765101 79.05867
## 114 114 7.825503 85.42876
## 115 115 7.885906 87.84944
## 116 116 7.946309 87.09723
## 117 117 8.006711 86.43613
## 118 118 8.067114 83.57140
## 119 119 8.127517 82.85622
## 120 120 8.187919 82.27932
## 121 121 8.248322 86.96723
## 122 122 8.308725 82.82755
## 123 123 8.369128 84.77603
## 124 124 8.429530 85.83469
## 125 125 8.489933 94.35531
## 126 126 8.550336 84.49287
## 127 127 8.610738 88.16302
## 128 128 8.671141 87.65413
## 129 129 8.731544 83.61566
## 130 130 8.791946 87.29866
## 131 131 8.852349 93.48290
## 132 132 8.912752 89.63152
## 133 133 8.973154 88.11124
## 134 134 9.033557 86.37713
## 135 135 9.093960 79.97493
## 136 136 9.154362 92.83407
## 137 137 9.214765 82.58697
## 138 138 9.275168 91.51013
## 139 139 9.335570 96.30756
## 140 140 9.395973 83.01637
## 141 141 9.456376 91.71989
## 142 142 9.516779 87.98477
## 143 143 9.577181 82.86579
## 144 144 9.637584 83.21650
## 145 145 9.697987 82.98983
## 146 146 9.758389 87.39315
## 147 147 9.818792 83.79056
## 148 148 9.879195 92.51006
## 149 149 9.939597 98.27963
## 150 150 10.000000 84.85188plot(data$jam_belajar,data$nilai,
pch = 19,
col = "blue",
xlab = "Jam Belajar",
ylab = "Nilai")
Membuat Breakpoint
c <- 5
# Variabel Tambahan
data$x_piece <- pmax(0,data$jam_belajar - c)
data## X jam_belajar nilai x_piece
## 1 1 1.000000 45.75810 0.00000000
## 2 2 1.060403 47.56251 0.00000000
## 3 3 1.120805 55.20128 0.00000000
## 4 4 1.181208 49.73170 0.00000000
## 5 5 1.241611 50.45004 0.00000000
## 6 6 1.302013 57.27637 0.00000000
## 7 7 1.362416 52.74299 0.00000000
## 8 8 1.422819 46.32231 0.00000000
## 9 9 1.483221 49.11836 0.00000000
## 10 10 1.543624 50.56635 0.00000000
## 11 11 1.604027 57.72854 0.00000000
## 12 12 1.664430 54.75469 0.00000000
## 13 13 1.724832 55.40174 0.00000000
## 14 14 1.785235 54.72461 0.00000000
## 15 15 1.845638 52.54174 0.00000000
## 16 16 1.906040 62.39597 0.00000000
## 17 17 1.966443 57.72295 0.00000000
## 18 18 2.026846 48.34830 0.00000000
## 19 19 2.087248 59.50341 0.00000000
## 20 20 2.147651 55.29004 0.00000000
## 21 21 2.208054 53.39313 0.00000000
## 22 22 2.268456 57.27575 0.00000000
## 23 23 2.328859 54.52685 0.00000000
## 24 24 2.389262 56.19853 0.00000000
## 25 25 2.449664 57.09716 0.00000000
## 26 26 2.510067 53.33376 0.00000000
## 27 27 2.570470 63.91491 0.00000000
## 28 28 2.630872 61.66047 0.00000000
## 29 29 2.691275 56.97765 0.00000000
## 30 30 2.751678 67.02868 0.00000000
## 31 31 2.812081 64.20250 0.00000000
## 32 32 2.872483 61.79958 0.00000000
## 33 33 2.932886 67.04359 0.00000000
## 34 34 2.993289 67.45884 0.00000000
## 35 35 3.053691 67.71585 0.00000000
## 36 36 3.114094 67.66731 0.00000000
## 37 37 3.174497 67.61164 0.00000000
## 38 38 3.234899 65.63155 0.00000000
## 39 39 3.295302 65.13857 0.00000000
## 40 40 3.355705 65.32375 0.00000000
## 41 41 3.416107 64.55003 0.00000000
## 42 42 3.476510 66.98041 0.00000000
## 43 43 3.536913 63.23372 0.00000000
## 44 44 3.597315 77.45435 0.00000000
## 45 45 3.657718 74.09359 0.00000000
## 46 46 3.718121 65.25253 0.00000000
## 47 47 3.778523 68.61665 0.00000000
## 48 48 3.838926 68.84479 0.00000000
## 49 49 3.899329 74.31449 0.00000000
## 50 50 3.959732 71.34438 0.00000000
## 51 51 4.020134 73.17435 0.00000000
## 52 52 4.080537 72.53011 0.00000000
## 53 53 4.140940 72.95603 0.00000000
## 54 54 4.201342 79.08515 0.00000000
## 55 55 4.261745 73.19088 0.00000000
## 56 56 4.322148 80.64306 0.00000000
## 57 57 4.382550 68.86539 0.00000000
## 58 58 4.442953 77.88208 0.00000000
## 59 59 4.503356 76.52226 0.00000000
## 60 60 4.563758 77.37383 0.00000000
## 61 61 4.624161 78.51185 0.00000000
## 62 62 4.684564 75.46722 0.00000000
## 63 63 4.744966 76.62690 0.00000000
## 64 64 4.805369 74.36865 0.00000000
## 65 65 4.865772 74.63901 0.00000000
## 66 66 4.926174 80.62351 0.00000000
## 67 67 4.986577 81.68546 0.00000000
## 68 68 5.046980 80.30598 0.04697987
## 69 69 5.107383 83.90383 0.10738255
## 70 70 5.167785 88.53591 0.16778523
## 71 71 5.228188 78.49225 0.22818792
## 72 72 5.288591 71.34051 0.28859060
## 73 73 5.348993 84.72094 0.34899329
## 74 74 5.409396 77.98199 0.40939597
## 75 75 5.469799 78.18756 0.46979866
## 76 76 5.530201 85.16269 0.53020134
## 77 77 5.590604 80.04212 0.59060403
## 78 78 5.651007 76.41914 0.65100671
## 79 79 5.711409 82.14803 0.71140940
## 80 80 5.771812 80.98806 0.77181208
## 81 81 5.832215 81.68749 0.83221477
## 82 82 5.892617 83.32636 0.89261745
## 83 83 5.953020 80.42340 0.95302013
## 84 84 6.013423 84.60435 1.01342282
## 85 85 6.073826 81.26570 1.07382550
## 86 86 6.134228 83.59558 1.13422819
## 87 87 6.194631 86.77662 1.19463087
## 88 88 6.255034 84.25079 1.25503356
## 89 89 6.315436 81.32715 1.31543624
## 90 90 6.375839 87.34691 1.37583893
## 91 91 6.436242 86.84650 1.43624161
## 92 92 6.496644 85.18688 1.49664430
## 93 93 6.557047 84.06902 1.55704698
## 94 94 6.617450 80.72328 1.61744966
## 95 95 6.677852 88.79831 1.67785235
## 96 96 6.738255 81.07547 1.73825503
## 97 97 6.798658 92.34665 1.79865772
## 98 98 6.859060 89.84856 1.85906040
## 99 99 6.919463 82.89612 1.91946309
## 100 100 6.979866 79.85405 1.97986577
## 101 101 7.040268 81.23891 2.04026846
## 102 102 7.100671 85.22888 2.10067114
## 103 103 7.161074 83.33538 2.16107383
## 104 104 7.221477 83.05278 2.22147651
## 105 105 7.281879 80.75728 2.28187919
## 106 106 7.342282 84.50445 2.34228188
## 107 107 7.402685 81.66575 2.40268456
## 108 108 7.463087 78.25441 2.46308725
## 109 109 7.523490 83.52607 2.52348993
## 110 110 7.583893 88.84377 2.58389262
## 111 111 7.644295 82.98720 2.64429530
## 112 112 7.704698 87.84125 2.70469799
## 113 113 7.765101 79.05867 2.76510067
## 114 114 7.825503 85.42876 2.82550336
## 115 115 7.885906 87.84944 2.88590604
## 116 116 7.946309 87.09723 2.94630872
## 117 117 8.006711 86.43613 3.00671141
## 118 118 8.067114 83.57140 3.06711409
## 119 119 8.127517 82.85622 3.12751678
## 120 120 8.187919 82.27932 3.18791946
## 121 121 8.248322 86.96723 3.24832215
## 122 122 8.308725 82.82755 3.30872483
## 123 123 8.369128 84.77603 3.36912752
## 124 124 8.429530 85.83469 3.42953020
## 125 125 8.489933 94.35531 3.48993289
## 126 126 8.550336 84.49287 3.55033557
## 127 127 8.610738 88.16302 3.61073826
## 128 128 8.671141 87.65413 3.67114094
## 129 129 8.731544 83.61566 3.73154362
## 130 130 8.791946 87.29866 3.79194631
## 131 131 8.852349 93.48290 3.85234899
## 132 132 8.912752 89.63152 3.91275168
## 133 133 8.973154 88.11124 3.97315436
## 134 134 9.033557 86.37713 4.03355705
## 135 135 9.093960 79.97493 4.09395973
## 136 136 9.154362 92.83407 4.15436242
## 137 137 9.214765 82.58697 4.21476510
## 138 138 9.275168 91.51013 4.27516779
## 139 139 9.335570 96.30756 4.33557047
## 140 140 9.395973 83.01637 4.39597315
## 141 141 9.456376 91.71989 4.45637584
## 142 142 9.516779 87.98477 4.51677852
## 143 143 9.577181 82.86579 4.57718121
## 144 144 9.637584 83.21650 4.63758389
## 145 145 9.697987 82.98983 4.69798658
## 146 146 9.758389 87.39315 4.75838926
## 147 147 9.818792 83.79056 4.81879195
## 148 148 9.879195 92.51006 4.87919463
## 149 149 9.939597 98.27963 4.93959732
## 150 150 10.000000 84.85188 5.00000000Pemodelan
model <- lm(nilai~jam_belajar+x_piece,
data=data)
summary(model)##
## Call:
## lm(formula = nilai ~ jam_belajar + x_piece, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.5727 -2.4193 -0.2783 2.4877 9.5527
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.9877 1.1320 35.32 <2e-16 ***
## jam_belajar 8.0881 0.3051 26.51 <2e-16 ***
## x_piece -6.4081 0.4827 -13.28 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.795 on 147 degrees of freedom
## Multiple R-squared: 0.9122, Adjusted R-squared: 0.911
## F-statistic: 764 on 2 and 147 DF, p-value: < 2.2e-16Prediksi
Prediksi <- predict(model)
Prediksi## 1 2 3 4 5 6 7 8
## 48.07581 48.56436 49.05290 49.54145 50.02999 50.51854 51.00708 51.49563
## 9 10 11 12 13 14 15 16
## 51.98417 52.47272 52.96126 53.44981 53.93835 54.42690 54.91544 55.40399
## 17 18 19 20 21 22 23 24
## 55.89254 56.38108 56.86963 57.35817 57.84672 58.33526 58.82381 59.31235
## 25 26 27 28 29 30 31 32
## 59.80090 60.28944 60.77799 61.26653 61.75508 62.24362 62.73217 63.22071
## 33 34 35 36 37 38 39 40
## 63.70926 64.19780 64.68635 65.17489 65.66344 66.15199 66.64053 67.12908
## 41 42 43 44 45 46 47 48
## 67.61762 68.10617 68.59471 69.08326 69.57180 70.06035 70.54889 71.03744
## 49 50 51 52 53 54 55 56
## 71.52598 72.01453 72.50307 72.99162 73.48016 73.96871 74.45725 74.94580
## 57 58 59 60 61 62 63 64
## 75.43434 75.92289 76.41144 76.89998 77.38853 77.87707 78.36562 78.85416
## 65 66 67 68 69 70 71 72
## 79.34271 79.83125 80.31980 80.50729 80.60877 80.71024 80.81172 80.91320
## 73 74 75 76 77 78 79 80
## 81.01467 81.11615 81.21763 81.31911 81.42058 81.52206 81.62354 81.72501
## 81 82 83 84 85 86 87 88
## 81.82649 81.92797 82.02944 82.13092 82.23240 82.33388 82.43535 82.53683
## 89 90 91 92 93 94 95 96
## 82.63831 82.73978 82.84126 82.94274 83.04422 83.14569 83.24717 83.34865
## 97 98 99 100 101 102 103 104
## 83.45012 83.55160 83.65308 83.75455 83.85603 83.95751 84.05899 84.16046
## 105 106 107 108 109 110 111 112
## 84.26194 84.36342 84.46489 84.56637 84.66785 84.76933 84.87080 84.97228
## 113 114 115 116 117 118 119 120
## 85.07376 85.17523 85.27671 85.37819 85.47966 85.58114 85.68262 85.78410
## 121 122 123 124 125 126 127 128
## 85.88557 85.98705 86.08853 86.19000 86.29148 86.39296 86.49444 86.59591
## 129 130 131 132 133 134 135 136
## 86.69739 86.79887 86.90034 87.00182 87.10330 87.20477 87.30625 87.40773
## 137 138 139 140 141 142 143 144
## 87.50921 87.61068 87.71216 87.81364 87.91511 88.01659 88.11807 88.21955
## 145 146 147 148 149 150
## 88.32102 88.42250 88.52398 88.62545 88.72693 88.82841Visualisasi
plot(data$jam_belajar,data$nilai,
pch = 19,
col = "blue",
xlab = "Jam Belajar",
ylab = "Nilai")
lines(data$jam_belajar,
Prediksi,
col = "red",
lwd = 4)