Tugas Akhir Anreg Analisis
Alur = Input data -> Cek eksploratif -> Cek gauss markov dan normalitas -> Cek Pencilan dll
library(readxl)
data<- read_excel("C:/Users/User/Documents/raziq/semes 4/anreg/tugas ahir/data tugas akhir.xlsx")
data## # A tibble: 29 × 17
## daerah y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Merauke 10.2 45013. 230932 3.43 260 29.7 503 366296 70.1 67 1.62e6
## 2 Jayawi… 37.1 2629. 269553 2.51 153 9.62 481 461058 58.0 59.6 1.46e6
## 3 Jayapu… 12.1 14082. 166171 10.3 174 30.0 302 601005 71.7 67.0 1.21e6
## 4 Nabire 23.8 11806. 169136 6.65 141 21.6 271 612872 68.8 68.1 1.61e6
## 5 Kepula… 26.1 2429. 112676 5.3 152 41.2 122 653819 67.7 69.1 1.07e6
## 6 Biak N… 24.4 2340. 134650 10.4 221 35.6 435 574402 72.2 68.2 1.18e6
## 7 Paniai 36.6 5307. 220410 0 110 61.3 18 512058 56.3 66.4 9.01e5
## 8 Puncak… 36 5986. 224527 1.5 38 31.9 2 639503 48.4 65.2 2.04e6
## 9 Mimika 14.2 18299. 311969 7.8 152 13.5 647 870355 74.2 72.3 1.54e6
## 10 Boven … 19.9 23558. 64285 8.09 112 36.2 127 486179 61.5 60.0 1.18e6
## # … with 19 more rows, and 5 more variables: x11 <dbl>, x12 <dbl>, x13 <dbl>,
## # x14 <dbl>, x15 <dbl>Model Regresi
modelreg <- lm(y~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13+x14+x15,data= data)
modelreg##
## Call:
## lm(formula = y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 +
## x10 + x11 + x12 + x13 + x14 + x15, data = data)
##
## Coefficients:
## (Intercept) x1 x2 x3 x4 x5
## -4.910e+00 8.103e-05 -9.974e-05 4.161e-01 -5.601e-02 6.304e-03
## x6 x7 x8 x9 x10 x11
## 1.706e-02 -9.222e-06 -2.809e-01 6.591e-01 -2.152e-07 -1.379e-04
## x12 x13 x14 x15
## 1.360e-06 4.627e-01 1.778e+00 3.753e-02Summary
summary(modelreg)##
## Call:
## lm(formula = y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 +
## x10 + x11 + x12 + x13 + x14 + x15, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.1117 -1.5951 -0.1434 1.6801 8.9780
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.910e+00 3.168e+01 -0.155 0.87921
## x1 8.103e-05 2.139e-04 0.379 0.71096
## x2 -9.974e-05 4.868e-05 -2.049 0.06125 .
## x3 4.161e-01 6.746e-01 0.617 0.54805
## x4 -5.601e-02 7.660e-02 -0.731 0.47761
## x5 6.304e-03 7.480e-02 0.084 0.93412
## x6 1.706e-02 1.899e-02 0.898 0.38532
## x7 -9.223e-06 1.343e-05 -0.687 0.50418
## x8 -2.809e-01 2.262e-01 -1.242 0.23624
## x9 6.591e-01 5.290e-01 1.246 0.23480
## x10 -2.152e-07 3.773e-06 -0.057 0.95538
## x11 -1.379e-04 2.264e-04 -0.609 0.55294
## x12 1.360e-06 1.641e-06 0.829 0.42205
## x13 4.627e-01 1.480e-01 3.126 0.00803 **
## x14 1.778e+00 7.619e-01 2.334 0.03630 *
## x15 3.753e-02 2.363e-02 1.588 0.13627
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.614 on 13 degrees of freedom
## Multiple R-squared: 0.8956, Adjusted R-squared: 0.7752
## F-statistic: 7.436 on 15 and 13 DF, p-value: 0.0004026Anova
anova(modelreg)## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x1 1 676.27 676.27 31.7703 8.111e-05 ***
## x2 1 67.15 67.15 3.1549 0.099097 .
## x3 1 956.01 956.01 44.9123 1.467e-05 ***
## x4 1 0.03 0.03 0.0015 0.969818
## x5 1 43.07 43.07 2.0232 0.178465
## x6 1 7.52 7.52 0.3534 0.562398
## x7 1 105.78 105.78 4.9693 0.044066 *
## x8 1 197.75 197.75 9.2902 0.009336 **
## x9 1 1.49 1.49 0.0702 0.795270
## x10 1 0.01 0.01 0.0004 0.984677
## x11 1 92.29 92.29 4.3355 0.057644 .
## x12 1 12.65 12.65 0.5941 0.454607
## x13 1 92.24 92.24 4.3336 0.057693 .
## x14 1 68.36 68.36 3.2115 0.096413 .
## x15 1 53.69 53.69 2.5222 0.136269
## Residuals 13 276.72 21.29
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Cek eksploratif
plot(modelreg)
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Asumsi GAUSS MARKOV # 1. Nilai Harapan galat sama dengan nol
t.test(modelreg$residuals,
mu = 0,
conf.level = 0.95)##
## One Sample t-test
##
## data: modelreg$residuals
## t = 4.9633e-18, df = 28, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -1.195797 1.195797
## sample estimates:
## mean of x
## 2.897437e-182. galat saling bebas
library(randtests)
runs.test(modelreg$residuals)##
## Runs Test
##
## data: modelreg$residuals
## statistic = 1.5407, runs = 19, n1 = 14, n2 = 14, n = 28, p-value =
## 0.1234
## alternative hypothesis: nonrandomnesslibrary(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericdwtest(modelreg)##
## Durbin-Watson test
##
## data: modelreg
## DW = 1.7203, p-value = 0.1173
## alternative hypothesis: true autocorrelation is greater than 0bgtest(modelreg)##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: modelreg
## LM test = 0.76559, df = 1, p-value = 0.38163. Ragam galat homogen
cek.homogen = lm(formula = abs(modelreg$residuals) ~ data$y,
data = data)
summary(cek.homogen)##
## Call:
## lm(formula = abs(modelreg$residuals) ~ data$y, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.1818 -1.7791 -0.4564 1.4330 6.9180
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.305044 1.352882 1.704 0.0999 .
## data$y -0.006463 0.045174 -0.143 0.8873
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.326 on 27 degrees of freedom
## Multiple R-squared: 0.0007575, Adjusted R-squared: -0.03625
## F-statistic: 0.02047 on 1 and 27 DF, p-value: 0.8873library(lmtest)
bptest(modelreg)##
## studentized Breusch-Pagan test
##
## data: modelreg
## BP = 12.999, df = 15, p-value = 0.6023library(car)## Loading required package: carDatancvTest(modelreg)## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 0.2095992, Df = 1, p = 0.647084. cek normalitas
ks.test(modelreg$residuals, "pnorm", mean=mean(modelreg$residuals), sd=sd(modelreg$residuals))##
## Exact one-sample Kolmogorov-Smirnov test
##
## data: modelreg$residuals
## D = 0.14338, p-value = 0.5426
## alternative hypothesis: two-sidedshapiro.test(modelreg$residuals)##
## Shapiro-Wilk normality test
##
## data: modelreg$residuals
## W = 0.9472, p-value = 0.1547Kesimpulan
y=data$y
x1=data$x1
x2=data$x2
x3=data$x3
x4=data$x4
x5=data$x5
x6=data$x6
x7=data$x7
x8=data$x8
x9=data$x9
x10=data$x10
x11=data$x11
x12=data$x12
x13=data$x13
x14=data$x14
x15=data$x15
data<-data.frame(cbind(y,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15))
data## y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
## 1 10.16 45013.35 230932 3.43 260 29.67 503 366296 70.09 67.00 1619834
## 2 37.09 2629.01 269553 2.51 153 9.62 481 461058 58.03 59.64 1459370
## 3 12.13 14082.21 166171 10.33 174 29.95 302 601005 71.69 67.05 1210925
## 4 23.83 11806.09 169136 6.65 141 21.57 271 612872 68.83 68.06 1606658
## 5 26.09 2429.03 112676 5.30 152 41.20 122 653819 67.66 69.12 1071327
## 6 24.45 2339.78 134650 10.38 221 35.56 435 574402 72.19 68.25 1180692
## 7 36.59 5306.87 220410 0.00 110 61.31 18 512058 56.31 66.44 901010
## 8 36.00 5986.19 224527 1.50 38 31.86 2 639503 48.37 65.15 2037148
## 9 14.17 18298.95 311969 7.80 152 13.52 647 870355 74.19 72.32 1536464
## 10 19.90 23558.27 64285 8.09 112 36.22 127 486179 61.53 59.97 1176631
## 11 26.09 24262.23 108295 5.77 172 23.58 127 351801 58.15 65.11 701155
## 12 24.83 25015.31 110105 2.38 149 91.81 23 383790 50.55 58.05 814912
## 13 37.64 16365.94 350880 3.88 187 30.59 26 428433 49.37 65.93 1077844
## 14 30.46 13751.92 77872 4.12 99 68.47 12 580393 45.44 64.44 1266742
## 15 32.60 2990.01 236986 1.07 86 21.35 51 404812 49.50 65.71 1177982
## 16 13.84 14068.37 41515 4.83 87 32.01 42 535586 63.63 66.36 1073259
## 17 16.00 9526.32 61623 2.56 102 22.71 175 677050 66.40 66.69 798421
## 18 29.85 10778.76 33943 4.76 66 41.77 68 691544 64.94 66.33 1578129
## 19 37.91 660.61 22547 4.12 58 15.06 82 471401 62.30 65.94 1099147
## 20 28.78 28042.39 36483 2.55 74 92.60 13 727830 51.78 57.77 544272
## 21 37.18 5886.89 106533 0.00 38 6.69 0 360779 31.55 55.27 1462880
## 22 38.73 2339.87 196399 0.00 82 6.37 6 490508 47.86 66.06 1505891
## 23 36.76 4101.50 50685 0.00 46 2.40 75 412574 47.57 63.59 1096064
## 24 33.25 3148.29 101973 0.00 69 54.25 0 347171 48.34 65.42 1683573
## 25 36.26 7701.03 114741 0.00 55 31.65 0 664865 43.04 65.74 1007631
## 26 28.81 3792.93 116206 0.00 69 21.17 0 512654 54.84 65.73 485881
## 27 41.66 5334.45 135043 1.22 31 61.99 0 662465 47.79 65.60 1230693
## 28 40.59 2846.41 99091 0.00 46 51.50 0 608868 49.46 65.24 1055174
## 29 11.39 835.48 398478 11.62 94 22.88 4 1021759 79.94 70.45 1819277
## x11 x12 x13 x14 x15
## 1 16026.18 3264222 22.89 1.67 5.24
## 2 8255.38 4309795 81.71 3.23 38.34
## 3 15974.73 3651343 16.61 4.03 14.89
## 4 11178.38 3559535 36.75 2.68 15.22
## 5 4150.23 3314294 27.04 3.11 54.96
## 6 5223.67 3195686 38.02 0.60 51.75
## 7 4283.39 3881394 65.98 3.69 44.17
## 8 1387.23 4036841 46.07 8.30 34.41
## 9 63716.34 5926620 31.75 5.54 14.42
## 10 4820.54 3053268 13.86 1.43 3.62
## 11 2991.71 3017944 26.91 2.86 12.91
## 12 2569.01 5137378 25.12 3.70 7.02
## 13 2504.26 5825556 71.76 7.87 20.46
## 14 1968.75 4967729 23.03 1.76 13.94
## 15 1672.32 4493501 44.88 7.55 21.59
## 16 2937.45 3443388 5.70 2.33 1.53
## 17 2925.04 3527627 9.42 2.42 2.56
## 18 2044.75 3601837 9.44 3.26 1.06
## 19 1042.05 2684956 7.78 3.57 33.24
## 20 1722.34 3112124 6.98 7.11 1.53
## 21 1269.94 4015607 36.54 3.03 83.56
## 22 1930.04 3095693 68.62 2.83 156.74
## 23 1213.55 4178269 17.72 2.52 22.55
## 24 1283.66 2875730 20.84 7.22 47.04
## 25 1438.05 3169255 42.43 2.10 14.24
## 26 1355.63 5566846 28.31 3.27 27.42
## 27 1273.03 2613058 20.46 12.80 34.43
## 28 1435.66 3909419 30.98 4.78 184.39
## 29 32019.13 4123268 33.80 4.50 425.76#deteksi pencilan
s = sqrt(21.29)
n = dim(data)[1]
p = length(modelreg$coefficients)
hii=hatvalues(modelreg)
Obs = c(1:n)
ei = modelreg$residuals
ri = ei/(s*sqrt(1-hii))
summ <- cbind.data.frame(Obs, data, hii, ri)
summ## Obs y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
## 1 1 10.16 45013.35 230932 3.43 260 29.67 503 366296 70.09 67.00 1619834
## 2 2 37.09 2629.01 269553 2.51 153 9.62 481 461058 58.03 59.64 1459370
## 3 3 12.13 14082.21 166171 10.33 174 29.95 302 601005 71.69 67.05 1210925
## 4 4 23.83 11806.09 169136 6.65 141 21.57 271 612872 68.83 68.06 1606658
## 5 5 26.09 2429.03 112676 5.30 152 41.20 122 653819 67.66 69.12 1071327
## 6 6 24.45 2339.78 134650 10.38 221 35.56 435 574402 72.19 68.25 1180692
## 7 7 36.59 5306.87 220410 0.00 110 61.31 18 512058 56.31 66.44 901010
## 8 8 36.00 5986.19 224527 1.50 38 31.86 2 639503 48.37 65.15 2037148
## 9 9 14.17 18298.95 311969 7.80 152 13.52 647 870355 74.19 72.32 1536464
## 10 10 19.90 23558.27 64285 8.09 112 36.22 127 486179 61.53 59.97 1176631
## 11 11 26.09 24262.23 108295 5.77 172 23.58 127 351801 58.15 65.11 701155
## 12 12 24.83 25015.31 110105 2.38 149 91.81 23 383790 50.55 58.05 814912
## 13 13 37.64 16365.94 350880 3.88 187 30.59 26 428433 49.37 65.93 1077844
## 14 14 30.46 13751.92 77872 4.12 99 68.47 12 580393 45.44 64.44 1266742
## 15 15 32.60 2990.01 236986 1.07 86 21.35 51 404812 49.50 65.71 1177982
## 16 16 13.84 14068.37 41515 4.83 87 32.01 42 535586 63.63 66.36 1073259
## 17 17 16.00 9526.32 61623 2.56 102 22.71 175 677050 66.40 66.69 798421
## 18 18 29.85 10778.76 33943 4.76 66 41.77 68 691544 64.94 66.33 1578129
## 19 19 37.91 660.61 22547 4.12 58 15.06 82 471401 62.30 65.94 1099147
## 20 20 28.78 28042.39 36483 2.55 74 92.60 13 727830 51.78 57.77 544272
## 21 21 37.18 5886.89 106533 0.00 38 6.69 0 360779 31.55 55.27 1462880
## 22 22 38.73 2339.87 196399 0.00 82 6.37 6 490508 47.86 66.06 1505891
## 23 23 36.76 4101.50 50685 0.00 46 2.40 75 412574 47.57 63.59 1096064
## 24 24 33.25 3148.29 101973 0.00 69 54.25 0 347171 48.34 65.42 1683573
## 25 25 36.26 7701.03 114741 0.00 55 31.65 0 664865 43.04 65.74 1007631
## 26 26 28.81 3792.93 116206 0.00 69 21.17 0 512654 54.84 65.73 485881
## 27 27 41.66 5334.45 135043 1.22 31 61.99 0 662465 47.79 65.60 1230693
## 28 28 40.59 2846.41 99091 0.00 46 51.50 0 608868 49.46 65.24 1055174
## 29 29 11.39 835.48 398478 11.62 94 22.88 4 1021759 79.94 70.45 1819277
## x11 x12 x13 x14 x15 hii ri
## 1 16026.18 3264222 22.89 1.67 5.24 0.9235368 1.63994541
## 2 8255.38 4309795 81.71 3.23 38.34 0.7289329 -0.09379946
## 3 15974.73 3651343 16.61 4.03 14.89 0.2572984 -0.96671410
## 4 11178.38 3559535 36.75 2.68 15.22 0.1985838 -0.03424250
## 5 4150.23 3314294 27.04 3.11 54.96 0.5340996 0.53344888
## 6 5223.67 3195686 38.02 0.60 51.75 0.6351222 -0.13085041
## 7 4283.39 3881394 65.98 3.69 44.17 0.6622514 0.75610975
## 8 1387.23 4036841 46.07 8.30 34.41 0.4718231 -0.47568672
## 9 63716.34 5926620 31.75 5.54 14.42 0.9683480 0.03853330
## 10 4820.54 3053268 13.86 1.43 3.62 0.4635449 -0.07634986
## 11 2991.71 3017944 26.91 2.86 12.91 0.4902806 -0.04352685
## 12 2569.01 5137378 25.12 3.70 7.02 0.5595174 -0.11934429
## 13 2504.26 5825556 71.76 7.87 20.46 0.7003607 1.38367875
## 14 1968.75 4967729 23.03 1.76 13.94 0.6029280 0.11745027
## 15 1672.32 4493501 44.88 7.55 21.59 0.3741765 -0.55595861
## 16 2937.45 3443388 5.70 2.33 1.53 0.1993608 -1.96474269
## 17 2925.04 3527627 9.42 2.42 2.56 0.4271202 -1.21236425
## 18 2044.75 3601837 9.44 3.26 1.06 0.4533809 1.16869338
## 19 1042.05 2684956 7.78 3.57 33.24 0.2994890 2.32480333
## 20 1722.34 3112124 6.98 7.11 1.53 0.6354963 0.25462704
## 21 1269.94 4015607 36.54 3.03 83.56 0.6914667 -0.12344408
## 22 1930.04 3095693 68.62 2.83 156.74 0.5668155 -1.43851639
## 23 1213.55 4178269 17.72 2.52 22.55 0.2798056 1.05364438
## 24 1283.66 2875730 20.84 7.22 47.04 0.5787016 -0.78699111
## 25 1438.05 3169255 42.43 2.10 14.24 0.6589532 0.73036278
## 26 1355.63 5566846 28.31 3.27 27.42 0.4743302 -0.50137743
## 27 1273.03 2613058 20.46 12.80 34.43 0.5842732 0.03646352
## 28 1435.66 3909419 30.98 4.78 184.39 0.6306886 -0.26093304
## 29 32019.13 4123268 33.80 4.50 425.76 0.9493138 1.17353825#pencilan jika rii lebih dari 2 ada di amatan ke 19deteksi titik leverannce
for (i in 1:dim(summ)[1]){
cutoff <- 2*p/n
titik_leverage <- which(hii > cutoff)
}
titik_leverage## named integer(0)