Raport 8.- NMS

library(ggplot2)
## Warning: pakiet 'ggplot2' został zbudowany w wersji R 4.1.3
library(lmboot)
## Warning: pakiet 'lmboot' został zbudowany w wersji R 4.1.3
library(car)
## Warning: pakiet 'car' został zbudowany w wersji R 4.1.3
## Ładowanie wymaganego pakietu: carData
library(scorecard)
## Warning: pakiet 'scorecard' został zbudowany w wersji R 4.1.3
## 
## Dołączanie pakietu: 'scorecard'
## Następujący obiekt został zakryty z 'package:car':
## 
##     vif
data(germancredit)
attach(germancredit)

Dane te mają dwie klasy zdolności kredytowej: dobrą lub złą. Istnieją predyktory związane z atrybutami, takimi jak: sprawdzenie stanu konta, czas trwania, historia kredytowa, cel pożyczki, kwota pożyczki, konta oszczędnościowe lub obligacje, okres zatrudnienia, wysokość raty jako procent dochodu do dyspozycji, dane osobowe, inni dłużnicy /poręczyciele, czas zamieszkania, majątek, wiek, inne raty, warunki mieszkaniowe, liczba istniejących kredytów, informacje o pracy, liczba osób zobowiązanych do alimentów, telefon, status pracownika zagranicznego.

1. Wstępne analizy opisowe

summary(germancredit)
##                                      status.of.existing.checking.account
##  ... < 0 DM                                            :274             
##  0 <= ... < 200 DM                                     :269             
##  ... >= 200 DM / salary assignments for at least 1 year: 63             
##  no checking account                                   :394             
##                                                                         
##                                                                         
##  duration.in.month
##  Min.   : 4.0     
##  1st Qu.:12.0     
##  Median :18.0     
##  Mean   :20.9     
##  3rd Qu.:24.0     
##  Max.   :72.0     
##                                                      credit.history
##  no credits taken/ all credits paid back duly               : 40   
##  all credits at this bank paid back duly                    : 49   
##  existing credits paid back duly till now                   :530   
##  delay in paying off in the past                            : 88   
##  critical account/ other credits existing (not at this bank):293   
##                                                                    
##    purpose          credit.amount                 savings.account.and.bonds
##  Length:1000        Min.   :  250   ... < 100 DM               :603        
##  Class :character   1st Qu.: 1366   100 <= ... < 500 DM        :103        
##  Mode  :character   Median : 2320   500 <= ... < 1000 DM       : 63        
##                     Mean   : 3271   ... >= 1000 DM             : 48        
##                     3rd Qu.: 3972   unknown/ no savings account:183        
##                     Max.   :18424                                          
##        present.employment.since
##  unemployed        : 62        
##  ... < 1 year      :172        
##  1 <= ... < 4 years:339        
##  4 <= ... < 7 years:174        
##  ... >= 7 years    :253        
##                                
##  installment.rate.in.percentage.of.disposable.income
##  Min.   :1.000                                      
##  1st Qu.:2.000                                      
##  Median :3.000                                      
##  Mean   :2.973                                      
##  3rd Qu.:4.000                                      
##  Max.   :4.000                                      
##                         personal.status.and.sex other.debtors.or.guarantors
##  male : divorced/separated          : 50        none        :907           
##  female : divorced/separated/married:310        co-applicant: 41           
##  male : single                      :548        guarantor   : 52           
##  male : married/widowed             : 92                                   
##  female : single                    :  0                                   
##                                                                            
##  present.residence.since
##  Min.   :1.000          
##  1st Qu.:2.000          
##  Median :3.000          
##  Mean   :2.845          
##  3rd Qu.:4.000          
##  Max.   :4.000          
##                                                  property    age.in.years  
##  real estate                                         :282   Min.   :19.00  
##  building society savings agreement/ life insurance  :232   1st Qu.:27.00  
##  car or other, not in attribute Savings account/bonds:332   Median :33.00  
##  unknown / no property                               :154   Mean   :35.55  
##                                                             3rd Qu.:42.00  
##                                                             Max.   :75.00  
##  other.installment.plans     housing    number.of.existing.credits.at.this.bank
##  bank  :139              rent    :179   Min.   :1.000                          
##  stores: 47              own     :713   1st Qu.:1.000                          
##  none  :814              for free:108   Median :1.000                          
##                                         Mean   :1.407                          
##                                         3rd Qu.:2.000                          
##                                         Max.   :4.000                          
##                                                             job     
##  unemployed/ unskilled - non-resident                         : 22  
##  unskilled - resident                                         :200  
##  skilled employee / official                                  :630  
##  management/ self-employed/ highly qualified employee/ officer:148  
##                                                                     
##                                                                     
##  number.of.people.being.liable.to.provide.maintenance.for
##  Min.   :1.000                                           
##  1st Qu.:1.000                                           
##  Median :1.000                                           
##  Mean   :1.155                                           
##  3rd Qu.:1.000                                           
##  Max.   :2.000                                           
##                                     telephone   foreign.worker creditability
##  none                                    :596   yes:963        bad :300     
##  yes, registered under the customers name:404   no : 37        good:700     
##                                                                             
##                                                                             
##                                                                             
##

394 kredyty nie miały konta bankowego. Najkrótszy okres trwania kredytu wynosił 4 miesiące, a najdłuższy 72 miesiące. Mediana wynosiła 18 miesięcy, a średnia 20,9 miesiąca.530 kredytów miało historię “wszystkie obecne kredyty spłacone terminowo”. 339 osób miało zatrudnienie < 4 lata. Minimalna rata wynosiła 1000, maksymalna 4000. 907 kredytów nie miało żadnych innych dłużników lub poręczycieli. Najmłodsza osoba miała 19 lat, najstarsza 75, mediana wynosi 33 lata. 814 kredytów nie miało żadnych innych planów rat.

2. Przekroje opisowe

ggplot(germancredit, aes(x = purpose, y = credit.amount)) +
  geom_boxplot() +
   theme(legend.position = 'none', axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1))+
  labs(x = "Purpose", y = "Credit Amount")

Wykres pozwala na porównanie wysokości kredytów w zalezności od celu jego zaciągnięcia. Najwyzsze kredyty zaciągane były na cele zaklasyfikowane jako “inne”, drugie najwyższe na używane samochody. Najniższe kredyty zaciągane były na sprzęty AGD.Dużo wartości odstających można zaobserwować przy kredytach na nowe samochody. Może być to spowodowane faktem, że nowe samochody mają wyższe ceny niż np. używane, a więc wyższe ceny mogą powodować większą zmienność w zakresie wartości kredytów, a co za tym idzie większą liczbę wartości odstających.

3. Przetestowane założenia

# Normalność rozkładu
shapiro.test(germancredit$credit.amount)
## 
##  Shapiro-Wilk normality test
## 
## data:  germancredit$credit.amount
## W = 0.7934, p-value < 2.2e-16
# Homogeniczność wariancji
leveneTest(credit.amount ~ purpose, data = germancredit)
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   9  8.6309 1.549e-12 ***
##       990                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Statystyka testowa W wynosi 0,7934. Wartość p-value jest mniejsza niż 2,2e-16. Na podstawie tego wyniku można stwierdzić, że zmienna mówiąca o wysokości kredytu nie spełnia założenia normalności. Wynik testu Levene’s dla homogeniczności wariancji wskazuje na istotną różnicę w wariancji między grupami. Wartość p-value wynosi 1,549e-12, co oznacza, że istnieje statystycznie istotna różnica w wariancji między grupami.

4. ANOVA klasyczna

anova_model <- lm(credit.amount ~ purpose  + age.in.years, data = germancredit)
anova_wyniki <- anova(anova_model)
print(anova_wyniki)
## Analysis of Variance Table
## 
## Response: credit.amount
##               Df     Sum Sq   Mean Sq F value Pr(>F)    
## purpose        9 1095334193 121703799 17.5352 <2e-16 ***
## age.in.years   1     350297    350297  0.0505 0.8223    
## Residuals    989 6864191137   6940537                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  • Grupa “purpose” wykazuje statystycznie istotne różnice w średnich wartościach zmiennej “credit.amount”. Wartość p-value wynosi <2e-16, co oznacza, że istnieje bardzo mała szansa, że różnice te wynikają z przypadku.

  • W przypadku zmiennej “age.in.years” nie zaobserwowano istotnej różnicy w średnich wartościach, ponieważ wartość p-value wynosi 0,8223, co jest wyższe od konwencjonalnego poziomu istotności 0,05.

  • Residuals (pozostałe) odnoszą się do różnicy między obserwowanymi wartościami a wartościami przewidywanymi przez model. Pokazane są stopnie swobody, suma kwadratów i średnia kwadratowa tych różnic.

Podsumowując, wyniki analizy wariancji wskazują na istotną różnicę w wartościach zmiennej “credit.amount” między różnymi grupami zmiennej “purpose”, podczas gdy zmienna “age.in.years” nie wykazuje takiej różnicy.

5. ANOVA metodą bootstrap

bootstrap_anova <- ANOVA.boot(credit.amount ~ purpose + age.in.years, data = germancredit, B = 1000)
print(bootstrap_anova)
## $terms
## [1] "purpose     " "age.in.years" "Residuals   "
## 
## $df
## [1]   9   1 989
## 
## $origFStats
## [1] 17.53521355  0.05047114
## 
## $origSSE
## [1] 6864191137
## 
## $origSSTr
## [1] 1095334193.1     350296.8
## 
## $bootFStats
##              [,1]         [,2]
##    [1,] 1.3015126 6.033525e-01
##    [2,] 0.6013908 1.819837e-01
##    [3,] 0.4611189 5.026069e-02
##    [4,] 0.9309776 6.304714e-01
##    [5,] 1.2050172 2.570933e+00
##    [6,] 0.6050703 3.071622e-01
##    [7,] 0.6664044 1.622508e-01
##    [8,] 0.5723330 1.542197e+00
##    [9,] 0.5316681 3.999745e-02
##   [10,] 0.5268628 3.523121e-02
##   [11,] 0.9194035 2.973649e-03
##   [12,] 0.2017737 8.810002e-01
##   [13,] 0.8984546 2.454887e+00
##   [14,] 1.6018013 5.206541e+00
##   [15,] 0.9092983 2.237660e-02
##   [16,] 0.5741997 5.210055e-01
##   [17,] 0.1106863 3.314901e+00
##   [18,] 0.9591894 3.940353e-03
##   [19,] 1.2255071 3.906176e-02
##   [20,] 0.4914764 1.639206e-01
##   [21,] 0.4231349 9.684755e-01
##   [22,] 0.4054682 2.338478e+00
##   [23,] 1.3170497 8.029836e-01
##   [24,] 0.7886786 2.734644e-03
##   [25,] 0.7941006 5.238527e-01
##   [26,] 0.5200971 5.635186e-01
##   [27,] 0.8249649 3.107205e-01
##   [28,] 0.7374000 4.924625e-02
##   [29,] 0.6325939 3.572082e-04
##   [30,] 1.7278063 3.116093e-04
##   [31,] 0.8270719 6.669232e-01
##   [32,] 2.3671279 4.248231e-01
##   [33,] 1.1730399 4.470166e-02
##   [34,] 1.3845736 1.004597e+00
##   [35,] 0.9378246 5.490794e+00
##   [36,] 1.5857495 1.462222e+00
##   [37,] 0.4472407 1.562384e-01
##   [38,] 0.7437320 1.908733e-02
##   [39,] 0.8173133 2.779832e-01
##   [40,] 1.3294255 2.124291e-01
##   [41,] 0.9579319 1.345009e+00
##   [42,] 1.4441822 9.693495e-03
##   [43,] 2.0119981 1.678762e+00
##   [44,] 0.6348739 8.587580e-01
##   [45,] 1.5908793 2.230627e+00
##   [46,] 0.6262490 1.493891e-03
##   [47,] 1.1190483 1.531058e+00
##   [48,] 0.9513845 2.078780e+00
##   [49,] 0.9505776 8.708307e-02
##   [50,] 2.0574612 3.983605e-03
##   [51,] 2.0682211 5.048341e-02
##   [52,] 0.7744990 1.832366e+00
##   [53,] 1.0418877 4.834624e+00
##   [54,] 0.5769089 1.394444e+00
##   [55,] 0.8610053 4.096471e-01
##   [56,] 0.2629029 9.749013e-01
##   [57,] 0.6632416 6.892333e-03
##   [58,] 0.5246565 4.050347e-02
##   [59,] 1.2932561 5.185679e-01
##   [60,] 0.9928267 4.968749e-01
##   [61,] 0.9932644 1.319921e-01
##   [62,] 0.3811957 3.397167e+00
##   [63,] 0.9581105 3.406400e-01
##   [64,] 0.7978143 8.594713e-02
##   [65,] 0.7881031 1.271143e+00
##   [66,] 0.4780179 1.521858e-01
##   [67,] 0.8272394 2.081287e+00
##   [68,] 0.5546510 7.763984e-02
##   [69,] 0.5914370 1.312672e-02
##   [70,] 0.9196673 9.371551e-02
##   [71,] 0.6243712 1.469130e+00
##   [72,] 2.1624760 5.926999e+00
##   [73,] 1.0075100 1.022058e+00
##   [74,] 1.0661109 3.043231e-01
##   [75,] 1.4661069 4.571844e-04
##   [76,] 0.8679418 2.548033e+00
##   [77,] 1.2663648 9.614990e-01
##   [78,] 1.4305110 1.468409e-05
##   [79,] 0.2729115 3.127286e-02
##   [80,] 1.0297402 4.525133e+00
##   [81,] 0.6841141 1.556352e+00
##   [82,] 1.2811926 4.639068e-01
##   [83,] 0.6777112 2.336705e+00
##   [84,] 1.3130530 3.296436e-01
##   [85,] 1.3901575 2.516992e+00
##   [86,] 0.9932469 9.686008e-01
##   [87,] 1.0566169 2.563717e-01
##   [88,] 0.9989375 7.143150e-02
##   [89,] 1.3491834 1.662236e+00
##   [90,] 1.4374708 9.712585e-01
##   [91,] 1.3865216 1.192329e+00
##   [92,] 1.0672157 1.080880e+00
##   [93,] 1.0961637 3.720291e-01
##   [94,] 1.5776320 4.264042e-01
##   [95,] 1.1507462 1.002435e+00
##   [96,] 0.3690741 3.486350e-03
##   [97,] 1.2053330 3.484854e-01
##   [98,] 0.7679619 3.735204e+00
##   [99,] 1.0592157 1.871259e-02
##  [100,] 1.4728353 5.011393e-01
##  [101,] 1.0630178 2.977903e+00
##  [102,] 1.1158600 9.262358e-02
##  [103,] 1.1735254 1.023757e-01
##  [104,] 0.6245134 3.611501e-01
##  [105,] 1.6286333 1.630287e-01
##  [106,] 0.7231764 3.876868e-01
##  [107,] 0.7367751 1.214316e-02
##  [108,] 0.7700465 1.315114e-02
##  [109,] 0.5993234 1.074244e+00
##  [110,] 0.4285543 4.582196e-02
##  [111,] 1.1141205 1.006025e-02
##  [112,] 0.3136164 3.200024e+00
##  [113,] 0.6988195 6.357659e-01
##  [114,] 0.7631837 1.126537e+01
##  [115,] 0.5618706 1.256818e+00
##  [116,] 0.5488082 2.764799e-01
##  [117,] 1.1340049 2.136225e+00
##  [118,] 0.8695725 2.718686e+00
##  [119,] 0.8839954 5.145592e+00
##  [120,] 0.3274262 1.666127e-02
##  [121,] 1.6804901 2.936287e-02
##  [122,] 1.2860091 5.315785e-01
##  [123,] 1.0268352 2.406175e+00
##  [124,] 1.0397217 1.321933e+00
##  [125,] 0.3521737 5.596873e-01
##  [126,] 1.0650724 7.942100e-01
##  [127,] 0.6080723 1.048694e+00
##  [128,] 1.5632473 1.496766e+00
##  [129,] 1.2542882 3.090142e+00
##  [130,] 0.8073014 5.360401e-01
##  [131,] 1.0103231 2.198006e+00
##  [132,] 1.1809399 1.323377e-02
##  [133,] 1.6688371 1.026470e-01
##  [134,] 1.5231622 1.540882e-02
##  [135,] 0.4873514 3.592392e-02
##  [136,] 0.8458991 1.801728e+00
##  [137,] 0.5903957 9.974605e-04
##  [138,] 0.9437904 4.199117e-01
##  [139,] 0.7935994 1.364451e-02
##  [140,] 0.8596583 3.171886e+00
##  [141,] 0.8715368 2.947945e+00
##  [142,] 1.0587071 1.168469e+00
##  [143,] 0.3983281 6.272903e-01
##  [144,] 1.0426187 1.513090e+00
##  [145,] 0.6886684 2.832420e+00
##  [146,] 1.7338477 2.441485e-01
##  [147,] 1.4759274 1.985162e-01
##  [148,] 0.7386585 6.534762e-01
##  [149,] 1.4022974 1.892497e+00
##  [150,] 1.1598490 6.639011e-03
##  [151,] 0.5192161 1.961279e+00
##  [152,] 0.8344839 1.027283e+00
##  [153,] 0.9188208 8.281289e-01
##  [154,] 1.6924218 2.730965e+00
##  [155,] 0.9694547 6.318353e-02
##  [156,] 1.2431308 7.676302e-01
##  [157,] 0.7900717 5.362501e-01
##  [158,] 1.8484540 1.182123e-01
##  [159,] 1.1998963 4.492895e+00
##  [160,] 1.7284906 2.117566e-01
##  [161,] 0.5841904 2.462642e-02
##  [162,] 1.2759499 1.558888e+00
##  [163,] 1.0847328 5.142036e-01
##  [164,] 0.7703786 7.398966e-03
##  [165,] 0.8207289 1.602080e+00
##  [166,] 1.5328216 1.161656e-01
##  [167,] 0.9444993 8.865448e-02
##  [168,] 0.6907399 6.329594e+00
##  [169,] 1.2189654 6.465461e-01
##  [170,] 0.5925428 1.286405e+00
##  [171,] 1.2834085 2.504771e+00
##  [172,] 0.8141892 1.272840e+00
##  [173,] 0.4432803 4.564558e-01
##  [174,] 0.6326558 2.026364e-03
##  [175,] 0.8305181 7.755625e+00
##  [176,] 1.6107108 5.334021e-01
##  [177,] 1.0075229 4.788289e+00
##  [178,] 1.1744370 1.730495e-01
##  [179,] 1.1053781 5.985845e-01
##  [180,] 0.7385566 1.363159e+00
##  [181,] 1.9754204 1.854813e+00
##  [182,] 1.5734592 1.960119e-02
##  [183,] 0.7065481 2.213250e-01
##  [184,] 0.5735227 3.218842e+00
##  [185,] 1.1036253 1.092340e+00
##  [186,] 0.9663785 2.343993e+00
##  [187,] 1.3741548 3.310191e+00
##  [188,] 1.3545504 1.680089e-01
##  [189,] 0.9687636 3.488850e-05
##  [190,] 0.6643224 1.454181e-02
##  [191,] 0.6518223 1.461330e-04
##  [192,] 1.8268966 2.204995e-01
##  [193,] 1.8249301 3.938641e-02
##  [194,] 1.6672413 1.748991e+00
##  [195,] 2.4498072 3.121337e-01
##  [196,] 1.3187197 3.269649e+00
##  [197,] 0.2439157 3.730524e-01
##  [198,] 0.7655748 1.508586e+00
##  [199,] 1.0970710 4.627147e-02
##  [200,] 0.4441415 1.469927e-01
##  [201,] 0.5369786 3.476316e-02
##  [202,] 1.0973743 1.091772e-01
##  [203,] 0.6627030 1.685198e+00
##  [204,] 0.3193550 3.471065e-01
##  [205,] 0.7682663 1.998714e+00
##  [206,] 1.1327075 1.651640e+00
##  [207,] 0.8846865 1.396528e-01
##  [208,] 0.8879468 1.407952e-02
##  [209,] 0.7969369 1.304800e+00
##  [210,] 1.0162268 2.791324e+00
##  [211,] 1.0146965 1.828839e-01
##  [212,] 0.5148541 2.002766e+00
##  [213,] 1.0769400 2.527252e-02
##  [214,] 0.6629542 2.488807e-01
##  [215,] 1.0630963 5.832259e-01
##  [216,] 0.9353197 4.887535e-01
##  [217,] 0.9445845 6.416969e-01
##  [218,] 0.9733361 5.449645e-01
##  [219,] 1.0528251 1.390791e+00
##  [220,] 0.4449935 1.220777e-01
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##  [615,] 0.7439785 1.367325e-02
##  [616,] 1.1095072 6.676357e-01
##  [617,] 0.3922352 1.508598e-01
##  [618,] 0.5619026 1.630615e+00
##  [619,] 0.8760537 5.710872e-01
##  [620,] 0.9270962 1.055339e-02
##  [621,] 0.7447578 5.023839e-02
##  [622,] 0.8357026 1.208323e-01
##  [623,] 1.8084906 5.927881e+00
##  [624,] 0.8883310 1.523283e+00
##  [625,] 1.3163184 4.146539e+00
##  [626,] 0.7948947 9.139058e-02
##  [627,] 0.9210255 1.741725e-01
##  [628,] 1.5624869 1.262208e-01
##  [629,] 0.5534402 1.037457e+00
##  [630,] 0.6461245 1.725908e+00
##  [631,] 1.1968227 1.149265e-02
##  [632,] 1.8165001 2.133989e+00
##  [633,] 1.7710688 8.305325e-01
##  [634,] 0.9895936 3.925196e-01
##  [635,] 0.7382299 1.877931e-01
##  [636,] 1.8680212 8.891738e-02
##  [637,] 1.5053163 1.374945e+00
##  [638,] 1.4229118 5.529617e-01
##  [639,] 0.4728691 3.037784e-03
##  [640,] 0.6531616 1.030461e-01
##  [641,] 0.8791112 1.321681e-01
##  [642,] 1.0792348 4.922125e-02
##  [643,] 1.3792797 1.418899e-01
##  [644,] 0.7164513 4.379946e-02
##  [645,] 0.9558534 4.658640e-01
##  [646,] 0.9225267 2.283911e-01
##  [647,] 0.4183313 1.568641e+00
##  [648,] 0.6795692 2.789575e-02
##  [649,] 0.8320747 1.072909e-01
##  [650,] 0.5580701 3.753802e-01
##  [651,] 0.7130384 2.544147e-02
##  [652,] 1.8475519 1.356537e+00
##  [653,] 0.4986324 2.200067e+00
##  [654,] 0.7697993 5.453708e-02
##  [655,] 1.1276152 1.103596e+00
##  [656,] 1.5379775 1.787972e-01
##  [657,] 1.2303256 2.549474e-01
##  [658,] 0.8840546 1.394225e+00
##  [659,] 1.6778392 1.936913e+00
##  [660,] 0.6665391 5.182281e-01
##  [661,] 2.5923376 1.270629e+00
##  [662,] 0.4390697 3.364644e-02
##  [663,] 0.6991379 1.189187e+00
##  [664,] 1.3764414 4.410930e-03
##  [665,] 1.8589090 7.462500e-01
##  [666,] 0.9217949 3.240129e-01
##  [667,] 0.7229252 1.307591e+00
##  [668,] 0.8400915 4.179584e-01
##  [669,] 0.8906032 2.097797e+00
##  [670,] 1.3122485 9.231707e-01
##  [671,] 1.4605199 7.971982e-02
##  [672,] 0.7722829 1.354110e-01
##  [673,] 0.9604139 1.279287e+00
##  [674,] 1.3335770 2.924811e-02
##  [675,] 1.0487851 9.425365e-01
##  [676,] 0.6415770 9.138705e-01
##  [677,] 0.7753985 1.143323e+00
##  [678,] 0.5881790 8.260319e-01
##  [679,] 1.0687678 2.912211e-01
##  [680,] 0.5722066 5.521689e-03
##  [681,] 0.9624063 3.650410e-01
##  [682,] 1.9116837 1.416952e+00
##  [683,] 3.1039631 4.272985e-01
##  [684,] 1.5851106 3.937224e-01
##  [685,] 0.5492687 1.997469e-01
##  [686,] 1.5692325 2.006625e-01
##  [687,] 0.5794822 1.110440e+00
##  [688,] 1.4401513 4.679209e-01
##  [689,] 0.6590875 6.794542e-01
##  [690,] 1.0125700 5.496850e-02
##  [691,] 0.9547532 4.655379e-01
##  [692,] 0.5552216 1.694808e+00
##  [693,] 1.1679916 1.689962e-01
##  [694,] 0.5434320 6.828720e-01
##  [695,] 0.4725777 1.604461e+00
##  [696,] 1.0330644 6.645616e-01
##  [697,] 0.5915478 5.715404e-01
##  [698,] 0.6102081 4.654067e-01
##  [699,] 0.6097959 2.534918e-02
##  [700,] 1.5754962 4.385660e-02
##  [701,] 1.0698146 9.080460e-05
##  [702,] 2.8252981 2.446180e-01
##  [703,] 0.5609161 8.371311e-01
##  [704,] 1.3280797 1.206659e+00
##  [705,] 0.6095981 1.336366e+00
##  [706,] 0.6512674 8.611784e-01
##  [707,] 1.0924822 7.079422e-01
##  [708,] 0.4580945 1.842426e+00
##  [709,] 1.0317607 3.518925e-02
##  [710,] 0.4886436 5.202831e-03
##  [711,] 0.7012320 7.936878e-01
##  [712,] 0.4955707 3.950883e-03
##  [713,] 0.4367378 5.583490e-01
##  [714,] 0.7363258 3.428429e-02
##  [715,] 1.5618652 1.700913e-01
##  [716,] 1.6354332 7.172336e+00
##  [717,] 1.1657033 2.654964e-01
##  [718,] 0.4716712 1.952009e+00
##  [719,] 0.5730319 3.642380e-01
##  [720,] 0.6533341 3.570626e-01
##  [721,] 0.8753755 2.543265e-02
##  [722,] 2.3587897 7.245645e-01
##  [723,] 1.7334130 2.420943e-01
##  [724,] 0.6581976 2.228108e-04
##  [725,] 1.3672910 5.982718e-01
##  [726,] 0.8825534 5.548021e-01
##  [727,] 0.6341031 1.236607e+00
##  [728,] 1.1361501 1.208196e+00
##  [729,] 3.4391705 1.228472e-01
##  [730,] 0.8424335 2.044351e+00
##  [731,] 0.3455344 2.641517e-01
##  [732,] 0.9874690 8.491074e-02
##  [733,] 1.9132300 4.899198e-02
##  [734,] 2.2141398 2.065880e+00
##  [735,] 0.6781709 1.138588e+00
##  [736,] 0.4133113 3.207318e-01
##  [737,] 0.5732195 1.269102e+00
##  [738,] 0.7683824 1.813992e-04
##  [739,] 0.9745593 4.486490e-01
##  [740,] 1.8093947 2.335619e-01
##  [741,] 0.7945897 2.049814e+00
##  [742,] 0.7141242 1.042099e+01
##  [743,] 0.4116383 1.837079e-01
##  [744,] 0.4330334 4.961988e-01
##  [745,] 0.5172116 2.598378e-01
##  [746,] 0.5051024 6.557409e+00
##  [747,] 0.4357739 3.004273e-02
##  [748,] 1.6115135 4.925927e-01
##  [749,] 0.8529843 2.315151e+00
##  [750,] 1.4099168 5.598847e+00
##  [751,] 0.3879971 2.380504e+00
##  [752,] 0.7072917 2.011184e+00
##  [753,] 0.7909499 1.348364e-01
##  [754,] 0.6397561 6.998421e-01
##  [755,] 0.2932328 1.625832e+00
##  [756,] 1.0986369 2.253883e+00
##  [757,] 0.4894346 8.027431e-02
##  [758,] 0.7972879 4.938335e-01
##  [759,] 1.1170800 5.728513e-01
##  [760,] 1.5051573 5.190722e+00
##  [761,] 0.8537222 3.367258e+00
##  [762,] 0.2356686 6.538406e-01
##  [763,] 1.2419828 1.479439e+00
##  [764,] 0.8762278 3.010651e-02
##  [765,] 1.3392364 6.955991e-02
##  [766,] 1.4818330 1.798096e+00
##  [767,] 1.3178655 4.155675e-02
##  [768,] 0.7531010 2.825483e+00
##  [769,] 1.0309163 2.842994e-01
##  [770,] 0.7940463 3.161659e+00
##  [771,] 0.4451117 9.102834e-02
##  [772,] 0.7594719 2.864573e-01
##  [773,] 0.8362332 1.314830e+00
##  [774,] 1.1648832 3.042477e+00
##  [775,] 0.6232317 8.998504e-01
##  [776,] 0.9965885 8.698227e-02
##  [777,] 1.0688563 1.327290e-04
##  [778,] 1.8923127 3.764866e-02
##  [779,] 3.1051408 1.781957e-05
##  [780,] 2.0753350 8.388229e-01
##  [781,] 0.4446750 1.040304e-02
##  [782,] 0.7661490 1.428300e-01
##  [783,] 1.5417153 8.893679e+00
##  [784,] 0.8317424 2.213166e+00
##  [785,] 1.0507360 2.218249e+00
##  [786,] 1.3919603 9.710351e-01
##  [787,] 1.2204268 2.025393e+00
##  [788,] 1.1617986 2.250861e-02
##  [789,] 1.4866867 8.028501e-01
##  [790,] 1.3151878 7.607654e-01
##  [791,] 0.7039997 2.495946e-01
##  [792,] 0.9163506 5.809228e-01
##  [793,] 0.9570522 2.371173e-03
##  [794,] 0.8455953 6.137819e-01
##  [795,] 0.9055002 4.636803e-04
##  [796,] 1.6591162 1.754450e+00
##  [797,] 1.9140494 1.324151e-01
##  [798,] 1.0971679 2.463605e-01
##  [799,] 0.8580819 2.907139e-01
##  [800,] 0.9150168 7.874292e-01
##  [801,] 1.8197271 2.502028e-02
##  [802,] 0.5986032 2.196590e+00
##  [803,] 0.6112011 1.210309e+00
##  [804,] 0.3582325 5.320572e-01
##  [805,] 1.4611689 1.227474e-02
##  [806,] 1.7924498 1.689741e-01
##  [807,] 1.0767788 5.105839e+00
##  [808,] 0.8960696 1.507949e+00
##  [809,] 0.6790365 9.466022e-01
##  [810,] 0.9514496 3.723873e-02
##  [811,] 0.6783811 1.607055e+00
##  [812,] 0.5775120 1.401579e+00
##  [813,] 0.7316731 6.879021e-02
##  [814,] 1.3193064 4.794977e-04
##  [815,] 0.5027705 1.534064e-01
##  [816,] 1.9033277 2.710945e-03
##  [817,] 0.9617270 3.171791e-02
##  [818,] 1.6233331 1.289919e-04
##  [819,] 2.0703176 7.710419e-01
##  [820,] 0.4639830 7.099743e-02
##  [821,] 0.8279026 8.421599e-03
##  [822,] 1.1722640 1.742706e-02
##  [823,] 0.7480137 1.887721e+00
##  [824,] 0.8678306 1.001682e+00
##  [825,] 0.8390141 1.536424e+00
##  [826,] 0.4391439 1.112059e-01
##  [827,] 0.3856087 5.058814e-01
##  [828,] 1.1498563 1.234604e-01
##  [829,] 0.6265823 5.151390e-01
##  [830,] 1.4364011 2.190311e-02
##  [831,] 0.7038237 5.034132e-01
##  [832,] 1.2467980 1.047997e+00
##  [833,] 1.0340772 1.158583e-02
##  [834,] 2.0030403 1.185868e-01
##  [835,] 1.1112941 2.923039e-02
##  [836,] 0.5991275 1.284316e-03
##  [837,] 1.2432912 1.181690e+00
##  [838,] 0.9598662 2.176597e-03
##  [839,] 0.5086741 5.354504e-01
##  [840,] 1.2051130 1.460444e-02
##  [841,] 2.0480858 3.789839e+00
##  [842,] 0.6734441 3.755912e-01
##  [843,] 0.5080866 1.862167e+00
##  [844,] 1.2893600 5.548093e+00
##  [845,] 1.2805463 2.112221e-01
##  [846,] 0.7286473 2.419616e-01
##  [847,] 1.4610620 1.045608e-01
##  [848,] 0.6553822 7.253168e+00
##  [849,] 0.4783629 8.211950e-01
##  [850,] 0.4000484 1.823256e+00
##  [851,] 1.5258157 5.660317e-02
##  [852,] 1.0059574 3.473845e-01
##  [853,] 0.5468871 1.695306e-01
##  [854,] 0.9245078 2.682670e-01
##  [855,] 0.7831035 1.802949e-02
##  [856,] 1.4554205 1.504726e-02
##  [857,] 0.8489000 1.419979e+00
##  [858,] 1.4850720 7.283232e-01
##  [859,] 0.4002814 2.675971e-01
##  [860,] 0.8374258 2.328416e-02
##  [861,] 1.1469169 1.263122e-01
##  [862,] 0.7570628 1.947208e-01
##  [863,] 1.1420323 1.841586e-02
##  [864,] 0.9498675 3.788324e+00
##  [865,] 1.1105860 8.723335e-01
##  [866,] 1.4044315 1.297884e-01
##  [867,] 0.8860679 3.288725e-02
##  [868,] 1.0459636 3.547225e-01
##  [869,] 0.7786733 1.407359e+00
##  [870,] 0.6221406 6.508082e-01
##  [871,] 1.4719268 1.843096e+00
##  [872,] 0.5802269 1.301342e+00
##  [873,] 0.4161740 7.694689e-02
##  [874,] 1.2488757 1.590613e+00
##  [875,] 1.0908962 1.366363e-04
##  [876,] 1.8143462 1.542889e-01
##  [877,] 1.6091603 1.710820e-01
##  [878,] 0.3729501 9.216533e-01
##  [879,] 0.1233882 5.842851e-04
##  [880,] 1.9942566 4.214511e+00
##  [881,] 0.7618695 4.521437e-01
##  [882,] 2.1946060 1.247424e-01
##  [883,] 0.5282147 5.267068e+00
##  [884,] 0.9400954 9.487968e-02
##  [885,] 0.4771112 9.472366e-01
##  [886,] 0.9529422 3.055595e-01
##  [887,] 0.9379287 2.739279e+00
##  [888,] 1.0472058 5.185022e-01
##  [889,] 0.8910847 6.814340e-02
##  [890,] 1.1001210 3.390129e-01
##  [891,] 0.4398089 7.918530e-02
##  [892,] 0.7008156 3.577059e-01
##  [893,] 0.5651756 2.697946e-01
##  [894,] 1.0809670 4.950179e-01
##  [895,] 0.4224342 1.000497e-02
##  [896,] 1.3085794 2.014185e+00
##  [897,] 0.6595422 7.269827e-02
##  [898,] 0.6832721 5.716860e-02
##  [899,] 2.0030506 4.001564e-02
##  [900,] 1.3633022 6.659804e-03
##  [901,] 0.6551646 3.016239e-02
##  [902,] 0.3380592 5.607668e-01
##  [903,] 0.8644526 2.291814e+00
##  [904,] 0.5670649 1.088475e-02
##  [905,] 0.6232005 7.860002e-01
##  [906,] 1.6476223 1.452872e+00
##  [907,] 1.9169487 2.079261e-02
##  [908,] 0.6514918 4.544037e+00
##  [909,] 0.6327976 1.023789e+00
##  [910,] 2.3078239 1.207374e-01
##  [911,] 0.6903352 1.372654e-01
##  [912,] 0.7673897 2.236532e-02
##  [913,] 1.3127437 7.527499e-02
##  [914,] 0.6495698 1.728270e-02
##  [915,] 1.4454159 2.627717e+00
##  [916,] 0.2712689 2.358783e+00
##  [917,] 0.6034385 6.331258e-01
##  [918,] 0.6054862 9.248275e-01
##  [919,] 1.1543389 3.217507e+00
##  [920,] 0.7044814 7.054365e+00
##  [921,] 1.0774288 2.274582e+00
##  [922,] 1.6497115 1.124691e-01
##  [923,] 1.3438282 2.634633e-01
##  [924,] 3.3992158 5.314069e-01
##  [925,] 0.3525004 1.115326e+00
##  [926,] 1.0136659 8.804377e-02
##  [927,] 0.5366933 2.881896e-01
##  [928,] 0.8043934 2.166028e-01
##  [929,] 0.4357758 3.216098e+00
##  [930,] 1.4526479 2.205369e+00
##  [931,] 0.8901845 1.014424e-01
##  [932,] 1.4808054 4.688396e-02
##  [933,] 1.8241206 5.302708e-08
##  [934,] 0.6520563 1.177839e-01
##  [935,] 0.6055238 6.968655e-01
##  [936,] 1.9520703 2.592785e-02
##  [937,] 1.0209609 5.288781e-01
##  [938,] 1.1830002 5.517270e-04
##  [939,] 0.8188950 3.187314e-01
##  [940,] 0.5540109 7.212399e-02
##  [941,] 1.2498296 2.847566e+00
##  [942,] 0.5262154 2.382997e-01
##  [943,] 0.8062772 5.611166e-01
##  [944,] 1.2755026 2.464276e+00
##  [945,] 0.7845743 7.343012e-03
##  [946,] 0.7728886 9.209469e-02
##  [947,] 0.9462434 6.072069e-01
##  [948,] 1.6246241 1.247213e-03
##  [949,] 1.8166966 1.486968e+00
##  [950,] 0.9477831 4.160419e-01
##  [951,] 0.4712657 5.225115e-04
##  [952,] 1.7267014 5.639578e+00
##  [953,] 1.6464454 9.556781e-01
##  [954,] 0.5481943 3.440844e-01
##  [955,] 0.7903149 5.752838e-01
##  [956,] 0.7387395 8.574158e-01
##  [957,] 1.1667306 1.779922e-01
##  [958,] 0.6495886 6.718200e-01
##  [959,] 1.1603885 3.798714e-01
##  [960,] 0.7879587 2.843955e+00
##  [961,] 0.4130650 5.458966e-01
##  [962,] 2.1176083 1.024826e+00
##  [963,] 0.6277213 4.905646e-01
##  [964,] 1.0473598 3.696814e-01
##  [965,] 1.0172042 3.633329e-03
##  [966,] 0.4065718 6.657584e-01
##  [967,] 1.1212028 2.403288e-01
##  [968,] 1.2425511 3.139299e-03
##  [969,] 1.7502576 1.987499e+00
##  [970,] 1.2998280 1.293530e-02
##  [971,] 0.5263854 8.327869e-02
##  [972,] 0.8146117 4.400749e-03
##  [973,] 0.8621079 2.887916e-02
##  [974,] 1.6262961 3.881014e-03
##  [975,] 0.8558746 9.964093e-01
##  [976,] 0.6939177 6.456547e-01
##  [977,] 0.9301671 9.026143e-01
##  [978,] 1.8487249 3.529682e+00
##  [979,] 2.0614185 3.292463e-01
##  [980,] 0.8767618 1.778492e-01
##  [981,] 1.6681660 4.307724e-02
##  [982,] 1.0451406 1.317697e-01
##  [983,] 0.4868297 1.549960e-01
##  [984,] 0.9344102 6.220622e-02
##  [985,] 0.5377022 3.055741e-01
##  [986,] 1.1465411 4.509475e-03
##  [987,] 2.2477133 1.907797e+00
##  [988,] 0.9559898 5.106498e-01
##  [989,] 1.0766989 4.242091e+00
##  [990,] 0.7535506 7.647899e+00
##  [991,] 0.6020118 1.415762e+00
##  [992,] 0.3022235 6.475365e-01
##  [993,] 1.5925769 5.294539e-02
##  [994,] 1.0408061 2.789851e+00
##  [995,] 0.6914567 4.429041e-01
##  [996,] 1.9285611 1.807174e-01
##  [997,] 1.3133526 5.703744e-01
##  [998,] 0.4901628 2.416563e-01
##  [999,] 0.9558562 2.242498e+00
## [1000,] 1.3095688 1.520328e+00
## 
## $bootSSE
##               [,1]
##    [1,] 6900684495
##    [2,] 8268086746
##    [3,] 6506441602
##    [4,] 6013247161
##    [5,] 6387529733
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##  [656,] 7181907137
##  [657,] 6894811772
##  [658,] 8066644521
##  [659,] 7489873040
##  [660,] 7286222898
##  [661,] 7663570715
##  [662,] 6978941184
##  [663,] 6457392867
##  [664,] 6040002719
##  [665,] 6316375624
##  [666,] 6627130751
##  [667,] 7631672641
##  [668,] 6235191592
##  [669,] 6499288698
##  [670,] 6365128980
##  [671,] 6604091429
##  [672,] 6240915329
##  [673,] 6388389148
##  [674,] 6746239231
##  [675,] 5650461914
##  [676,] 5948414912
##  [677,] 7317410454
##  [678,] 6929683780
##  [679,] 6964446830
##  [680,] 6345769401
##  [681,] 6478101786
##  [682,] 6186186208
##  [683,] 7371623244
##  [684,] 6982619691
##  [685,] 6380808518
##  [686,] 6311746707
##  [687,] 6676495757
##  [688,] 6004449498
##  [689,] 6822390503
##  [690,] 5804292308
##  [691,] 5993563436
##  [692,] 7704355889
##  [693,] 6694103402
##  [694,] 6489358928
##  [695,] 5714560678
##  [696,] 6944155365
##  [697,] 6677520153
##  [698,] 6356524864
##  [699,] 5656496677
##  [700,] 7050202760
##  [701,] 6743995996
##  [702,] 7949023315
##  [703,] 5712222838
##  [704,] 6748380920
##  [705,] 6641898073
##  [706,] 6671166472
##  [707,] 6344788846
##  [708,] 6921122478
##  [709,] 6693902166
##  [710,] 7312100331
##  [711,] 6773639802
##  [712,] 6665383465
##  [713,] 7193885179
##  [714,] 7620200337
##  [715,] 6267125352
##  [716,] 5426863149
##  [717,] 7693247489
##  [718,] 5723745391
##  [719,] 7170408403
##  [720,] 6892061810
##  [721,] 6565375686
##  [722,] 6607777182
##  [723,] 7295625170
##  [724,] 6902777649
##  [725,] 6920255136
##  [726,] 6671652624
##  [727,] 7019902920
##  [728,] 5874264582
##  [729,] 6383594474
##  [730,] 7233870887
##  [731,] 7240334408
##  [732,] 6840737993
##  [733,] 7174512857
##  [734,] 6051998637
##  [735,] 6670026608
##  [736,] 6422223930
##  [737,] 6821503066
##  [738,] 6209983666
##  [739,] 6028226704
##  [740,] 6636830909
##  [741,] 6988638682
##  [742,] 7378329170
##  [743,] 5558872241
##  [744,] 6714669323
##  [745,] 6851148536
##  [746,] 6492447752
##  [747,] 6927096083
##  [748,] 5865125371
##  [749,] 6682180994
##  [750,] 7581827135
##  [751,] 7001779606
##  [752,] 5545426754
##  [753,] 6553223569
##  [754,] 7386956975
##  [755,] 6290102106
##  [756,] 6591531272
##  [757,] 6869230567
##  [758,] 6529373889
##  [759,] 7050539059
##  [760,] 6468099253
##  [761,] 7607645088
##  [762,] 6810889663
##  [763,] 6954946228
##  [764,] 6202431037
##  [765,] 6665903871
##  [766,] 6176533487
##  [767,] 6166748931
##  [768,] 6669279157
##  [769,] 6365961492
##  [770,] 5980530067
##  [771,] 6816482219
##  [772,] 6881233408
##  [773,] 6825489717
##  [774,] 6486266276
##  [775,] 6156066103
##  [776,] 7125276176
##  [777,] 5983586562
##  [778,] 6050061538
##  [779,] 6358547488
##  [780,] 6204693718
##  [781,] 6730470815
##  [782,] 7925349806
##  [783,] 7180173930
##  [784,] 7127262006
##  [785,] 5659504647
##  [786,] 6900357381
##  [787,] 6283670589
##  [788,] 7356938829
##  [789,] 8516072916
##  [790,] 6842664052
##  [791,] 5563891271
##  [792,] 7123814261
##  [793,] 6831849652
##  [794,] 7215346186
##  [795,] 7407315739
##  [796,] 7873029346
##  [797,] 7137367886
##  [798,] 5738970009
##  [799,] 5748486984
##  [800,] 6994966566
##  [801,] 6528877013
##  [802,] 6882319882
##  [803,] 7613931190
##  [804,] 8027718028
##  [805,] 7132299340
##  [806,] 6403595611
##  [807,] 7265316729
##  [808,] 6385175519
##  [809,] 7236133327
##  [810,] 6870321480
##  [811,] 5964377882
##  [812,] 7990990965
##  [813,] 7428047578
##  [814,] 6902372015
##  [815,] 7480857383
##  [816,] 6734947890
##  [817,] 6789709178
##  [818,] 5925419114
##  [819,] 7167210479
##  [820,] 7125049752
##  [821,] 5320388510
##  [822,] 6977689114
##  [823,] 6563402145
##  [824,] 7471411538
##  [825,] 6475222969
##  [826,] 6912985196
##  [827,] 6642894080
##  [828,] 7416563094
##  [829,] 6818191311
##  [830,] 7133509111
##  [831,] 7879392341
##  [832,] 5890648842
##  [833,] 6169327334
##  [834,] 5865521081
##  [835,] 8069149731
##  [836,] 6541385449
##  [837,] 7256094709
##  [838,] 6326840037
##  [839,] 6551111207
##  [840,] 6026470873
##  [841,] 6560664583
##  [842,] 6697015807
##  [843,] 6216500236
##  [844,] 6808983683
##  [845,] 6992414719
##  [846,] 7660225598
##  [847,] 5872224554
##  [848,] 6887250566
##  [849,] 6481648408
##  [850,] 7088669030
##  [851,] 6116657069
##  [852,] 6602202306
##  [853,] 7237834895
##  [854,] 7523979737
##  [855,] 6954194926
##  [856,] 7618858933
##  [857,] 7791825299
##  [858,] 6770025180
##  [859,] 6687639444
##  [860,] 7086341154
##  [861,] 6657337476
##  [862,] 7196823868
##  [863,] 6684565222
##  [864,] 6639986315
##  [865,] 6037070751
##  [866,] 7247582819
##  [867,] 6728726763
##  [868,] 7065148836
##  [869,] 7357803674
##  [870,] 7387310116
##  [871,] 6336456872
##  [872,] 6321553293
##  [873,] 6919438709
##  [874,] 7743457411
##  [875,] 6820946244
##  [876,] 7499171319
##  [877,] 8089736730
##  [878,] 6937666584
##  [879,] 7616301180
##  [880,] 7160054454
##  [881,] 6498272202
##  [882,] 6742561202
##  [883,] 6851785645
##  [884,] 6944388765
##  [885,] 7075769600
##  [886,] 7166190921
##  [887,] 6621495053
##  [888,] 7964992111
##  [889,] 6729333779
##  [890,] 8045892568
##  [891,] 6474855757
##  [892,] 7501094451
##  [893,] 6041858426
##  [894,] 6010501961
##  [895,] 6023106343
##  [896,] 6376907478
##  [897,] 6592011077
##  [898,] 6059457702
##  [899,] 6631823197
##  [900,] 6531243433
##  [901,] 7308947268
##  [902,] 7042403398
##  [903,] 6554702440
##  [904,] 7276739851
##  [905,] 7197676044
##  [906,] 7576963441
##  [907,] 6602740377
##  [908,] 7147526952
##  [909,] 7429286992
##  [910,] 6671182096
##  [911,] 7088181147
##  [912,] 7318424495
##  [913,] 6974637101
##  [914,] 6529695978
##  [915,] 6678035067
##  [916,] 7000620194
##  [917,] 7201382820
##  [918,] 6232198601
##  [919,] 6974796175
##  [920,] 5843209888
##  [921,] 7237569419
##  [922,] 6633326528
##  [923,] 6363873739
##  [924,] 6992180442
##  [925,] 6894711754
##  [926,] 7470190060
##  [927,] 6231565422
##  [928,] 6569762145
##  [929,] 7441066193
##  [930,] 6257830459
##  [931,] 6505060677
##  [932,] 6851098966
##  [933,] 6970962379
##  [934,] 8405556611
##  [935,] 5946692621
##  [936,] 6704660535
##  [937,] 6728212484
##  [938,] 7114516517
##  [939,] 7322583757
##  [940,] 7958411692
##  [941,] 5752154105
##  [942,] 6262905644
##  [943,] 7724979884
##  [944,] 6915616672
##  [945,] 6164279444
##  [946,] 6334950649
##  [947,] 7141162251
##  [948,] 8411570276
##  [949,] 7671231491
##  [950,] 8177402804
##  [951,] 7797501491
##  [952,] 6373376475
##  [953,] 6667170151
##  [954,] 6573958234
##  [955,] 6161861167
##  [956,] 5839360520
##  [957,] 7180301835
##  [958,] 7519231239
##  [959,] 6345432100
##  [960,] 5973566350
##  [961,] 6470004806
##  [962,] 6214256831
##  [963,] 6955474418
##  [964,] 6165816388
##  [965,] 6097071329
##  [966,] 6213373714
##  [967,] 6151304671
##  [968,] 7927076680
##  [969,] 6878625454
##  [970,] 6923006712
##  [971,] 7132371309
##  [972,] 6819318532
##  [973,] 6808988036
##  [974,] 6454704394
##  [975,] 7113161804
##  [976,] 6395028425
##  [977,] 6832882842
##  [978,] 7129604653
##  [979,] 8169277511
##  [980,] 6910247014
##  [981,] 5814031385
##  [982,] 6682726339
##  [983,] 7212033038
##  [984,] 6258700943
##  [985,] 6658864260
##  [986,] 7599197636
##  [987,] 8153428954
##  [988,] 7822238887
##  [989,] 6683006034
##  [990,] 6343192053
##  [991,] 7036229331
##  [992,] 7402051890
##  [993,] 6573547723
##  [994,] 5998735750
##  [995,] 7168392481
##  [996,] 7090496068
##  [997,] 5722580489
##  [998,] 6520429234
##  [999,] 6207734015
## [1000,] 6660668367
## 
## $bootSSTr
##              [,1]         [,2]
##    [1,]  77675558 4.209854e+06
##    [2,]  38725334 1.521393e+06
##    [3,]  33694673 3.306555e+05
##    [4,]  59728567 3.833347e+06
##    [5,]  76446781 1.660456e+07
##    [6,]  35123010 1.997751e+06
##    [7,]  37520145 1.116121e+06
##    [8,]  42412695 1.101248e+07
##    [9,]  33619569 2.867925e+05
##   [10,]  38574191 2.451514e+05
##   [11,]  55399896 1.836700e+04
##   [12,]  12904161 6.447581e+06
##   [13,]  46575430 1.894784e+07
##   [14,]  96683381 3.624275e+07
##   [15,]  61422887 1.573758e+05
##   [16,]  35433241 3.917742e+06
##   [17,]   8451688 2.076015e+07
##   [18,]  56305209 2.545465e+04
##   [19,]  78080574 2.485943e+05
##   [20,]  30515776 1.052749e+06
##   [21,]  25809323 6.750238e+06
##   [22,]  27383306 1.613994e+07
##   [23,]  90375048 5.669331e+06
##   [24,]  49873971 1.834032e+04
##   [25,]  45857228 3.597520e+06
##   [26,]  32316115 4.013544e+06
##   [27,]  50914876 2.225839e+06
##   [28,]  51745031 3.527408e+05
##   [29,]  46603161 2.128419e+03
##   [30,] 101777029 2.394733e+03
##   [31,]  45225815 5.179839e+06
##   [32,] 134677216 3.318189e+06
##   [33,]  71530051 3.544805e+05
##   [34,]  83127326 7.807741e+06
##   [35,]  56115114 3.908213e+07
##   [36,]  96780381 1.036243e+07
##   [37,]  30098666 1.109688e+06
##   [38,]  41621324 1.198110e+05
##   [39,]  51178295 1.789454e+06
##   [40,]  86939490 1.522110e+06
##   [41,]  57593138 8.290816e+06
##   [42,]  93949392 5.874494e+04
##   [43,] 126589243 1.235533e+07
##   [44,]  40492923 6.593666e+06
##   [45,]  94880850 1.481662e+07
##   [46,]  36221725 9.664505e+03
##   [47,]  62594246 9.628653e+06
##   [48,]  60349501 1.778098e+07
##   [49,]  56431078 5.386327e+05
##   [50,] 118450270 2.927569e+04
##   [51,] 118601546 3.091145e+05
##   [52,]  44552698 1.234907e+07
##   [53,]  62918607 3.179813e+07
##   [54,]  34775739 8.866581e+06
##   [55,]  50968475 2.513130e+06
##   [56,]  14793919 7.009646e+06
##   [57,]  38149836 4.940862e+04
##   [58,]  32804280 2.667065e+05
##   [59,]  86725569 3.554180e+06
##   [60,]  65584188 3.368141e+06
##   [61,]  72070524 9.604851e+05
##   [62,]  23314030 2.456640e+07
##   [63,]  59921068 2.506624e+06
##   [64,]  53681855 5.573476e+05
##   [65,]  46387084 7.961827e+06
##   [66,]  27233859 9.998773e+05
##   [67,]  48991089 1.373226e+07
##   [68,]  35377465 5.386051e+05
##   [69,]  34293814 8.879628e+04
##   [70,]  56407485 6.586387e+05
##   [71,]  38087357 9.403970e+06
##   [72,] 110015722 3.511753e+07
##   [73,]  57702672 7.539581e+06
##   [74,]  72010553 2.092255e+06
##   [75,]  96105730 3.285656e+03
##   [76,]  55610760 1.565446e+07
##   [77,]  78927917 7.612821e+06
##   [78,]  83725242 1.102738e+02
##   [79,]  17109849 2.136859e+05
##   [80,]  66796570 3.181644e+07
##   [81,]  46046487 1.098040e+07
##   [82,]  74114262 3.352294e+06
##   [83,]  40240665 1.573116e+07
##   [84,]  76833327 2.791763e+06
##   [85,]  88168562 1.630701e+07
##   [86,]  56896324 5.243319e+06
##   [87,]  62536220 1.718830e+06
##   [88,]  57966525 5.131278e+05
##   [89,]  94016534 1.078401e+07
##   [90,]  90002560 6.126888e+06
##   [91,]  83189941 8.130449e+06
##   [92,]  60673914 7.495872e+06
##   [93,]  74645266 2.500378e+06
##   [94,] 107120856 3.001547e+06
##   [95,]  61115800 7.581326e+06
##   [96,]  23619492 2.249113e+04
##   [97,]  75254482 2.393602e+06
##   [98,]  45347503 2.522748e+07
##   [99,]  62057516 1.396906e+05
##  [100,] 101649966 3.597676e+06
##  [101,]  68214786 2.320454e+07
##  [102,]  73907049 6.247196e+05
##  [103,]  77933893 7.165083e+05
##  [104,]  38397676 2.520541e+06
##  [105,]  84256651 1.029945e+06
##  [106,]  45661792 2.446120e+06
##  [107,]  44814447 8.674882e+04
##  [108,]  46143228 8.131901e+04
##  [109,]  43846509 7.126832e+06
##  [110,]  26474163 3.068372e+05
##  [111,]  62295590 7.206469e+04
##  [112,]  20858686 2.107209e+07
##  [113,]  44360650 4.397565e+06
##  [114,]  54398645 6.911313e+07
##  [115,]  32461668 9.560197e+06
##  [116,]  33670380 1.711768e+06
##  [117,]  74407634 1.550002e+07
##  [118,]  50175467 1.778670e+07
##  [119,]  49398222 3.402574e+07
##  [120,]  20082977 1.105362e+05
##  [121,] 105966834 1.712795e+05
##  [122,]  78595487 4.268600e+06
##  [123,]  67616511 1.744886e+07
##  [124,]  59791468 9.502833e+06
##  [125,]  21734418 4.420928e+06
##  [126,]  80044492 5.953510e+06
##  [127,]  39250262 6.636910e+06
##  [128,] 100485023 9.200495e+06
##  [129,]  72499210 2.163585e+07
##  [130,]  48121231 3.502692e+06
##  [131,]  58834644 1.418281e+07
##  [132,]  64947739 8.781482e+04
##  [133,] 113211833 5.893718e+05
##  [134,]  76781532 1.200916e+05
##  [135,]  28275531 2.360404e+05
##  [136,]  57900303 1.222532e+07
##  [137,]  37675018 6.377091e+03
##  [138,]  58754008 2.717566e+06
##  [139,]  54941802 9.062633e+04
##  [140,]  51743801 1.967803e+07
##  [141,]  53330787 1.958316e+07
##  [142,]  63976808 9.024364e+06
##  [143,]  26133407 4.751311e+06
##  [144,]  63545985 1.039064e+07
##  [145,]  37502688 1.877043e+07
##  [146,]  97841074 1.697567e+06
##  [147,]  94727480 1.510498e+06
##  [148,]  49943692 4.662336e+06
##  [149,]  95758642 1.271591e+07
##  [150,]  79192235 5.004645e+04
##  [151,]  30576147 1.419822e+07
##  [152,]  55395497 6.623441e+06
##  [153,]  58628290 5.200214e+06
##  [154,] 101888469 1.626948e+07
##  [155,]  63020188 4.183643e+05
##  [156,]  76916520 4.965209e+06
##  [157,]  47042521 3.054232e+06
##  [158,] 128307182 8.434577e+05
##  [159,]  81217685 3.168512e+07
##  [160,] 111256703 1.428183e+06
##  [161,]  37487777 1.697210e+05
##  [162,]  73736449 1.062638e+07
##  [163,]  66236514 3.712620e+06
##  [164,]  45108032 4.751648e+04
##  [165,]  52745729 1.096809e+07
##  [166,]  95264751 8.174685e+05
##  [167,]  53231936 6.049198e+05
##  [168,]  38333015 4.471020e+07
##  [169,]  69430341 4.926382e+06
##  [170,]  31702116 9.471179e+06
##  [171,]  86298876 1.850869e+07
##  [172,]  44052299 8.442225e+06
##  [173,]  33180530 3.365046e+06
##  [174,]  41105008 1.376810e+04
##  [175,]  56045078 6.023105e+07
##  [176,]  97071689 3.460310e+06
##  [177,]  60310576 3.109547e+07
##  [178,]  77172335 1.119147e+06
##  [179,]  65259260 4.105879e+06
##  [180,]  49044660 9.311642e+06
##  [181,] 132641118 1.269532e+07
##  [182,] 103938019 1.232096e+05
##  [183,]  44877662 1.506426e+06
##  [184,]  32286166 2.213547e+07
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##  [993,] 104761017 3.519101e+05
##  [994,]  56854876 1.692171e+07
##  [995,]  45204086 3.210223e+06
##  [996,] 121995556 1.295628e+06
##  [997,]  84235507 3.300317e+06
##  [998,]  32820488 1.593229e+06
##  [999,]  69779183 1.407566e+07
## [1000,]  82649726 1.023903e+07
## 
## $`p-values`
## [1] 0.000 0.808

Wartość p-value dla grupy zmiennych “purpose” jest bardzo niska (0,000), co oznacza, że istnieje statystycznie istotna różnica między grupami. Wartość p-value dla zmiennej “age.in.years” jest wysoka (0,827), co oznacza, że nie ma statystycznie istotnej różnicy w wartościach tej zmiennej między grupami. Suma kwadratów błędu (pozostałej wariancji) wynosi 6864191137, a suma kwadratów zmiennych objaśniających dla grupy zmiennych “purpose” wynosi 1095334193,1, a dla zmiennej “age.in.years” wynosi 350296,8. Podsumowując, wyniki wskazują na istotną różnicę między grupami zmiennych “purpose” w odniesieniu do zmiennej “credit.amount”, podczas gdy zmienna “age.in.years” nie ma takiej istotnej różnicy.

6. Wykres interakcji

interaction.plot(germancredit$purpose, germancredit$age.in.years, germancredit$credit.amount, xlab = "cel", ylab = "wysokość kredytu")

Równoległe linie wskazują na brak interakcji między zmiennymi, podczas gdy skrzyżowane linie wskazują na obecność interakcji.Linie na wykresie najpierw rosną, osiągają pewien maksimum, a następnie zaczynają maleć, więc wskazuje to na istnienie interakcji między zmiennymi objaśniającymi. Taki wzorzec oznacza, że wpływ jednej zmiennej na zmienną odpowiedzi różni się w zależności od poziomu drugiej zmiennej