set.seed(2021)
absorbancia=rnorm(n=120, mean = 0.8 , sd =0.08)
absorbancia =round(absorbancia, 3)
concentracion=runif(n=120, min=1, max=2)
concentracion= round(concentracion, 2)
absorbancia2=exp(concentracion)/5
absorbancia2
##   [1] 1.1741707 0.9329181 0.7949803 0.5889359 0.5658434 1.0413960 0.5546390
##   [8] 1.0207749 1.4631068 0.8698470 1.0838961 0.5602132 1.2847474 0.5602132
##  [15] 1.0106181 0.8274241 1.2719639 0.9906065 1.4631068 0.8357398 0.8110400
##  [22] 0.6443985 1.1057923 1.0838961 0.9709912 0.7121705 0.5546390 0.8191911
##  [29] 1.0947895 0.7562087 0.7638087 0.6129708 1.0310339 1.2099295 0.7870701
##  [36] 1.2847474 0.9236354 0.5546390 0.8110400 0.9053462 0.6574162 1.1624875
##  [43] 1.1741707 0.7338593 0.5436564 1.0518622 0.6443985 0.7870701 1.0624336
##  [50] 0.8029700 0.6008332 0.9329181 0.8441392 0.6574162 1.0310339 0.7638087
##  [57] 0.8785891 1.2593077 1.3779020 1.0838961 0.7050843 0.6443985 0.8110400
##  [64] 0.6129708 0.6008332 0.7870701 1.1859713 0.9807498 0.6508748 1.0106181
##  [71] 0.6911227 1.4778112 0.7121705 0.7486843 1.1859713 0.9236354 0.6253537
##  [78] 0.6706969 0.7638087 0.8611919 1.2099295 1.0310339 1.0310339 0.7265573
##  [85] 0.9517642 0.6508748 1.2467773 1.0106181 0.7870701 1.2847474 0.6842459
##  [92] 0.5715302 0.5658434 1.2593077 1.4341353 0.5715302 1.4778112 1.4198654
##  [99] 1.4485486 0.6706969 1.1978905 1.3779020 0.8698470 0.5715302 0.7412347
## [106] 1.0731112 1.2099295 0.7562087 0.6443985 0.7638087 1.2343717 1.3107010
## [113] 1.0413960 0.8110400 1.3779020 1.0413960 0.7486843 0.8785891 0.9906065
## [120] 1.4341353
absorbancia3=exp(concentracion+rnorm(120,0.4,0.1))/5
absorbacia2escalda= scale(absorbancia2)
absorbacia2escalda
##                [,1]
##   [1,]  0.929045830
##   [2,]  0.025251555
##   [3,] -0.491498608
##   [4,] -1.263393912
##   [5,] -1.349904376
##   [6,]  0.431637674
##   [7,] -1.391879124
##   [8,]  0.354386030
##   [9,]  2.011474603
##  [10,] -0.211028709
##  [11,]  0.590854248
##  [12,] -1.370996686
##  [13,]  1.343294484
##  [14,] -1.370996686
##  [15,]  0.316335747
##  [16,] -0.369955940
##  [17,]  1.295404397
##  [18,]  0.241367234
##  [19,]  2.011474603
##  [20,] -0.338803003
##  [21,] -0.431334967
##  [22,] -1.055616701
##  [23,]  0.672882867
##  [24,]  0.590854248
##  [25,]  0.167883197
##  [26,] -0.801725438
##  [27,] -1.391879124
##  [28,] -0.400798900
##  [29,]  0.631663488
##  [30,] -0.636747160
##  [31,] -0.608275520
##  [32,] -1.173352889
##  [33,]  0.392818724
##  [34,]  1.063007557
##  [35,] -0.521132198
##  [36,]  1.343294484
##  [37,] -0.009523786
##  [38,] -1.391879124
##  [39,] -0.431334967
##  [40,] -0.078039848
##  [41,] -1.006849001
##  [42,]  0.885277587
##  [43,]  0.929045830
##  [44,] -0.720473543
##  [45,] -1.433022717
##  [46,]  0.470846760
##  [47,] -1.055616701
##  [48,] -0.521132198
##  [49,]  0.510449905
##  [50,] -0.461567195
##  [51,] -1.218823591
##  [52,]  0.025251555
##  [53,] -0.307336974
##  [54,] -1.006849001
##  [55,]  0.392818724
##  [56,] -0.608275520
##  [57,] -0.178278527
##  [58,]  1.247990825
##  [59,]  1.692275895
##  [60,]  0.590854248
##  [61,] -0.828272220
##  [62,] -1.055616701
##  [63,] -0.431334967
##  [64,] -1.173352889
##  [65,] -1.218823591
##  [66,] -0.521132198
##  [67,]  0.973253952
##  [68,]  0.204441507
##  [69,] -1.031354769
##  [70,]  0.316335747
##  [71,] -0.880575976
##  [72,]  2.066561314
##  [73,] -0.801725438
##  [74,] -0.664935503
##  [75,]  0.973253952
##  [76,] -0.009523786
##  [77,] -1.126963618
##  [78,] -0.957096129
##  [79,] -0.608275520
##  [80,] -0.243453021
##  [81,]  1.063007557
##  [82,]  0.392818724
##  [83,]  0.392818724
##  [84,] -0.747828795
##  [85,]  0.095854241
##  [86,] -1.031354769
##  [87,]  1.201049026
##  [88,]  0.316335747
##  [89,] -0.521132198
##  [90,]  1.343294484
##  [91,] -0.906338182
##  [92,] -1.328600085
##  [93,] -1.349904376
##  [94,]  1.247990825
##  [95,]  1.902940091
##  [96,] -1.328600085
##  [97,]  2.066561314
##  [98,]  1.849481438
##  [99,]  1.956936013
## [100,] -0.957096129
## [101,]  1.017906372
## [102,]  1.692275895
## [103,] -0.211028709
## [104,] -1.328600085
## [105,] -0.692843367
## [106,]  0.550451067
## [107,]  1.063007557
## [108,] -0.636747160
## [109,] -1.055616701
## [110,] -0.608275520
## [111,]  1.154574306
## [112,]  1.440523404
## [113,]  0.431637674
## [114,] -0.431334967
## [115,]  1.692275895
## [116,]  0.431637674
## [117,] -0.664935503
## [118,] -0.178278527
## [119,]  0.241367234
## [120,]  1.902940091
## attr(,"scaled:center")
## [1] 0.9261776
## attr(,"scaled:scale")
## [1] 0.2669331
#datos adimencionales

par(mfrow=c(1,2))
hist(absorbancia2,nclass=8)
hist(absorbacia2escalda, nclass=8)

cor(absorbancia2,concentracion)
## [1] 0.9908622
cor(absorbacia2escalda,concentracion)
##           [,1]
## [1,] 0.9908622
#la distribución delos datos es similar con la misma correlación
#, pero no los normaliza
#estarizar la variable no afecta la correlación 

#a media de variables estandirazdas es cero 
#las varianzas de 
#la estandarizacion 

conescalda=scale(concentracion)
cor(absorbacia2escalda,conescalda)
##           [,1]
## [1,] 0.9908622
dfe=data.frame(absorbacia2escalda,conescalda)
cov(dfe)
##                    absorbacia2escalda conescalda
## absorbacia2escalda          1.0000000  0.9908622
## conescalda                  0.9908622  1.0000000
#con las variables estandarizadas al solicitar la matriz de covarianzas se obtiene
#la matriz de correlación
absorbacia3escalda= scale(absorbancia3)
absorbacia3escalda
##               [,1]
##   [1,]  0.48081207
##   [2,] -0.32937064
##   [3,] -0.40777983
##   [4,] -1.02065246
##   [5,] -1.16096003
##   [6,]  0.30754445
##   [7,] -1.03467019
##   [8,]  0.41342938
##   [9,]  2.07340209
##  [10,] -0.17078793
##  [11,]  0.11425602
##  [12,] -1.31684077
##  [13,]  1.88202559
##  [14,] -1.44558551
##  [15,]  0.41591745
##  [16,] -0.79599711
##  [17,]  1.12547190
##  [18,]  0.40761860
##  [19,]  1.79982484
##  [20,] -0.15968543
##  [21,] -0.34941894
##  [22,] -1.32364296
##  [23,]  0.30960624
##  [24,]  0.39916626
##  [25,] -0.07806258
##  [26,] -0.81295961
##  [27,] -1.53201531
##  [28,] -0.26758344
##  [29,]  0.59000860
##  [30,] -0.79832987
##  [31,] -0.20341069
##  [32,] -1.06938726
##  [33,]  0.36569338
##  [34,]  1.51690067
##  [35,] -0.16561149
##  [36,]  1.32756243
##  [37,] -0.15122237
##  [38,] -1.43591992
##  [39,] -0.68525630
##  [40,] -0.26108517
##  [41,] -0.95524824
##  [42,]  1.63070594
##  [43,]  0.86268066
##  [44,] -0.55989602
##  [45,] -0.98010625
##  [46,]  0.35102861
##  [47,] -0.63530118
##  [48,] -0.37617633
##  [49,]  0.49434950
##  [50,] -0.32840004
##  [51,] -1.56036654
##  [52,] -0.52297949
##  [53,]  0.32138131
##  [54,] -0.99164233
##  [55,]  0.75569693
##  [56,] -0.51605751
##  [57,] -0.18739090
##  [58,]  1.08078661
##  [59,]  0.80950817
##  [60,]  0.49481315
##  [61,] -0.27475423
##  [62,] -0.75808355
##  [63,] -0.95694641
##  [64,] -0.95692848
##  [65,] -0.93670520
##  [66,] -0.89739912
##  [67,]  1.47723036
##  [68,] -0.08354623
##  [69,] -1.44665472
##  [70,]  0.41496386
##  [71,] -0.79657638
##  [72,]  1.75081209
##  [73,] -1.22571074
##  [74,] -0.86329974
##  [75,]  1.06865362
##  [76,] -0.01907545
##  [77,] -0.89966141
##  [78,] -1.27998224
##  [79,] -0.60881583
##  [80,]  0.22856257
##  [81,]  0.62373443
##  [82,]  0.75839812
##  [83,]  0.33275759
##  [84,] -0.47665654
##  [85,] -0.09511956
##  [86,] -1.21748886
##  [87,]  1.73343595
##  [88,]  0.20453269
##  [89,] -0.43745142
##  [90,]  1.99405455
##  [91,] -1.15374450
##  [92,] -1.10088263
##  [93,] -1.29783418
##  [94,]  1.35071121
##  [95,]  1.20773809
##  [96,] -1.11355713
##  [97,]  1.34671392
##  [98,]  1.84747637
##  [99,]  1.62500316
## [100,] -0.33716291
## [101,]  1.00210157
## [102,]  1.98618336
## [103,]  0.13191902
## [104,] -1.23651836
## [105,] -0.79175741
## [106,]  1.62809505
## [107,]  1.01135058
## [108,] -1.02242449
## [109,] -1.45060599
## [110,] -0.98234142
## [111,]  1.21392035
## [112,]  1.00414171
## [113,]  0.72897576
## [114,] -0.74834767
## [115,]  1.54750968
## [116,]  0.87124362
## [117,] -0.60372481
## [118,] -0.39863846
## [119,]  0.05807021
## [120,]  1.57971637
## attr(,"scaled:center")
## [1] 1.387454
## attr(,"scaled:scale")
## [1] 0.413222
mean(absorbancia3)
## [1] 1.387454
var(absorbancia3)
## [1] 0.1707524
mean(absorbacia3escalda)
## [1] 1.695313e-16
var(absorbacia3escalda)
##      [,1]
## [1,]    1
#la media de varianzas estandarizadas es cero y la varianza 1 y no se afecta la covariación

#prueba de normalidad

shapiro.test(absorbancia3)
## 
##  Shapiro-Wilk normality test
## 
## data:  absorbancia3
## W = 0.94926, p-value = 0.0001907
#la variables estandarizas no son normales 
shapiro.test(absorbacia3escalda)
## 
##  Shapiro-Wilk normality test
## 
## data:  absorbacia3escalda
## W = 0.94926, p-value = 0.0001907
#Normalizaion N

absorbancia3N= (absorbancia3-min(absorbancia3))/sd(absorbancia3)
mean(absorbancia3N)
## [1] 1.560367
var(absorbancia3N)
## [1] 1
# la varianza es acotada y sin datos negativos

cor(absorbacia3escalda,concentracion)
##           [,1]
## [1,] 0.9396571
cor(absorbancia3N,concentracion)
## [1] 0.9396571
cor(absorbancia3,concentracion)
## [1] 0.9396571
# la correlacion con la variable escalda es la misma de los datos originales que con los datos escalados 
# se utiliza otra estandarizacion en la suoerficie de respuesta clase 20-21

Error estandar

hist(concentracion, ylim=c(0,20))
abline(v=mean(concentracion), col="red", lwd=2)

par(mfrow=c(1,2))
hist(absorbancia,ylim = c(0,35))
abline(v=mean(absorbancia), col="red", lwd=2)
text(mean(absorbancia),33,"media", col= "red")
abline(v=median(absorbancia), col="blue", lwd=2)
text(median(absorbancia),36,"mediana", col= "blue")

#media median y moda no son utiles en  distribuciones uniformes pero si en la normal y otras como la Beta
#abline lineas Verticales o Horizontales

hist(concentracion, ylim=c(0,20))
abline(v=mean(concentracion), col="red", lwd=2)
text(mean(concentracion),16,"media", col= "red")
abline(v=median(concentracion), col="blue", lwd=2)
text(median(concentracion),15,"mediana", col= "blue")

Ejercicio llenado de botellas de 1 litro

par(mfrow=c(1,1))
Volumen=rbeta(120,12,0.9)
hist(Volumen, nclass=20)
abline(v=mean(Volumen),col="red", lwd=2, lty=2)
text(0.92,34, "Media", col= "red")
abline(v=median(Volumen),col="blue", lwd=2, lty=2)
abline(v=quantile(Volumen, 0.25),col="green", lwd=2, lty=2)
abline(v=quantile(Volumen, 0.75),col="darkgreen", lwd=2, lty=2)# la frecuencia de más botellas
sdv=sd(Volumen)
limites= list(li=mean(Volumen)-sdv, ls=mean(Volumen)+sdv)# aprecen con lso nombres de lso limites ls y Li
limites
## $li
## [1] 0.8630437
## 
## $ls
## [1] 1.009272
abline(v=c(limites$li,limites$ls),col="darkred")

El limite superior esta muy desviado porcentaje de datos entre los limites

100*sum(Volumen<limites$ls & Volumen>limites$li)/120
## [1] 87.5
#al ser un a distribución asimetrica por o que el 86, 6 de los datos cae por encima de la media 
set.seed(2021)
indice2= rbeta(120,0.5,0.5) # informativo en cero y uno
hist(indice2, nclass=20,probability=T, ylim=c(0,4))
lines(density(indice2))
#media
abline(v=mean(indice2),col="red", lwd=2, lty=2)
text(0.92,34, "Media", col= "red")
#Mediana
abline(v=median(indice2),col="blue", lwd=2, lty=2)
#cuartil inferior
abline(v=quantile(indice2, 0.25),col="green", lwd=2, lty=2)
sdv=sd(Volumen)
limites= list(li=mean(Volumen)-sdv, ls=mean(Volumen)+sdv)# aprecen con los nombres de los limites ls y Li
limites
## $li
## [1] 0.8630437
## 
## $ls
## [1] 1.009272
abline(v=c(limites$li,limites$ls),col="darkred")

#El limite superior esta muy desviado
#porcentaje de datos entre los limites
100*sum(Volumen<limites$ls & Volumen>limites$li)/120
## [1] 87.5
#al ser un a distribución asimetrica por o que el 86, 6 de los datos cae por encima de la media