Clase 1

Primer documento RMarkdown - Publicacion en RPubs.com

Creando primeras funciones:

Elevar al cubo

cubos <- function(x) x**3
cubos(1:5)

## [1]   1   8  27  64 125

v1 = seq(from = 0, to = 20, by = 2) #Seq: secuencias desde-hasta-paso
v1; cubos(v1) 

##  [1]  0  2  4  6  8 10 12 14 16 18 20

##  [1]    0    8   64  216  512 1000 1728 2744 4096 5832 8000

fun() Estandarizar varaible

No la conierte en una distribucion normal, solo hace su media = 0 y desv = 1

estandarizar <- function(x){
  med = mean(x)
  dv = x - med #Desvios
  z = dv/sd(x)
  par(mfrow=c(2,2)) #Parametro para varias graficas en una ventana
  hist(x)
  hist(dv)
  hist(z)
  return(list(med.dat = med, med.des = mean(dv),
              var.dat = var(x), var.des = var(dv),
              med.z = mean(z), var.z = var(z),
              z = z))
}
set.seed(123) #se fija una semilla
estandarizar(rnorm(100, 5, 1))

## $med.dat
## [1] 5.090406
## 
## $med.des
## [1] -1.865435e-16
## 
## $var.dat
## [1] 0.8332328
## 
## $var.des
## [1] 0.8332328
## 
## $med.z
## [1] -2.043797e-16
## 
## $var.z
## [1] 1
## 
## $z
##   [1] -0.71304802 -0.35120270  1.60854170 -0.02179795  0.04259548
##   [6]  1.77983218  0.40589817 -1.48492941 -0.85149566 -0.58726835
##  [11]  1.24195461  0.29513939  0.34000892  0.02221347 -0.70797086
##  [16]  1.85854263  0.44636008 -2.25349176  0.66930255 -0.61698896
##  [21] -1.26885349 -0.33783464 -1.22304003 -0.89754917 -0.78377819
##  [26] -1.94683206  0.81876439  0.06898128 -1.34588242  1.27452758
##  [31]  0.36815564 -0.42229479  0.88157948  0.86296437  0.80101058
##  [36]  0.65537241  0.50778230 -0.16686565 -0.43422620 -0.51585092
##  [41] -0.86009994 -0.32681639 -1.48529653  2.27707482  1.22429519
##  [46] -1.32941869 -0.54040552 -0.61026684  0.75541982 -0.19037243
##  [51]  0.17847258 -0.13031397 -0.14600575  1.40027842 -0.34637532
##  [56]  1.56226982 -1.79571669  0.54141021  0.03664303  0.13752572
##  [61]  0.31685861 -0.64934164 -0.46407310 -1.21490140 -1.27319995
##  [66]  0.23347834  0.39197814 -0.04097396  0.91131364  2.14685001
##  [71] -0.63697081 -2.62876100  1.00275711 -0.87597805 -0.85276181
##  [76]  1.02448422 -0.41101270 -1.43635058  0.09957931 -0.25119772
##  [81] -0.09272595  0.32303830 -0.50510289  0.60688103 -0.34058618
##  [86]  0.26443017  1.10255872  0.37770550 -0.45610238  1.15949090
##  [91]  0.98935390  0.50173432  0.16249260 -0.78691881  1.39156928
##  [96] -0.75663177  2.29720706  1.57995139 -0.35725306 -1.22349625

estandarizar(runif(100,2,6))

## $med.dat
## [1] 3.944207
## 
## $med.des
## [1] -7.103042e-17
## 
## $var.dat
## [1] 1.386103
## 
## $var.des
## [1] 1.386103
## 
## $med.z
## [1] -5.748874e-17
## 
## $var.z
## [1] 1
## 
## $z
##   [1] -0.84029420  1.61826399  0.39178189  0.09845350 -0.28361946
##   [6]  1.33928538 -0.41436110 -0.67207186 -1.07160013 -1.06641378
##  [11] -0.01362095 -0.79191722 -0.91664070  0.63983716 -1.48943276
##  [16]  0.72979231 -0.45582182 -0.26197502  1.13782862  1.47046642
##  [21] -0.69147494  1.61400301  0.82336460  0.68060298 -1.47183253
##  [26] -0.30860214 -0.02788111  0.25210142  0.72098766  1.45968333
##  [31]  0.44949049 -0.19579977  0.19035862 -1.45268904 -0.76510423
##  [36] -0.30203874 -0.97952900  1.17512063 -1.13193336  1.07826062
##  [41]  0.20648254  0.59886732 -1.06802166  0.49944809 -0.59178685
##  [46]  0.81031784 -0.29596441  1.64203806  1.63538557  0.81761637
##  [51] -0.77747158 -0.89784172  0.36351426 -0.74246119  0.15295202
##  [56]  1.01667419 -1.08038077 -0.27741613 -0.04918052  1.29804038
##  [61]  1.49374150  1.34516655  0.63919318  1.57684155  0.10326156
##  [66]  0.30736468 -0.50867853 -0.47132813 -1.58333796  0.05694706
##  [71]  1.30801756 -1.62996390 -1.40655533 -1.09345982  0.96585544
##  [76]  0.84643335  1.65059718 -0.06652113 -1.39864798  0.55300242
##  [81]  0.92596547 -1.18555012 -0.30396636 -0.88697851 -1.45445550
##  [86] -0.30631712 -1.43077566 -0.88391699 -1.46576738  0.62592653
##  [91] -0.63978691 -1.30916723 -1.40707525  1.33994459  0.91120063
##  [96]  1.12306491  1.68547184 -1.29938895 -1.31487422  1.06267643

##Regresion Se crean variables de N y P para ver la importancia de la escala de grafica ademas de el valor de estandarizar

set.seed(123)
N = sort(rnorm(50, 4, 0.5))
P = sort(rnorm(50, 0.5, 0.01))
plot(N,P, pch = 19, col = 'blue', cex= 1.5,
     ylim= c(0, 5), xlim = c(0,5))
grid(10)
#Regresion lineal simple####
mod1 = lm(P~N)
mod1

## 
## Call:
## lm(formula = P ~ N)
## 
## Coefficients:
## (Intercept)            N  
##     0.42369      0.01936

summary(mod1)

## 
## Call:
## lm(formula = P ~ N)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0051859 -0.0008680  0.0003719  0.0008153  0.0021135 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.4236910  0.0016234  260.99   <2e-16 ***
## N           0.0193600  0.0004015   48.22   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.001301 on 48 degrees of freedom
## Multiple R-squared:  0.9798, Adjusted R-squared:  0.9794 
## F-statistic:  2325 on 1 and 48 DF,  p-value: < 2.2e-16

abline(a = 0.423, b = 0.0193, col ='red')
abline(h = 0.423, lty = 2)
abline(v = 0, lty = 2)
text(1,0.423, expression(theta), pos=3)
angulo = atan(0.0193)*180/pi
angulo

## [1] 1.105671

text(1.6,0.423, paste('= ', round(angulo,2)), pos=3)

#Estandarizando valores N y P
N2 = estandarizar(N)$z
mean(N2); sd(N2)

## [1] 1.251386e-16

## [1] 1

P2 = estandarizar(P)$z

mean(P2); sd(P2)

## [1] -5.273074e-15

## [1] 1

plot(P2~N2, col = 'blue', pch = 19)

mod2 = lm(P2~N2)
summary(mod2)

## 
## Call:
## lm(formula = P2 ~ N2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.57274 -0.09587  0.04108  0.09004  0.23342 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -5.381e-15  2.032e-02    0.00        1    
## N2           9.898e-01  2.053e-02   48.22   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1437 on 48 degrees of freedom
## Multiple R-squared:  0.9798, Adjusted R-squared:  0.9794 
## F-statistic:  2325 on 1 and 48 DF,  p-value: < 2.2e-16

angulo2 = atan(9.898e-1)*180/pi
angulo2

## [1] 44.7063

#Calculo de correlaciones
cor(P,N)

## [1] 0.9898341

cor(P2,N2)

## [1] 0.9898341

fert = gl(2, 25, 50, labels = c('control','quimico'))
tbl1 = data.frame(P,N,P2,N2,fert)
#View(tbl1)

fun() para prueba t

Prueba de Hipotesis t-student

Ho: mu(control(N)) == mu(quimico(N))

Ha: mu(control(N)) != mu(quimico(N))

mi.pt <- function(x1,x2, conf.lev){
  n1 = length(x1)
  n2 = length(x2)
  s1 = sd(x1)
  s2 = sd(x2)
  tc = abs((mean(x1)-mean(x2))/
             sqrt(((((n1-1)*s1^2)+((n2-1)*s2^2))/
                     (n1+n2-2))*((1/n1)+(1/n2))))
  p_v = pt(q = tc, df = (n1+n2-2), lower.tail = FALSE)
  desi = ifelse(p_v < (1-conf.lev)/2, 'Rechazo Ho', 'NO rechazo Ho')
  return(desi)
}

mi.pt(tbl1$P[1:25],tbl1$P[26:50], 0.95)

## [1] "Rechazo Ho"

mi.pt(tbl1$P2[1:25],tbl1$P2[26:50], 0.95)

## [1] "Rechazo Ho"

t.test(tbl1$P[1:25],tbl1$P[26:50])

## 
##  Welch Two Sample t-test
## 
## data:  tbl1$P[1:25] and tbl1$P[26:50]
## t = -8.6607, df = 47.974, p-value = 2.262e-11
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.01724883 -0.01074889
## sample estimates:
## mean of x mean of y 
## 0.4944647 0.5084635

tbl2 = split(tbl1$P, tbl1$fert)
PC = tbl2$control
PQ = tbl2$quimico
mi.pt(PC,PQ, 0.95)

## [1] "Rechazo Ho"

(x = 1:10)

##  [1]  1  2  3  4  5  6  7  8  9 10

y = 1:10

ley.gases <- function(n, R = 0.082, Tp, v, gra = F){ #Argumentos fijos: logicos, numericos, caracteres
  p = n*R*Tp/v
  if(gra) plot3d(Tp, v, p, col = rainbow(100))
  return(p)
}
p1 = ley.gases(n = 1, Tp = 273, v = seq(1,20))
plot(seq(1,20), p1, type = 'l')

require(rgl)

## Loading required package: rgl

p2 = ley.gases(n = 1,
               Tp = rep(seq(273,303,5), each = 20),
               v = rep(seq(1,20), 7), gra = )

#Tamaño de muestra####
set.seed(123)
var = replicate(200, sample(c(0,1),
                           size = 100,
                           replace = T,
                           prob = c(0.2,0.8)))
colSums(var)

##   [1] 82 81 81 81 81 73 78 79 87 79 85 82 78 84 75 85 78 72 77 87 81 79 77
##  [24] 82 84 80 82 78 79 81 77 80 75 77 82 78 80 72 80 74 80 82 84 80 85 85
##  [47] 81 79 89 82 73 79 83 83 79 79 86 83 78 71 82 78 87 85 79 80 79 81 86
##  [70] 78 77 80 77 81 81 85 86 84 75 76 78 81 82 90 88 80 78 82 84 86 82 81
##  [93] 83 80 77 81 87 79 77 74 80 83 86 70 84 84 78 87 76 77 79 81 80 76 78
## [116] 80 77 78 81 81 77 76 84 74 76 81 85 76 77 80 76 77 79 79 79 88 77 73
## [139] 78 82 73 80 83 80 79 83 80 81 80 77 83 81 83 79 85 82 80 78 83 80 84
## [162] 80 76 84 76 79 73 79 80 74 86 76 75 89 79 80 83 77 77 83 80 82 82 82
## [185] 82 84 86 87 74 84 77 85 82 81 84 84 82 79 86 82

hist(colSums(var))

hist(round(runif(200,0,1)))

var2 = replicate(2000,round(runif(200,0,1)))
pg2 = (colSums(var2)/200)*100
hist(pg2)

Otra funcion

TM <- function(N,p,e,Z){
  (N*p*(1-p))/(((N-1)*(e/Z))^2+(p*(1-p)))
}

Probando codigo python de salida

sal = 'Hola Carlos.'
n1 = 2
n2 = 3
str(sal)

## 'Hola Carlos.'

print('Suma = ', n1+n2)

## Suma =  5

Nota: dentro del documento el parametro echo = FALSE puede ocultar el codigo R, auqneu si muestra las salidas