Brian.R

Brian <- read.csv("~/Desktop/Brian.csv")
x<-Brian$Concentración
y<-Brian$Absorbancia

#Covarianza
cov(x,y)

## [1] 0.007944821

#Correlación
cor(x,y)

## [1] 0.9920163

#Normalidad 
library(pastecs)
stat.desc(Brian, norm = TRUE)

##              Concentración Absorbancia
## nbr.val        8.000000000  8.00000000
## nbr.null       0.000000000  0.00000000
## nbr.na         0.000000000  0.00000000
## min            0.005000000  0.04300000
## max            0.080000000  0.82500000
## range          0.075000000  0.78200000
## sum            0.325000000  3.31400000
## median         0.040000000  0.39550000
## mean           0.040625000  0.41425000
## SE.mean        0.010019512  0.09991456
## CI.mean.0.95   0.023692382  0.23626040
## var            0.000803125  0.07986336
## std.dev        0.028339460  0.28260106
## coef.var       0.697586711  0.68219929
## skewness       0.058117154  0.09412565
## skew.2SE       0.038636513  0.06257510
## kurtosis      -1.840910489 -1.70561644
## kurt.2SE      -0.621559442 -0.57587917
## normtest.W     0.934752632  0.95913164
## normtest.p     0.560298420  0.80178816

#Prueba de Spearman
cor.test(x,y, method = "spearman")

## 
##  Spearman's rank correlation rho
## 
## data:  x and y
## S = 0, p-value = 4.96e-05
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho 
##   1

library(psych)
pairs.panels(x=Brian, ellipses = FALSE, lm = TRUE, method = "spearman")

#Regresión lineal
Reg<-lm(y~x, Brian)
summary(Reg)

## 
## Call:
## lm(formula = y ~ x, data = Brian)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.072991 -0.008395  0.003933  0.020145  0.047857 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.01237    0.02490   0.497    0.637    
## x            9.89238    0.51340  19.268 1.26e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03849 on 6 degrees of freedom
## Multiple R-squared:  0.9841, Adjusted R-squared:  0.9814 
## F-statistic: 371.3 on 1 and 6 DF,  p-value: 1.265e-06

plot(y~x,Brian)
abline(Reg)

#ANOVA (para ver la relación entre las variable)
#Hó: No existe relación
#Ha: Existe relación
Cur_Polif<-aov(y~x,Brian)
anova(Cur_Polif)

## Analysis of Variance Table
## 
## Response: y
##           Df  Sum Sq Mean Sq F value    Pr(>F)    
## x          1 0.55015 0.55015  371.27 1.265e-06 ***
## Residuals  6 0.00889 0.00148                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Supuestos 
#Normalidad (no se rechaza, se cumple normalidad)
shapiro.test(Cur_Polif$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cur_Polif$residuals
## W = 0.92087, p-value = 0.437

#Homogeneidad de variaza (Breush-Pagan)(no se recahza, cumple la homogeneidad)
library(lmtest)

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

bptest(Cur_Polif)

## 
##  studentized Breusch-Pagan test
## 
## data:  Cur_Polif
## BP = 0.035607, df = 1, p-value = 0.8503

#Independencia (Durbin-Watson) (no hay independencia)
dwtest(y~x)

## 
##  Durbin-Watson test
## 
## data:  y ~ x
## DW = 2.3751, p-value = 0.5353
## alternative hypothesis: true autocorrelation is greater than 0

#Ho: hay independencia
#Ha: no hay independencia