Ejercicio2.R

#UNIVERSIDAD NACIONAL DEL ALTIPLANO
#INGENIERIA ESTADISTICA E INFORMATICA
#REGRESION AVANZADA
#REGRESION INTRISICAMENTE NO LINEAL

library(readxl)

## Warning: package 'readxl' was built under R version 4.0.2

Datos <- read_excel("E:/VII SEMESTRE/REGRESION AVANZADA/Trabajo 3/Datos.xlsx")
Datos

## # A tibble: 7 x 3
##       x     y1     y2
##   <dbl>  <dbl>  <dbl>
## 1   0.5   0.68   1.58
## 2   1     0.45   2.66
## 3   2     2.5    2.04
## 4   4     6.19   7.85
## 5   8    56.1   54.2 
## 6   9    89.8   90.2 
## 7  10   148.   146.

head(Datos)

## # A tibble: 6 x 3
##       x    y1    y2
##   <dbl> <dbl> <dbl>
## 1   0.5  0.68  1.58
## 2   1    0.45  2.66
## 3   2    2.5   2.04
## 4   4    6.19  7.85
## 5   8   56.1  54.2 
## 6   9   89.8  90.2

View(Datos)

#Representacion de Datos
plot(y1 ~ x, xlab="Log de Densidad", ylab="Residuales", data = Datos)

plot(y2 ~ x, xlab="Log de Densidad", ylab="Residuales", data = Datos)

foo = function(x,b1,b2,b3){(b2+b3*x+(log(b1)))}
x<- 2

#Plots of Regression No lineal 
plot(y1 ~ x,xlab="Log de Densidad",
     ylab="Mobilidad de los electrones",main="Prueba 1", data = Datos)
lines(lowess(Datos$y1 ~ Datos$x),col = "red")

plot(y2 ~ x,xlab="Log de Densidad",
     ylab="Mobilidad de los electrones",main="Prueba 2", data = Datos)
lines(lowess(Datos$y2 ~ Datos$x),col = "blue")

#Valors
m1start=list(b1=0,b2=0.3,b3=5.1)

B1=0
B2=0.3
B3=5.1
x=2

#Anova
m.lm <- lm(y1 ~ x,data = Datos)
summary(m.lm)

## 
## Call:
## lm(formula = y1 ~ x, data = Datos)
## 
## Residuals:
##       1       2       3       4       5       6       7 
##  15.750   8.924  -2.216 -24.907 -27.760  -7.250  37.459 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  -21.665     15.855  -1.366  0.23003   
## x             13.191      2.571   5.131  0.00367 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 25.22 on 5 degrees of freedom
## Multiple R-squared:  0.8404, Adjusted R-squared:  0.8085 
## F-statistic: 26.33 on 1 and 5 DF,  p-value: 0.003673

anova(m.lm)

## Analysis of Variance Table
## 
## Response: y1
##           Df  Sum Sq Mean Sq F value   Pr(>F)   
## x          1 16740.5 16740.5  26.327 0.003673 **
## Residuals  5  3179.3   635.9                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1