#UNIVERSIDAD NACIONAL DEL ALTIPLANO
#REGRESION AVANZADA
#FINESI
#TEMA: Regression Polynomial
library(knitr)
library(readxl)
## Warning: package 'readxl' was built under R version 4.0.2
# BUSCAR LA RUTA DE EXCEL
Caso1 <- read_excel("E:/VII SEMESTRE/REGRESION AVANZADA/Trabajo 2/Caso1.xlsx")
Caso1
## # A tibble: 12 x 2
## x y
## <dbl> <dbl>
## 1 4 24.6
## 2 4 24.7
## 3 4 23.9
## 4 5 39.5
## 5 5 39.6
## 6 6 57.1
## 7 6.5 67.1
## 8 6.5 67.2
## 9 6.75 67.2
## 10 7 77.9
## 11 7.1 80.1
## 12 7.3 84.7
head(Caso1)
## # A tibble: 6 x 2
## x y
## <dbl> <dbl>
## 1 4 24.6
## 2 4 24.7
## 3 4 23.9
## 4 5 39.5
## 5 5 39.6
## 6 6 57.1
View(Caso1)
RPL <- as.numeric(Caso1$y)
#GRAFICO LOWESS
plot(Caso1$x ~ Caso1$y)
lines(lowess(Caso1$x ~ Caso1$y))
#MODELO POLINOMIAL
m2<- lm(x ~ poly(y, 2, raw = T), data = Caso1)
m3<- lm(x ~ y + I(y^2), data = Caso1)
summary(m2)
##
## Call:
## lm(formula = x ~ poly(y, 2, raw = T), data = Caso1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.05267 -0.03117 -0.01789 -0.00567 0.20162
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.075e+00 1.589e-01 13.055 3.74e-07 ***
## poly(y, 2, raw = T)1 8.550e-02 6.941e-03 12.318 6.16e-07 ***
## poly(y, 2, raw = T)2 -2.812e-04 6.566e-05 -4.283 0.00204 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07538 on 9 degrees of freedom
## Multiple R-squared: 0.9972, Adjusted R-squared: 0.9966
## F-statistic: 1605 on 2 and 9 DF, p-value: 3.234e-12
summary(m3)
##
## Call:
## lm(formula = x ~ y + I(y^2), data = Caso1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.05267 -0.03117 -0.01789 -0.00567 0.20162
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.075e+00 1.589e-01 13.055 3.74e-07 ***
## y 8.550e-02 6.941e-03 12.318 6.16e-07 ***
## I(y^2) -2.812e-04 6.566e-05 -4.283 0.00204 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07538 on 9 degrees of freedom
## Multiple R-squared: 0.9972, Adjusted R-squared: 0.9966
## F-statistic: 1605 on 2 and 9 DF, p-value: 3.234e-12
#INTERPOLACION DE PUNTOS DENTRO DEL RANGO DEL PREDICTOR
limites <- range(Caso1$y)
nuevos_puntos <- seq(from = limites[1], to = limites[2], by = 1)
nuevos_puntos <- data.frame(y = nuevos_puntos)
#PREDICTION DE LA VARIABLE RESPUESTA Y DEL ERROR ESTANDAR
predicciones <- predict(m2, newdata = nuevos_puntos, se.fit = TRUE,
level = 0.95)
#CALCULO DEL INTERVALO DE CONFIANZA SUPERIOR E INFERIOR 95%
intervalo_conf <- data.frame(inferior = predicciones$fit -
1.96*predicciones$se.fit,
superior = predicciones$fit +
1.96*predicciones$se.fit)
#GRAFICO DE REGRESION POLINOMIAL
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.0.3
ggplot(data = Caso1, aes(x = x, y = y)) +
geom_point(color = "grey30", alpha = 0.3) +
geom_smooth(method = "lm", formula = y ~ poly(x, 4), color = "red") +
labs(title = "Regresion Polinomial") +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5))
#GRAFICO DE LINEA RECTA Y CURVA
ggplot(Caso1, aes(x=x, y=y)) +
geom_point() +
geom_smooth(method='lm', formula=y~x, se=FALSE, col='blue') +
geom_smooth(method='lm', formula=y~x+I(x^2), se=FALSE, col='green') +
theme_light()
#ANOVA
anova(m2, m3)
## Analysis of Variance Table
##
## Model 1: x ~ poly(y, 2, raw = T)
## Model 2: x ~ y + I(y^2)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 9 0.051135
## 2 9 0.051135 0 0
#GRAFICO DE MODELO LINEAL Y MODELO CUADRATICO
par(mfrow=c(1, 2))
plot(m2, which=1, caption='Modelo Lineal')
plot(m3, which=1, caption='Modelo Cuadratico')
