#UNIVERSIDAD NACIONAL DEL ALTIPLANO
#REGRESION AVANZADA
#FINESI
library(readxl)
## Warning: package 'readxl' was built under R version 4.0.2
Caso2 <- read_excel("E:/VII SEMESTRE/REGRESION AVANZADA/Trabajo 2/Caso2.xlsx")
Caso2
## # A tibble: 12 x 3
## y x1 x2
## <dbl> <dbl> <dbl>
## 1 2.6 31 21
## 2 2.4 31 21
## 3 17.3 31.5 24
## 4 15.6 31.5 24
## 5 16.1 31.5 24
## 6 5.36 30.5 22
## 7 6.19 31.5 22
## 8 10.2 30.5 23
## 9 2.62 31 21.5
## 10 2.98 30.5 21.5
## 11 6.92 31 22.5
## 12 7.06 30.5 22.5
head(Caso2)
## # A tibble: 6 x 3
## y x1 x2
## <dbl> <dbl> <dbl>
## 1 2.6 31 21
## 2 2.4 31 21
## 3 17.3 31.5 24
## 4 15.6 31.5 24
## 5 16.1 31.5 24
## 6 5.36 30.5 22
View(Caso2)
RPL <- as.numeric(Caso2$y)
#GRAFICO LOWESS
plot(Caso2$x1 ~ Caso2$y)
lines(lowess(Caso2$x1 ~ Caso2$y))
plot(Caso2$x2 ~ Caso2$y)
lines(lowess(Caso2$x2 ~ Caso2$y))
#MODELO POLINOMIAL
m2<- lm(x1 ~ poly(y, 2, raw = T), data = Caso2)
m3<- lm(x1 ~ y + I(y^2), data = Caso2)
m4<- lm(x2 ~ poly(y, 2, raw = T), data = Caso2)
m5<- lm(x2 ~ y + I(y^2), data = Caso2)
summary(m2)
##
## Call:
## lm(formula = x1 ~ poly(y, 2, raw = T), data = Caso2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.3899 -0.2770 0.0729 0.1018 0.7239
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 31.137367 0.358085 86.955 1.78e-14 ***
## poly(y, 2, raw = T)1 -0.105936 0.097989 -1.081 0.308
## poly(y, 2, raw = T)2 0.007686 0.004953 1.552 0.155
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3449 on 9 degrees of freedom
## Multiple R-squared: 0.4646, Adjusted R-squared: 0.3456
## F-statistic: 3.905 on 2 and 9 DF, p-value: 0.06013
summary(m3)
##
## Call:
## lm(formula = x1 ~ y + I(y^2), data = Caso2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.3899 -0.2770 0.0729 0.1018 0.7239
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 31.137367 0.358085 86.955 1.78e-14 ***
## y -0.105936 0.097989 -1.081 0.308
## I(y^2) 0.007686 0.004953 1.552 0.155
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3449 on 9 degrees of freedom
## Multiple R-squared: 0.4646, Adjusted R-squared: 0.3456
## F-statistic: 3.905 on 2 and 9 DF, p-value: 0.06013
summary(m4)
##
## Call:
## lm(formula = x2 ~ poly(y, 2, raw = T), data = Caso2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.22188 -0.10370 0.01841 0.09627 0.27211
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.390727 0.177311 115.000 1.44e-15 ***
## poly(y, 2, raw = T)1 0.338495 0.048521 6.976 6.49e-05 ***
## poly(y, 2, raw = T)2 -0.007239 0.002453 -2.952 0.0162 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1708 on 9 degrees of freedom
## Multiple R-squared: 0.9811, Adjusted R-squared: 0.9769
## F-statistic: 234 on 2 and 9 DF, p-value: 1.74e-08
summary(m5)
##
## Call:
## lm(formula = x2 ~ y + I(y^2), data = Caso2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.22188 -0.10370 0.01841 0.09627 0.27211
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.390727 0.177311 115.000 1.44e-15 ***
## y 0.338495 0.048521 6.976 6.49e-05 ***
## I(y^2) -0.007239 0.002453 -2.952 0.0162 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1708 on 9 degrees of freedom
## Multiple R-squared: 0.9811, Adjusted R-squared: 0.9769
## F-statistic: 234 on 2 and 9 DF, p-value: 1.74e-08
#INTERPOLATION DE PUNTOS DENTRO DEL RANGO DEL PREDICTOR
limites <- range(Caso2$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)
#CALC 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 = Caso2, aes(x = x1, 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))
## Warning: Computation failed in `stat_smooth()`:
## 'degree' must be less than number of unique points
ggplot(data = Caso2, aes(x = x2, 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(Caso2, aes(x = x1, 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()
ggplot(Caso2, aes(x = x2, 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: x1 ~ poly(y, 2, raw = T)
## Model 2: x1 ~ y + I(y^2)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 9 1.0708
## 2 9 1.0708 0 0
anova(m4, m5)
## Analysis of Variance Table
##
## Model 1: x2 ~ poly(y, 2, raw = T)
## Model 2: x2 ~ y + I(y^2)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 9 0.26255
## 2 9 0.26255 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')
plot(m4, which=1, caption='Modelo Lineal')
plot(m5, which=1, caption='Modelo Cuadratico')
