Capitulo 2 Regresión lineal simple
Figura 2.1
Ecuación de la recta
x <- c(0, 4)
y <- c(0, 4)
plot(x, y, type ="n", xlab = "X = Predictor", ylab = "E(Y|X=x)")
abline(0.8, 0.7)
x<-c(2, 3, 3)
y<-c(2.2, 2.2, 2.9)
lines(x, y, lty = 2)
lines(c(0, 0), c(0, 0.8), lty = 2)
#lines(c(0, 4), c(0, 0), lty=2)
text(3.05, 2.5, expression(beta[1] == Pendiente), adj = 0)
text(0.05, 0.4, expression(beta[0] == Intercepto), adj = 0)
text(2.5, 1.8, "1")
Figura 2.2
Error por falta de ajuste
x <- c(0, 4)
y <- c(0, 4)
plot(x, y, type = "n", xlab = "X = Predictor", ylab = "E(Y|X=x)")
abline(0.8, 0.7, lty = 2)
x <- seq(0, 4, length = 200)
y <- 0.175*x*x + 1.10625
lines(x, y)
lines( c(3.8, 3.8), c(3.46, 3.63325))
text(1, 2.7, "Función media lineal", adj = 0, cex = 0.8
text(1.5, 1.2, "Verdadera función media", adj = 0, cex = 0.8
text(3.5, 3.5, "Error por falta de ajuste", adj=1, cex = 0.8)
library(diagram)## Warning: package 'diagram' was built under R version 3.1.3## Loading required package: shape## Warning: package 'shape' was built under R version 3.1.3curvedarrow(from = c(3, 3.6), to = c(3.7, 3.7), lwd = 0.5, lty = 1, curve = -0.5)
Figura 2.3
Residuales en la regresión lineal simple
x <- c(0.45, 3.97, 1.12, 4.21, -0.23, 1.56, -0.01, 2.67, 1.51, 0.93, 2.08, 3.50,4.14, 1.92, 2.11, 3.25, 0.67, 0.68, -0.22, 3.96)
y <- c(-1.24, 4.87, 1.32, 4.14, -0.62, 0.66, 0.61, 3.27, 1.97, 0.40, 2.49, 4.00, 3.11, 2.08, 1.97, 2.70, 1.50, 1.77, -0.26, 2.11)
m1 <- lm(y ~ x)
yhat <- predict(m1)
plot(x, y, type = "p", xlab = expression(X==Predictor), ylab = expression(Y==Respuesta))
abline(m1)
for (i in 1:20){
lines(list(x=c(x[i], x[i]),y=c(y[i], yhat[i])))
}
Figura 2.4
Dos funciones media comparadas con el ANVA
x <- c(0.45, 3.97, 1.12, 4.21, -0.23, 1.56, -0.01, 2.67, 1.51, 0.93, 2.08, 3.50,4.14, 1.92, 2.11, 3.25, 0.67, 0.68, -0.22, 3.96)
y <- c(-1.24, 4.87, 1.32, 4.14, -0.62, 0.66, 0.61, 3.27, 1.97, 0.40, 2.49, 4.00, 3.11, 2.08, 1.97, 2.70, 1.50, 1.77, -0.26, 2.11)
m1 <- lm(y ~ x)
m0 <- lm(y ~ 1)
plot(x, y, type = "p", xlab = expression(X==Predictor), ylab = expression(Y==Respuesta))
abline(reg = m1)
abline(m0$coef[1],0)
text(2.5, 1.5, "Función media (2.7.1)", adj = 0
text(0.0, -0.2, "Función media (2.7.4)", adj = 0
ANVA para la data Forbes
Forbes.data <- read.table(file = "http://tarwi.lamolina.edu.pe/~clopez/Regresion/Forbes.txt", header = T)
attach(Forbes.data)
Forbes.m1 <- lm(LogPresion ~ Temperatura)
Forbes.m1##
## Call:
## lm(formula = LogPresion ~ Temperatura)
##
## Coefficients:
## (Intercept) Temperatura
## -42.1378 0.8955summary(Forbes.m1)##
## Call:
## lm(formula = LogPresion ~ Temperatura)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.32220 -0.14473 -0.06664 0.02184 1.35978
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -42.13778 3.34020 -12.62 2.18e-09 ***
## Temperatura 0.89549 0.01645 54.43 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.379 on 15 degrees of freedom
## Multiple R-squared: 0.995, Adjusted R-squared: 0.9946
## F-statistic: 2963 on 1 and 15 DF, p-value: < 2.2e-16anova(Forbes.m1)## Analysis of Variance Table
##
## Response: LogPresion
## Df Sum Sq Mean Sq F value Pr(>F)
## Temperatura 1 425.64 425.64 2962.8 < 2.2e-16 ***
## Residuals 15 2.15 0.14
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1confint(Forbes.m1, level = 0.90)## 5 % 95 %
## (Intercept) -47.9933161 -36.2822424
## Temperatura 0.8666529 0.9243344predict(Forbes.m1, data.frame(Temperatura = 200), level = 0.95, interval = "confidence")## fit lwr upr
## 1 136.961 136.7393 137.1826predict(Forbes.m1, data.frame(Temperatura = 200), level = 0.95, interval = "prediction")## fit lwr upr
## 1 136.961 136.1232 137.7987Figura 2.5
Residuales para la data Tallas
Tallas.data <- read.table(file = "http://tarwi.lamolina.edu.pe/~clopez/Regresion/Tallas.txt", header = T)
Tallas.m1 <- lm(HTalla ~ MTalla, data = Tallas.data)
plot(predict(Tallas.m1), residuals(Tallas.m1), cex = 0.5, xlab = "Valores estimados", ylab = "Residuales")
abline(h = 0, lty = 2)
Figura 2.6
Residuales para la data Forbes
plot(predict(Forbes.m1), residuals(Forbes.m1), cex = 0.5, xlab = "Valores estimados", ylab = "Residuales")
text(predict(Forbes.m1)[12], residuals(Forbes.m1)[12], labels = "12", adj = -1)
abline(h = 0, lty = 2)