# Sistema lineal A %*% [x,y] = b
m1 <- matrix(c(1, 1,
               2, -1), nrow = 2, byrow = TRUE)
v1 <- c(2, 1)

# Solucion
solve(m1) %*% v1

# Respuesta: area de dano (cm^2)
area_d <- c(0, 0, 0.01,
            0.8, 0.6, 0.5,
            1.2, 1.4, 1.5,
            2.5, 2.8, 2.6)

# Factor: dosis de fungicida
dosis <- c(rep(0, 3),
           rep(0.02, 3),
           rep(0.05, 3),
           rep(0.08, 3))

df <- data.frame(area_d, dosis = as.factor(dosis))

# Media global y por tratamiento
mu <- mean(df$area_d)
medias <- tapply(df$area_d, df$dosis, mean)
efectos <- medias - mu

mu
medias
efectos
sum(efectos)

# Descriptivo
boxplot(area_d ~ dosis,
        data = df,
        ylab = "Area de dano",
        xlab = "Dosis",
        col = c("green1", "yellow2", "orange", "red2"))
abline(h = mu, lwd = 2, col = "red")

# Inferencial: ANOVA de un factor
mod1 <- aov(area_d ~ dosis, data = df)
summary(mod1)

# Si p-valor < 0.05 => rechazar H0