######Simple linear regression######

datalr <- read.table("linreg.txt", h=T)
attach(datalr)
str(datalr)


#Assumption 1: Linear and causal relationship between x and y
plot(algae_density~phosphates)

#Assumption 2: Independence of the residuals


#####Model building#####
linmodel <- lm(algae_density~phosphates, data=datalr)
summary(linmodel)

# y = 0.084 + 0.115*x 

#Assumption 3: Normal distribution of model residuals
plot(linmodel,2)

aov_residuals <- residuals(object = linmodel)
shapiro.test(aov_residuals)

#Assumption 4: Homogeneity of variance
plot(linmodel,1)



#####Data visualization######
#Plotting the data#
install.packages(ggplot2)
library(ggplot2)

p1 <- ggplot(datalr, aes(x=phosphates, y=algae_density)) +
      geom_point(shape=1)+           # Use open circles
      geom_smooth(method=lm, se=T)+  # Add linear regression line with 95% CI
      theme_bw()+
      labs(x = expression(paste("PO"[4]^3^-{}, " (µM/L)")),
           y = expression(paste("Algae density", " (g/L)")))
p1