data <- read.csv("voltage.csv", header = TRUE)    

time <- data[,1]
voltage <- data[,2]
n <- length(time)

plot(voltage, time)
plot(voltage, 1/time)

lm1 <- lm(time ~ voltage) 
summary(lm1)
 
par(mfrow=c(1,2))            # making a 2-panel
plot(voltage, time) 
  lines(voltage, lm1$fit)
plot(lm1$fit, lm1$resid)


plot(voltage, time, log="y")

lm2 <- lm(log(time) ~ voltage)   # multi
summary(lm2)
 
par(mfrow=c(1,2)) 
plot(lm2$fit, lm2$resid)
qqnorm(lm2$resid)



 ## Islands example 


 data <- read.csv("islands.csv", header = TRUE)    
 attach(data)
 
 plot(AREA, SPECIES)
  plot(AREA, SPECIES, log="xy")

 lm3 <- lm( log(SPECIES) ~ log(AREA))
 summary(lm3)

 tstar <- qt(0.975, df=5)

 par(mfrow=c(1,2)) 
 plot(lm3$fit, lm3$resid)
 qqnorm(lm3$resid)