library(Stat2Data)
library(ggplot2) 
#------------------------------------------------------------------------

#Example 1: Can skull length predict overall body mass in blue jays?

#Get data
data(BlueJays)

#Test Assumptions

#Independence
  #depends on sample design and taken to be valid here

#Normality
hist(BlueJays$Mass, col='blue') #good

#Linear Relationship and Homeoscedasticity
plot(Mass~Skull, data=BlueJays, col='blue') #looks good for both
lm1 <- lm(Mass~Skull, data=BlueJays)    
plot(lm1, col="blue") #looks good for both

#Simple Linear Regression
lm1 <- lm(Mass~Skull, data=BlueJays)
summary(lm1)
#B=2.88, SE=0.3941, t=7.30, p<0.0001

#Graph
plot1 <- ggplot(data=BlueJays, aes(x=Skull, y=Mass)) +
  geom_point() + geom_smooth(method=lm, color="blue")
plot1
#------------------------------------------------------------------------

#Example 2: Can resting pulse rate predict active pulse rate in statistics students?
#Test Assumptions

#Get data
data(Pulse)

#Test Assumptions

#Independence
#depends on sample design and taken to be valid here

#Normality
hist(Pulse$Active, col='red') #little skewed but good enough

#Linear Relationship and Homeoscedasticity
plot(Active~Rest, data=Pulse, col='red') #looks good for both
lm2 <- lm(Active~Rest, data=Pulse)    
plot(lm2, col="red") #looks good enough for both

#Simple Linear Regression
lm2 <- lm(Active~Rest, data=Pulse)
summary(lm2)
#B=1.14, SE=0.10, t=11.50, p<0.0001

#Graph
plot2 <- ggplot(data=Pulse, aes(x=Rest, y=Active)) +
  geom_point() + geom_smooth(method=lm, color="Red")
plot2
#------------------------------------------------------------------------

#Example 3: Can sample depth predict iridium concentration in prehistoric rock layers?
#Test Assumptions

#Get Data
data(Dinosaurs)

#Independence
#depends on sample design and taken to be valid here

#Normality
hist(Dinosaurs$Iridium, col='forestgreen') #not normally distributed
hist(log(Dinosaurs$Iridium), col='forestgreen') #still not normally distributed (try anyways)

#Linear Relationship and Homeoscedasticity
plot(Iridium~Depth, data=Dinosaurs, col='forestgreen') #not linear
lm3 <- lm(Iridium~Depth, data=Dinosaurs)    
plot(lm3, col="forestgreen") #not linear, may also be heteroscedastic (try anyways)

#Simple Linear Regression
lm3 <- lm(Iridium~Depth, data=Dinosaurs) 
summary(lm3)
#B=-35.94, SE=23.71, t=-1.52, p=0.1420

#Graph
plot3 <- ggplot(data=Dinosaurs, aes(x=Depth, y=Iridium)) +
  geom_point() + geom_smooth(method=lm, color="forestgreen")
plot3