#
#
### Fun with Graphing small but complex models.
#
# Also demonstrates some interesting ways 
# variables can be related. 
#
#######################################

x <- seq(1:100)/10
z <- x^2 + x
y <- x + 5 
plot(x, y, cex = z, col="blue")

plot(jitter(x), jitter(y), cex = jitter(z), col="blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#######################################

x <- (seq(1:100)/10)*-1
z <- (x^2)
y <- z + 5 
plot(x, y, cex = z, col="blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#######################################

x <- (seq(1:100)/10)*-1
z <- (x^2)
y <- x + 5 
plot(x, y, cex = z, col="blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#######################################

x <- (seq(1:100)/10)
z <- (x^3)
y <- (x + 5)*-1 
plot(x, y, cex = z, col="blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

##############################

x <- seq(1:100)/10
z <- x * 4
y <- x + 4 
plot(x, y, cex = z, col = "blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

##############################

x <- seq(1:100)/10
y <- x * 4
z <- x + 4 
plot(jitter(x), jitter(z), cex = jitter(y), col = "blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

##############################

x <- seq(1:100)/10
y <- x * 4 + rnorm(100)
z <- x + 4 + rnorm(100)
plot(x, z, cex = y, col = "blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#############################

x <- rnorm(100, 5, 1)
y <- x + 2
z <- x + 4 
plot(x, z, cex = y, col = "blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

########################################

x <- rnorm(100, 5, 1)
y <- x^2
z <- 5 + x 
plot(x, z, cex = y, col = "blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

########################################

x <- rnorm(100, 5, 1)
y <- (x/2)^2
z <- 5 + x 
plot(x, z, cex = y, col = "blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#########################################

x <- rnorm(100, 10, 1.5)
y <- .95*x
z <- 5 + .9*x + .9*y #+ rnorm(100, 0, 1)
plot(x, z, cex = y, col = "blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#########################################

x <- rbinom(100, 5, .5)
y <- .95*x + rbinom(100, 5, .5)
z <- 5 + .9*x + .9*y + rnorm(100, 0, 1)
plot(x, z, cex = y, col = "blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#########################################

x <- rbinom(100, 5, .2)
y <- rbinom(100, 5, .5) + .9*x
z <- rbinom(100, 5, .5) + .9*x + .9*y
plot(x, y, cex = z, col="blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#######################################

x <- rbinom(100, 5, .5)
y <- x + c(rep(1, 20), rep(2, 20), rep(3, 20), rep(4, 20), rep(5, 20))
z <- x + y + rbinom(100, 5, .5)
plot(x, z, cex = y, col="blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#######################################

x <- (seq(1:100)/10)
z <- (x^3)
y <- (x^2 + 5)
plot(x, y, cex = z, col="blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#######################################

x <- (seq(1:100)/10)
z <- (x^3)
y <- (x^2 + 5)*-1 
plot(x, y, cex = z, col="blue")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

bill <- data.frame(x,y)
plot(bill, col = "blue", xlab="x", ylab="y")

lines(lowess(bill, f=.2), lwd=3, col="green")

#######################################

x <- (seq(1:100)/10)
z <- (x^2)
y <- (x^2 + 5)
plot(x, y, cex = z, col="red")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#######################################

x <- (seq(1:100)/10)
z <- (x^2)
y <- ((x - 1)^2 + 5)
plot(x, y, cex = z, col="purple")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)

#######################################

x <- (seq(1:100)/10)
z <- (x^3)
y <- ((x - 1)^2 + 5)
plot(x, y, cex = z, col="cyan")

bob <- data.frame(x, y, z)
summary(bob)
cor(bob)
pairs(bob)