## Paul Johnson Sept. 11, 2005 POLS 707 ## Plot Some functions x <- seq(from=0, to=50, length.out=200) y <- 3 + 4 * x plot (x, y, main="Linear Equation",type="l") y <- 3 + 4*x - 0.09 * x * x plot (x, y, main="Quadratic Equation", type="l") y <- 10 - 5 * (1/x) plot (x, y, main="Reciprocal with negative coefficient",type="l") #Recall (1/x) = x ^(-1) y <- 10 + 5 * (1/x) plot (x, y, main="Reciprocal with positive coefficient",type="l") y <- exp (x) plot (x, y, main="Exponential of x" , type="l") y <- exp (-x) plot (x, y, main="Exponential of -x", type="l") # Note exp(-x) is same as 1 / exp(x) y <- 1 / exp (x) plot (x, y, main="Reciprocal of Exponential of x", type="l") y <- exp ( - (x-24)^2 ) plot (x, y, main="Exponential of x^2",type="l") y <- exp ( - (1/100) * (x-24)^2 ) plot (x, y, main="Exponential of x^2",type="l") # If y has to be constrained (say, between 0 and 100 for percents) # there are many possibilities z <- -10 + .4*x y <- 100 * exp(z)/ (1 + exp(z)) # same as y <- 100 / (1 + exp(-z)) plot (x, y, main="S-shaped curve from the logistic",type="l") #Look in R's stats package for functions that start with SS. # The SSlogis function has this formula # y = Asym/(1+exp((xmid-input)/scale)) # you should see my example creates similar