source("http://www.uvm.edu/~rsingle/stat221/data/scripts-221.R")

 #The data give the speed of cars and the distances taken to stop. 
 data(cars)

 plot(dist~speed, data=cars)      #scatterplot
 mod <- lm(dist~speed, data=cars) #create a model using lm()
 mod
 mod$fitted   #fitted or predicted values for the model
 predict(mod) #fitted values via the predict() function
              #predictions are based on the observed x-values

#prediction & interval at a new x-values
 x.new.df <- data.frame(speed=12.5) #NOTE: the var.name must match (speed) 
 x.new.df
 predict(mod, x.new.df, interval="confidence") 
 predict(mod, x.new.df, interval="prediction")

#prediction & interval at a new x-values 
 x.new.df <- data.frame(x = seq(-3, 3, 0.5))
 x.new.df
 predict(mod, x.new.df, interval = "confidence")
 predict(mod, x.new.df, interval = "prediction")
 
#create a scatterplot with  95% (default) confidence or prediction bands
 conf.bands(cars$speed,cars$dist) #the syntax follows the plot() function: (X.var, Y.var)
 pred.bands(cars$speed,cars$dist)

#customize the confidence band plot
 conf.bands(cars$speed,cars$dist) 
 conf.bands(cars$speed,cars$dist, alpha=.01, xlab="speed", ylab="dist")
 title("99% Prediction Bands")

#NOTE: although it is possible to fit a model using lm() as below
#This syntax can be problematic when trying to use other functions such as predict()
  mod2 <- lm(cars$dist~cars$speed)
  mod2       #NOTE: the name of the variable for the slope coefficient (cars$speed)
  x.new.df <- data.frame(speed=12.5) 
  x.new.df   #NOTE: the var.name does not match above (it is 'speed' here, not cars$speed)
  predict(mod2, x.new.df, interval="confidence")  #gives an error
#It is not easy to name the variable on the new data.frame cars$speed to match (since $ is a reserved symbol)