# David Kauchak
# 11/20/2011
#
# Linear regression example

# start with some data
age = 18:29
height = c(76.1,77,78.1,78.2,78.8,79.7,79.9,81.1,81.2,81.8,82.8,83.5)

# we can plot the data using plot
plot(age, height)

do_built_in = TRUE

if( do_built_in ){
	# learn a linear model of height to age
	# tilde is just used to separate the left and right
	# hand sides of a model formula
	model = lm(height~age)

	# we can look at the model
	print(model)

	# we can plot the resulting line
	abline(model)
}else{
	# do it ourselves!
	# see http://people.hofstra.edu/Stefan_Waner/RealWorld/calctopic1/regression.html
	# for the basic equations for a single variable

	# ---------------------------------------------
	# some functions 
	
	slope <- function(x,y){
		# Calculate the slope of the best fit line for the data x, y
		
		numerator <- length(x) * sum(x*y) - sum(x)*sum(y)
		denominator <- length(x) * sum(x^2) - sum(x)^2
		return(numerator/denominator)
	}

	intercept <- function(x,y){
		# Calculate the intercept of the best fit line for the data x, y
	
		return((sum(y) - slope(x,y) * sum(x))/length(x))
	}
	# ---------------------------------------------

	# using the functions: get the slope and intercept
	m = slope(age, height)
	b = intercept(age, height)

	# print out the model parameters
	print(m)
	print(b)
	
	# draw the best fit line
	abline(b, m)
}