#
# script for topic 8a -- part 3
source("../gnrnd4.R")
gnrnd4(365340906, 6340400805, 2200003)
L1
L2
#
main_hold <- "Problem for Topic 8a, part3"
plot(L1,L2,main=main_hold,
     xlim=c(0,26), ylim=c(0,55),
     xaxp=c(0,26,13), yaxp=c(0,55,11), las=1,
     pch=16, col="red", mar=c(2,0,0,0)+0.2,
     ylab="y values", xlab="x values")
abline(h=seq(0,55,5), v=seq(0,26,1),
       lty="dotted", col="blue")
# get the two values for our regression equation,
#  the intercept and the slope
lm( L2 ~ L1)
#  From the output of that command we see that the
#  intercept is 13.81 and the slope is 1.27.  So
#  our regression equation is y = 13.81 + 1.27*x
#  We sill graph it on our plot
abline( 13.81, 1.27, col="darkred")
#
#  We can find the expected value when x=18
ev <- 13.81 + 1.27*18
ev
#  And then we can plot that point on the graph
#    with a green triangle
points( 18, ev, pch=17, col="darkgreen")
#  And we can find the expected value for x=7
ev <- 13.81 + 1.27*7
ev
#  And then we can plot that point on the graph
#  with a blue square
points( 7, ev, pch=15, col="blue")
#
#  Now find the correlation coefficient
cor( L1, L2 )
#
#  One other issue is to find some residual values.
#  Here we do that the hard way, we will compute the 
#  observed - expected value for a given x value.
#  Find the residual value when x=17.  The observed
#  value when x=17 is y=26.  We need to compute the
#  expected value and then subtract that from 26 to
#  get the residual value.
26 - ( 13.81 + 1.27*17)
#
#  If we find all of the 
#  residual values and 
#  then get a scatter plot 
#  of the x and residual 
#  values, we want to see 
#  the points all over the 
#  scatter plot.
res_vals <- L2 - 
       ( 13.81 + 1.27*L1)
plot( L1, res_vals,
      main="Residuals")