
# PROBLEM WITH ABLINE

# I have a question about a seemingly imprecise abline figure which I have
come accross now a few times.
# After reading variables a and b...
a<-c(3729,1796,1956,5177,3201,3138,4265,3042,3745,2060,5713,6811,4184,1221,4700,3171,8913,5565,5500,2428,4841,10428,11197,5946,2783,4842)
b<-c(7,3.4,4.8,11.2,7,5,8.2,6.2,7.4,7.4,18.4,13.8,8.8,3.6,7.2,8.8,23.2,11.8,10.4,5.4,13.7,26.4,27.8,12.8,6.2,15.4)
# ... I do a simple linear regression...
model<-lm(a~b)
summary(model)
# and plot it.
plot(a~b)
abline(model)
# abline drawn with the parameters intercept and slope taken from
summary(model) yield exactly the same.
abline(767.59,356.9)
predict(model,list(b=10))
# At b=10, the predicted value of a is 4336.543.
# Now my puzzling question comes: if I deduce the value of variable a from
b=10 from the already created figure,
# I conclude that a is about 4000 and clearly not something that even comes
close to 4300.

# If I plot only a small part of the regression, the line looks much better
although still there is a gap
# between what I observe in the figure and what is the calculated
prediction.
plot(a~b,xlim=c(10,12),ylim=c(4000,4500))
abline(model)
# If I do the prediction by hand
# from the regression results (summary(model)) then the same figure as the
calculated prediction is the result.
# My preliminar conclusion is that the figure is imprecise and that the
calculations are correct.

# So my QUESTION is: is abline imprecise or am I making errors?


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