At 21:10 14/06/01, you wrote:
>A friend of mine has asked for help with the following problem:
>
>Suppose a scatter diagram has perfect positive correlation and the graph is
>linear. Is there a proof that the equation of the line is y = a + bx?
Hi Paul (and list),
Its a tricky one to see exactly what you mean. I would guess that one
approach would be to calculate the predicted values, based on the equation
y = a + bx, and then plot the values of y against the predicted values,
based on the equation.
The plot would be a straight line, and the correlation (if you calculated
it) would be 1.00, showing that the equation gives perfect prediction of
the values of y in the data.
However, you are then (re) using the equation, and are stuck in a circular
argument, because proving that y = a + bx requires believing that y = a + bx.
Maybe that will help anyway,
JM
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Dr Jeremy Miles
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Phone: 01332 592090, Fax: 01332 593131, Mobile: 07941 228018
Inst. of Behavioural Sciences, Derby University, Derby, DE22 3HL, UK
http://ibs.derby.ac.uk/~jeremym / http://www.jeremymiles.co.uk
NOTE: After 1st August, 2001, Department of Health Sciences, University of
York, Heslington, York, YO10 5DD
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