Correlation of a Scatterplot

Date: 02/04/99 at 16:34:23
From: Rebecca
Subject: Correlation of a Scatterplot (Algebra I)

Hi Dr. Math,

In a recent test we had to draw a scatterplot to represent the 
following: no correlation, no positive correlation, and no negative 
correlation. To represent no correlation, one of our students drew 8 
points that were horizontal. At first, we marked it wrong thinking that 
since we could draw a line through, the scatterplot would have some 
correlation. But then we said it definitely isn't a positive 
correlation, and it's not negative. Could you give this student a grade 
and a reason for it on his test?

Thanks,
Becky Bosco

Date: 02/04/99 at 17:20:03
From: Doctor Pat
Subject: Re: Correlation of a Scatterplot (Algebra I)

Give that kid an A. The correlation coefficient is a measure of how 
well the variation of one value (y or the dependent variable) can be 
predicted from the variation of another (x or the independent 
variable). Since y does not change, knowledge about x provides NO 
knowledge about y. Keep in mind also that this is a measure of a LINEAR 
relation only. Actually the correlation of her line is NOT zero, which 
is the slope of the line, but it is undefined. The problem is that the 
formula involves dividing by the product of the standard deviation of 
both variables. Since one of these is obviously zero, we have the 
classic divide-by-zero problem. 
 
If you plot the five points (-2,4), (-1,1), (0,0), (1,1), and (2,4), 
the points will obviously fall into a predictable (quadratic) pattern. 
The correlation coefficient will be zero (but defined), a very 
different situation.  
  
Hope this helps.

- Doctor Pat, The Math Forum
  http://mathforum.org/dr.math/