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/
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