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### 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/
```
Associated Topics:
High School Statistics

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