Scatterplots and Regressions (page 2 of 4)

You may be asked about "correlation". Correlation can be used in at least two different ways: to refer to how well an equation matches the scatterplot, or to refer to the way in which the dots line up. If you're asked about "positive" or "negative" correlation, they're using the second definition, and they're asking if the dots line up with a positive or a negative slope, respectively. If you can't plausibly put a line through the dots, if the dots are just an amorphous cloud of specks, then there is probably no correlation.

• Tell whether the data graphed in the following scatterplots appear to have positive, negative, or no correlation.

 Plot A Plot B Plot C Plot D

Plot A: Low x-values correspond to high y-values, and high x-values correspond to low y-values. If I put a line through the dots, it would have a negative slope. This scatterplot shows a negative correlation.

Plot B: Low x-values correspond to low y-values, and high x-values correspond to high y-values. If I put a line through the dots, it would have a positive slope. This scatterplot shows a positive correlation.

Plot C: There doesn't seem to be any trend to the dots; they're just all over the place. This scatterplot shows no correlation. Copyright © Elizabeth Stapel 2005-2011 All Rights Reserved

Plot D: I might think that this plot shows a correlation, because I can clearly put a line through the dots. But the line would be horizontal, thus having a slope value of zero. These dots actually show that whatever is being measured on the x-axis has no bearing on whatever is being measured on the y-axis, because the value of x has no affect on the value of y. So even though I could draw a line through these points, this scatterplot still shows no correlation.

You may also be asked about "outliers", which are the dots that don't seem to fit with the rest of the dots. (There are more technical definitions of "outliers", but they will have to wait until you take statistics classes.) Maybe you dropped the crucible in chem lab, or maybe you should never have left your idiot lab partner alone with the Bunsen burner in the middle of the experiment. Whatever the cause, having outliers means you have points that don't line up with everything else.

• Identity any points that appear to be outliers.
• Most of the points seem to line up in a fairly straight line, but the dot at (6, 7) is way off to the side from the general trend-line of the points.

The outlier is the point at (6, 7)

Usually you'll be working with scatterplots where the dots line up in some sort of vaguely straight row. But you shouldn't expect everything to line up nice and neat, especially in "real life" (like, for instance, in a physics lab). And sometimes you'll need to pick a different sort of equation as a model, because the dots line up, but not in a straight line.

• Tell which sort of equation you think would best model the data in the following scatterplots, and why.

• Graph A: The dots look like they line up fairly straight, so a linear model would probably work well.

Graph B: The dots here do line up, but as more of a curvy line. A quadratic model might work better.

Graph C: The dots are very close to the x-axis, and then they shoot up, so an exponential or power-function model might work better here.

In general, expect only to need to recognize linear (straight-line) versus quadratic (curvy-line) models, and never anything that you haven't already covered in class. For instance, if you haven't done logs yet, you won't be expected to recognize the need for a logarithmic model for a given scatterplot. The next lesson explains how to define these models, called "regressions".

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 Cite this article as: Stapel, Elizabeth. "Scatterplots and Regressions." Purplemath. Available from     http://www.purplemath.com/modules/scattreg2.htm. Accessed [Date] [Month] 2016

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