Scatterplots and Regressions (page 1 of 4)

Real life is messy, so it is expected that measurements taken from real life will be messy as well. When you graph measurements of real life, it is expected that the dots won't line up exactly in a nice neat line, but will instead form a scattering of dots which, at best, might suggest a nice neat line. These dots are called a scatterplot.

• Create a scatterplot from the following data:
• (1, 49), (3, 51), (4, 52), (6, 52),
(6, 53), (7, 53), (8, 54), (11, 56),
(12, 56), (14, 57), (14, 58),
(17, 59), (18, 59), (20, 60), (20, 61)

One of the first things I have to do when graphing these points is figure out what my axis scale values are going to be. If I try doing an axis system with the "standard" –10 to 10 values, none of the above points will even show up on my graph. As is common with these sorts of data sets, all the x- and y-values are positive, so I only really need scales for the first quadrant. The y-values are much larger than the x-values, but instead of squeezing all the y-values together, I'll spread them out (so I can see them better) by using an interrupted scale.

The little "hicky-bob" at the bottom of my y-axis above shows that I've skipped some of the scale values. For some reason, this broken-axis notation seems almost never to be taught in schools, though it is very commonly used in "the real world". If you read financial journals, you're very likely to see many graphs with this sort of axis notation. If you use this notation in your homework, don't be surprised if you have to explain it to your instructor.

You will often need to adjust your WINDOW settings in order to have all your data points show up on the screen. I used window settings of 0 < X < 25 with an X-scale of 5 and 45 < Y < 65 with a Y-scale of 5 for the above graph.

When you're done with the scatterplot, don't forget to turn the STATPLOT "off", or the parameters for the statistics graphing could mess with your regular graphing utility.

I will give you fair warning now: It has become fashionable to insert the topic of scatterplots and regressions into algebra and other non-statistics classes, and to require students to use a graphing calculator to answer questions. While they may give you the slope formula and the Quadratic Formula and all sorts of other stuff on the test (even though you should have memorized them), they will NOT give you help with your calculator. They often don't seem to care if you've learned the math, but you had gosh-darned better know your calculator! So pull out your owners manual, or go to the manufacturer's web site, or search online, or get together with a friend NOW, because if you're doing this stuff in class, you ARE going to have to know it, and know it well, on the test.

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

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