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Tuesday, February 23, 2010

A Regression Project : Help

I'm planning a unit for Algebra 2 with Trig called "Function Transformations and Regressions." I'm all set with the transformations part, but I am trying to plan something interesting for the 3 to 4 days of regression analysis. My idea is to give the children a choice of relationships for which they will collect data, graph scatterplots, decide the best model, perform a regression. Then use the function they get to gain insight into the type of relationship and make preditions. Ideally they will present their findings to the group but I don't know if we will have time for that. Also, I'm in the annoying situation of needing to teach them how to do regressions on a TI, but that makes sharing their results very difficult.

I'd like to provide opportunities to explore data that kids might actually be interested in. I'm looking for any more brilliant ideas out there. Ideally where the data is not too difficult to obtain within a 43-minute class period, either by measuring or because it's available online and you can provide a link. (What I'm not looking for, please, pretty please, I beg you, is "SWINE FLU!". The growth and decline of influenza, while interesting, is not appropriate for my purposes. I mean what is that - quadratic growth, followed by linear decline, followed by exponential decay? Piecewise functions are beyond the scope, here.)

This is the best of what I have so far:
So, come on. Who's holding?

44 comments:

  1. A teacher at my school uses the pseudoscience of "biorhythms." Kids can then find their own and follow it up with keeping track of "good days" and "bad days." To model sinusoidal curves.

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  2. Percentage of the moon illuminated vs. calendar day. [data]
    Duration of a plane flight v. miles traveled. [data]

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  3. The % of the moon data is just the sinusoid I've been looking for. Thanks.

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  4. With regards to sharing - Can you have the kids do screen captures and put in an electronic document to share?

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  5. There is a way to upload lists, graphs, functions, et. al. from a TI to a computer with a cable, but bleah. You have to have the special proprietary TI software installed on the computers, have enough cables, the calculators have to have fresh batteries... Just thinking about it gives me a headache.

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  6. I hear that! I've liked TI Smartview, but I got it for free, and I see that it's $156. Bleah.

    In my stat class, I've started asking them to do these things in Excel instead of on the TI.

    I use minutes of daylight in trig class. [Data is here.] I'll email you the worksheet I use, in case it's any use to you.

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  7. Sunrise/sunset times. The available data might be "too accurate" for your taste. I had kids record data one year, but I didn't keep up with it well enough and we had to fill in with newspaper stuff.

    Anyway, it came out pretty nice, and we talked about daylight savings (a transformation!) and latitude.

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  8. True! We've been working on having the software installed on all the computers in math classerooms. Next up the entire school :)
    Do you have access to an ELMO or other document reader? We sometimes have the students use it to show their data.

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  9. Another thing about sunset is that kids can decide if they want to hang on to hh:mm (for ease of communication) or instead go for minutes since midnight (for ease of functional notation).

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  10. Just FYI: the airline miles thing didn't work well when I collected my own data... I'd just try it yourself before doing it.

    An idea related to that, that I had this year (but didn't get to do) was going to be called something like: "FORREST GUMP, SLOW DOWN AND WALK"

    1. Have students go on Google Maps and plot WALKING directions from the school to like 25 destinations -- maybe 1/3 near and 1/3 in the state and 1/3 far. Disneyland. The local pizzaria they love. Mt. Rushmore. The state capital. Etc. Then they plot the DISTANCE vs. TRAVEL TIME.

    Talk about why the data is linear, what the slope means, what that means Google is assuming about walkers, what a proper domain is for that function, what doesn't fit the pattern, what's a good way to graph all these different distances (feet vs. miles) etc.

    DANG. I want to write this lesson up now.

    Sam

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  11. If you want a low-tech solution, and you own a webcam, you could always put the TI in front of the webcam and project it onto your IWB.

    Alternatively, when we bought a batch of TIs, they came with an emulator program which lets you control a fake calculator with mouse clicks / board pen. Your HoD might have one.

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  12. Also, they can find data for Moore's Law!

    http://samjshah.com/2009/02/24/moores-law/

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  13. Force vs. displacement of a spring?

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  14. Potentially exponential (or maybe logistic if resources are running out?) - world or US population. The US page has a link to historical population estimates. I used the US data for a logistic growth regression as part of a project.

    As part of a different project, I have students model Olympic speeds or distances with a linear regression (speeds getting faster with time). It's often interesting to compare men's and women's regression lines for the same sport.

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  15. Oh, and this is really not what you're looking for, but I've always thought it might help to generate data that is contrived to fit a simple linear model exactly. Generate data by picking points on a line, and then adding something random (which would ideally follow a normal distribution, but whatever--I haven't really thought about this).

    Then you can have people generate data and give it to someone else, who is supposed to estimate the original line (and possibly variance).

    They can see how accuracy varies with the variance, and with how many data points they get. Again, not a real application like you want, but possibly neat, and is an explicit demonstration of the 'model' we're using for where all of the real data come from.

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  16. You can look at tidal tables and graph time vs height of tide.

    Here is what I do with my students

    1. Using the internet, students need to find data on tide levels at 2 different locations in Canada. Go to a search engine and search for Tide Tables. Look for Canadian Tide Tables
    ➢ Need to find data that is sinusoidal (This is important. Not all tidal data is sinusoidal)
    ➢ Need to create a table of the data for each location for a 24 hour period
    ➢ Need to create a graph of the data
    ➢ Need to form a sinusoidal regression equation for the data of each location.

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  17. I don't exactly know how you'd gather the data, but I'm thinking (with my science teacher mind) that something like Wein's law may be useful. It states that the intensity of light or heat drops as 1 over the square of the distance from the light/heat source.

    Perhaps a thermometer and a nice roaring fire and taking temperature data and various distances out (not up)?

    Or if you had a photometer, then light intensity as you moved away from a flashlight.

    It would certainly explain patterns that they wouldn't even realize they see.

    I forget if this works the same for sound decibels or not, but it would then explain why you need to be close to the earbuds to hear the song.

    Anyway, just trying to think of high schooler friendly data.

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  18. You can also look at the average monthly temp. for a city in Canada, Northern Europe or Northern US. There is enough of fluctuation in this data over 12 months that it makes for good sinusoidal data.

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  19. @Sue, Scott, Terry Your ideas are related and good ones. Nothing wrong with having more than one option that turns out to be periodic. I don't have a year to collect data, though, I'll see if I can find charts online.

    @Bratts, Alex, I don't have a document camera. We have TI-Smartview but not on the student laptops, only on the teacher presentation computers. I suppose we could take a photos of the calculator screen? Kind of gross, but it might get the job done.

    @Sam I didn't think of collecting time/distance data from Google Maps. I like it. Is there a reason to specify walking directions? Would driving directions get the job done? I'm sure if I went and played with it I'd see your point, but I'm not getting it off the top of my head.

    @Jasmin we do have photometers and temperature probes we can plug into the calculators. I don't know if I want to get into it for this (mo' hardware, mo' problems) but thanks for reminding me.

    @David I don't really get what you're trying to describe, with data contrived to fit a line but also not. I think I need a more fleshed out lesson plan for that.

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  20. Kate, two things my kids have found intersting are the relationship between "dog years" and "human years" and another one that generated a lot of disucession was the relationship between birth year and life expectency. We found data from 1900 to present and had a good time discussing the data. One interesting thing I discovered was an article that stated that the current generation is the first generation which will have a lower life expectency than their parents. I think they were blaming it on obesity.

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  21. To add to Nick's population, my kids were fascinated by Breathing Earth last year. It's running on equations and all already, but at least could be an exercise in deriving them. (Okay, really, this probably motivates more of writing an equation given pieces of info, but I saw population and got excited.)

    PS to Sam. I didn't realize how far walking directions had been rolled out. They even stay away from interstates where you're not supposed to hitchhike. Assuming walking vs driving because walking is expected to be a more constant speed? (Though, the variation could be interesting.)

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  22. For sinusoidal I give them my natural gas bill from my house; it gives the volume used and is typically a good fit. I also have the death numbers for our province, also sinusoidal.

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  23. @Kate: Actually I kept on rewriting my comment and I had a #1, but the #2 had something about doing driving directions. I don't know why I took that out. I'm sure I had a good reason at the time.

    So do all the work for me, make up a great worksheet, and then post it on your blog for me to use. Thank you.

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  24. @Kate: Another idea... for those who like chemistry... atomic number vs. atomic mass.... linear...ISH.

    Sam

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  25. If you have the time and/or resources, I would have the kids generate data via experiment. You can check out some great ones here:

    http://jwelker.lps.org/labs/index.html

    Simpler ideas...

    Linear: Superball bounce height as a function of drop height. Why is the slope less than one? What does the slope mean?

    Inverse: Length vs. width for a paragraph of text. See Measuring Paragraphs from eeps.com

    Quadratic: Length of hanging slinky vs. number of hanging coils

    Inverse Square: Do this experiment (perf board version), but put the perf board on an overhead projector that's on a cart. Wheel the cart from one end of the room to the other and take data as you go.

    Linear Indirect: Mass of a bag of Starbust candies as a function of how many candies we've eaten. (I'd use Starbust since they are individually wrapped.)

    eeps.com has more fun data at their Data Zoo

    Re: Pendulum -- Be sure to plot length on y-axis and period on x-axis if you want a quadratic (even though this goes against traditional independent and dependent variable graphing kids learn in science class).

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  26. Sarah, that's a really great link! I will definitely use with my kids when we get to exponential and logistic growth this year!!

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  27. I usually opt for sneaky "value of education" types of graphs or social good stuff. Like years of education vs. income or life expectancy. Or we do a survey of time spent studying vs. test score. A few years ago after our kids got their reading level scores we plotted it versus a whole bunch of self reported stuff. Not surprisingly, reading level correlated most highly with time spent reading for fun. Students were astonished.

    Got this link from freetech4teachers today.

    Then there's gapminder data.

    Of course, who can forget the relationship between pirates and global warming.

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  28. Total resistance vs number of resistors in parallel (rational). Get an ohmmeter and a bunch of the same size resistor. String 'em up and measure.

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  29. There are a bunch of activities that were developed for teaching regression by Statistics Canada - they have been posted around the web in a few places:
    http://www.keypress.com/x2812.xml
    http://www.teacherweb.com/ON/Statistics/Math/photo1.aspx

    Two things you won't like about these: they are Canadian, and they tend to use Fathom (rather than TI) as the technology of choice.

    Still, I think they are worth a look. It has been a few years since I've used these activities, and I can't say for sure if there is something there that would be useful to you.

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  30. You can try the DASL website, they have a lot of data some of it linear.

    http://lib.stat.cmu.edu/DASL/

    Also, I might take a look at any AP Stats textbook. There are generally many good examples in the regression parts of those books.

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  31. Measuring reaction time: students create a chain by holding hands and pass a "hand squeeze" along it. The time to reach the last person is proportional to the length of the chain. The slope is the reaction time of one person.

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  32. @Dan Location's way important. Not sure why NYC wouldn't work, but when I tried flying out of SoDak last year.... Even with student interest wasn't worth it.

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  33. My data is your data:
    http://www.box.net/shared/zrjxkzpn9z

    A couple years back, I collected data with a class where we had CBR's and CBL's: attachments for a TI graphing calculator that let you collect data directly to the calculator. I've got balls bouncing (quadratic) water cooling (exponential) and fluorescent lights flickering (periodic). Enjoy!

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  34. 1) # of books read in a year vs. # of facebook friends.

    2) # of texts sent/day vs. most expensive cell phone bill

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  35. I have not used it, but this looks like a very interesting (and free) way to explore patterns in data:

    http://ccsl.mae.cornell.edu/eureqa

    Maybe it will get past the problems people were talking about with projecting their TI calculators.

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  36. Thanks, but, I don't think you're hearing me: I HAVE TO teach them to do it on a TI. I am NOT ALLOWED to do it a better way, unless it's in addition to doing it on a TI, which I don't have time for.

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  37. Tracker video analysis is a great way to generate data sets from any sort of video. You could use a pendulum to get sinusoid data, a falling object for quadratic, constant speed motion for linear. Oh, and for an easy TI calc connection, see if your science department has an CBL equipment. A sonic range finder, voltage probe, temperature probes all give great opportunities for the students to create their own.

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  38. Just want to second the Gapminder comment - this data is amazing, and students can choose which relationships to explore.

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  39. Linear: A science experiment takes a closed container and measures volume and temperature.
    10oC, 500 ml; 20oC, 520 ml; 30oC, 531 ml; 40oC, 558 ml
    Find the equation, ask what happens if the volume goes to zero? The temperature, of course, gets to absolute zero (actually this regression has it about 283oC but that's pretty close).

    For a quadratic, I like having them put a grid over a stop motion image (google images: dartfish) of a snowboarder or cliffjumper. Determine the coordinates of each image - center of gravity only, please.

    Then, here's a set of points. Figure out which regression gives you the highest value of R^2 -- 2nd catalog > Diagnostics ON

    x: -3, -2, -1, 0, 1, 2, 3
    y: 3, -8, -7, 0, 7, 8, -3

    Additional note for anyone using TI: In all of these, I have them put the equation into the y= list. Let them retype a couple times, then mention that
    LinReg (VARS, Y-Yars, Y1) will automatically put the equation into Y1 if it is empty. Use a different Y if Y1 isn't empty. Then you can have the points and the regression showing together. This stunt works with any of the regressions.

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  40. Crayola's Law?

    http://www.crayola.com/colorcensus/history/chronology.cfm

    http://www.weathersealed.com/wp-content/uploads/2010/01/crayons_big2.png

    and an argument between Ray Kurzweil and Kevin Kelly on extrapolations of exponential curves: http://www.kurzweilai.net/meme/frame.html?main=memelist.html?m=17%23664

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  41. Based on twitter output and conversations between you and Sam, I'm sensing there is some correlation between math blogging and comedy... now, if only we could come up with a way to measure how "funny" something is in a quantitative and objective way

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  42. a way to measure how "funny" something is in a quantitative and objective way

    HAH!

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  43. There are some nice sets of linear data in the CMU Statistics course.

    https://oli.web.cmu.edu/openlearning/

    I've tutored with their data on gestation period/longevity and year/Olympic records, but never used it in the classroom.

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