Sunday – a quiet evening before President’s Day – checking out twitter – not looking for trouble – and then,
Wait..what’s this? Standard Deviation? It was my birthday this past Saturday, and the Desmos folks knew exactly what to get me as a present. Abandon all plans, it’s time to play. A lesson I picked up from Daren Starnes (of The Practice of Statistics fame) is a favorite of mine when looking at scatterplots. In the past, Fathom had been the tool of choice, but now it’s time to fly with Desmos. There are a few nuggets from AP Statistics here, and efforts to build conceptual understanding.
CORRELATION, LSRL’S AND STANDARD DEVIATION
Click the icon to the right to open a Desmos document, which contains a table of data from The Practice of Statistics. In you are playing along at home, this data set comes from page 194 of TPS5e and shows the body mess and resting metabolic rate of 12 adult female subjects. One of the points is “moveable” – find the ghosted point, give it a drag, and observe the change in the LSRL (least-squares regression line) – explore changes and think about what it means to be an “influential” point.
Next, click the “Means” folder to activate it. Here, we are given a vertical line and horizontal line, representing the means of the explanatory (x) and response (y) variables. Note the intersection of these lines. Having AP students buy into the importance of the (x-bar, y-bar) point in regression beyond a memorized fact is tricky in this unit. Drag the point, play, and hopefully we can develop the idea that this landmark point always lies on the LSRL.
Another “fact” from this unit which can easily wind up in the “just memorize it” bin is this formula which brings together slope, correlation, and standard deviation:
The formula is given on the exam, with b1 acting as the slope, so even memorizing it isn’t required, but we can develop a “feel” for the formula by looking at its components.
Click the “Means plus Std Devs” Folder and two new lines appear. we have moved one standard deviation in each direction for the x and y variables. Note that the intersection of these new lines is no longer on the LSRL. But it’s pretty close…seems like there is something going on here.
Ask students to play with the moveable point, and observe how close the rise comes to the intersection point. Can it ever reach the intersection? Can we ever over-shoot it? In the “Rise Over Run” folder, we can then verify that the slope of the LSRL can be found by taking a “rise” of one standard deviation of y, dividing by a “run” of one standard deviation of x, and multiplying by the correlation coefficient, r.
There’s other great stuff happening in the Desmos universe as well.
1. This summer brings the 4th edition of Twitter Math Camp, to be held at Harvey Mudd College in California. I’m thrilled to have latched onto a team leading a morning session on Desmos. Consider coming out for the free PD event, and join myself, Michael Fenton, Jed Butler, and Glenn Waddell for what promise to be awesome mornings. To be honest, I feel the Ringo of this crew….
2. Can’t make it to the west coast this summer? Join me at the ISTE conference in Philadelphia, where I will present a learning session: “Rethink Math Class with the Desmos Graphing Calculator“. Bring your own device and join in the fun!
3. Are you new to the world of Desmos? Michael Fenton has organized an outstanding series of challenges, with 3 difficulty levels, to help you learn by doing. Try them out – they promise to get you think about how you and your students approach relationships.
4. Merry GIFSmos everybody! The team at Desmos has developed GIFSmos to let you build your own animated gifs from Desmos files. EDIT – as Eli noted in the comments, credit for GIFSmos goes to Chris Lusto. Thanks for being so awesome, Chris!