Sine function ...

And another type of function. When something has a pattern that REPEATS, like the giant Ferris wheel we modeled in class, we call it a PERIODIC function. Some of the most well known of these are the trig functions, sine (SIN), cosine (COS), and tangent (TAN). Here's a little review:

 So, that Ferris wheel (the Singapore Flyer) :  We drew a picture to model the situation, and then used cosines to figure out the height off the ground each minute for the 30 minutes it takes to go around the circle once:

 You have to put your calculator in DEGREE mode (push the [MODE] button) before doing this!

 And then, the regression to a SINE function works just the same as to a linear, exponential, or logistic function:

(1) Put the data into L1 and L2 using [STAT] EDIT
(2) Get the regression equation (this time it's [STAT] CALC "C")
(3) Put the equation in using [Y=].
(4) Turn on the StatPlot using [2nd] [Y=] and adjust your [WINDOW]
(5) Graph

Special note: For some reason, even though you put the calculator in DEGREE mode earlier, the SINE regression doesn't use degrees, it uses RADIANS. So to make the graph match up right, switch the mode back to RADIAN.

If you take a look at all the options under [STAT] CALC, you'll see we've only done a few of the very many functions available for calculating regression equations.

Logistics ...

Okay, so we've done linear, and we've done exponential. But there are a lot more functions to consider.

For instance, sometimes things start off growing really fast like an exponential function, but then things happen to slow down the growth. We talked in class about how the flu spreads exponentially, but then slows down and levels off when people start taking medicine. This is called a LOGISTIC function.

Here's what it looks like in action (re-creation of the game we played in class, in case you missed it) - each turn, each person that is already sick picks a random person to get them sick. But when the numbers start repeating themselves, people can't get sick AGAIN, so the growth slows down.

0.

 1.

 2.

 3.

 a little while later ...

We can do a regression on this type of function, just like with linear or exponential. The calculator steps are:

(1) Put data in, with [STAT] EDIT
(2) [STAT] CALC "B" (LOGISTIC)
(3) Turn on the StatPlot ([2nd] [Y=]), set the [WINDOW], and type the regression into [Y=]
(4) Graph