HumanMemoryTheDiscovery

=__Human Memory: The Discovery__ Authors: Mai Okimoto, Kelly Robinson, Cheryl Chau, Bryan Choi; Group #3= = =

The What:
 * **Days (x)** || 1 || 2 || 3 || 4 || 5 || 6 ||
 * **Memory (y)** || 44 || 22 || 13 || 7 || 5 || 3 ||
 * **Memory (y)** || 44 || 22 || 13 || 7 || 5 || 3 ||

In this investigation, we looked to discover the fundamentals of human memory. The first observation made about the data was that it was an exponential function.

Some background information on human memory: There are 3 different stores in our brain... 3 different types of memory; sensory memory, short-term memory, and long-term memory. The sensory memory comes from eyes, ears, and touches. Whatever information enters the sensory store, through the three ways mentioned before. If it's something needed to be kept in the brain, it goes to the short-term memory. Information that is stored in memory, but used multiple times is sent to the lont-term memory store. Long-term memory store has a lot more capacity to store information compared to short-term memory store. more info on: http://human-factors.arc.nasa.gov/cognition/tutorials/ModelOf/Knowmore1.html

Some questions we came up were... How is human memory tested... is there a particular standarized test? What is considered short-term and long-term... is there a distinct line between the two memory storages?

The How: "Well, compared to power and log, the r^2 for exponential is closer to... uh... the um... I don't know, bite me. Okay, okay, I put power as log and after that I put it... somwhere... Oh I put it in the calculator as the correlation coefficient." -Kelly aka: By briefly comparing the R^2 of the data for ExpReg, PwrReg and LnReg and by seeing which correlation coefficient was closet to one, we were able to determine which line would fit the data best, which turned out to be ExpReg. i) Determine a common ratio by division Average of these numbers --> B = 0.5884 ii) Let t=0 represent the time for the first item in the data set... So if for the 0th term, 44/0.5884= 74.779 = a This gives us the final equation of: **y= 74.799 x 0.5884^x**
 * PART 1**
 * 1) 1. Find an exponential model by hand:
 * 1) 2. Using ExpReg on your calculator. Also check your residual plot!

=74.799 x 0.5884^x and by ExpReg, the function we obtained was **y**= 66.566 x 0.59^x. In our opinion, the ExpReg line fits the data better as compared to the hand-obtained line. This is because after comparing the residual plots, we determined that ExpReg's residual plot was better. This is because ExpReg's residual plot has an equal amount of points above and below the x-axis. In general they are also closer to the x-axis. On the other hand in the by-hand residual plot, all but one of the points are underneath the x-axis, showing an unequal distribution. These points are furthur away from the x-axis in general. Even though the by-hand equation goes straight through the first point, it is too far off the other points to be considered reasonable. Therefore, the line **y=66.566 x 0.59^x** is a better fit for the data (ExpReg line).
 * 3.** By hand, the function we obtained was **y**


 * 4.** By observing the exponential line of the data, we can predict that the person will steadily loose less and less memory, and will proabably hit a point after a certain number of days where they don't forget anything else. However, the amount of information they retain is little. If you apply this concept to real life, it's quite accurate. Imagine studying for a biology test. You read the chapter on the same day of the test (only once) and you retain about half of the information (since you didn't study it repeatedly). After taking the test, the next day you already forget about half of the stuff you learned, because that information had been retained by your short-term memory and the moment you finished the test you forgot it. Then slowly over the next few days you begin to forget certain terms and concepts, until finally you hit a time period where you only remember a few facts that stuck out to you. That's what's so fascinating about this data, it is a mathmetical representation of our studying lives.It would be interesting to see data on a person who studied repeatedly, in order to compare to this data.

We tried three different ways to linearize the data. We first tried (x, y^2) We then tried (logx, logy) Finally, we were able to linearize the data with **(x, logy)**
 * 5.
 * 1) 6. See number 3 above.**
 * PART 2: Linearizing Data**