LAB10

Shannon's entropy factors in probability while Hartley does not. Shannon's entropy is basically asking how many yes or no questions does it take to get to the root of the question. It factors in probability unlike Hartley's, though through some research on wikipedia I found that the two are very closely related and have joint theorems (entitled the Shannon-Hartley theorem) which ironically is what I've been studying in my Physics of Sound course, as it relates to the Nyquist theorem, which states how much information could travel through a telegram.

What I Learned...

There wasn't a whole lot that I learned about linear regression. I have always been a math sort of guy. The first time I played around with linear regression was my freshmen year of high school (algebra 2/trig). This is where I learned that linear regression is a method of seeing "how correlated" the data between the x and y data points, or the dependent and independent variables. There is a function on any TI-83 calculator which will run linear regression for you, including the r and r^2 values, which is how I originally performed the task. When graphing data points the data will rarely line up perfectly linearly. So linear regression tell you the best fit line that runs through the data (aka the slope, y-intercept, and the r value which is basically a percentage fit). R comes out say as .94 which means that the data points match a line with 94% accuracy or fit to the line.
What I did learn from this lab was a lot of about excel . I had never used excel before at least to this extent. It is extremely useful for doing many calculations at once, and I'm sure I'll being using it more in the future solely for convenience. It's very interesting seeing the relationship between two variables, and then having a relatively simple tool and set of equations that will tell you how likely it is that the data relates to each other, because the charts are basically scatter plots, but if the data relates then it will form a positive or negative relationship. It doesn't have to be linear either, there is of course every type of regression such as quadratic regression, exponential regression (probably the most useful out of any of them, in my experiences), and linear regression. Another very useful tool aside from showing there is a relationship is predicting future behavior because of it. If linear regression shows strong correlation you can predict fairly accurately population growths or bacteria growths (probably exponential regression though). For the example in the lab with shoe size in relation to height, you could fairly accurately predict how big the foot of someone who is, say, 7 feet tall.
However, as with any inductive modeling you can never be for certain, past events do not always relate to future events with perfect accuracy, which is why science is full of theories and not facts.