For this new section that we have started with exponential and power graphs, stat plots, regression, and other things there is a lot of definitions, equations and mathematical models that must be remembered to be successful. For this blog post I am going to hopefully cover a lot of that stuff.

First off: the goal of this section is to find a mathematical model the will fit a given set of data and decided what type will fit it the best. There are all kinds of equations that could work but the question is which one fits the data the best. The way to do this, if you’re allowed to use your calculator, is to plug the data into your calculator and try to fit a line to it. You do this by going to stat, calculate and then find the equation that gives an “r” value that is closest to 1. This number, “r”, is called the correlation coefficient. It tells how close the model fits the data. The goal is to find the one with the r value that is closest to 1. The r^2 value that some regression equations give is called the coefficient of determination. This is used because its units are the squares of the y-units.

The process behind finding the r value is very complicated (in my opinion.) first you must find the residuals or the vertical distance that each point is from the regression line. This is tedious work but is necessary if your not able to use a calculator (which does it all for you.) then you square each value to make sure they are all wither positive, or zero. Then you add them all together to get the SSres, or the sum of the squares of the residuals. Another process is to find the mean value (add all up and divide by number of terms) and then find the deviations of the mean, then square them all. When you add these up you get the SSdev, or the sum of the squares of the deviations. Most of the time the SSres will be much smaller because the line tends to fit the data a lot better than the horizontal line given by the SSdev.

The coefficient of determination is complicated as well. It is: r^2 = (SSdev-SSres)/SSdev.

*all of this information can be found between pages 325 – 330 in the book. It also gives diagrams that help in the explanation*