Let’s not forget that the main goal of our current unit is to choose an appropriate function to model whatever set of data we are looking at. Using that model will allow us to make predictions via interpolation and/or extrapolation.

So far we have one tool in our box and that is the coefficient of determination. We should never try and choose a model based only on this one value. As we will see tomorrow, end behavior is also an important consideration to make when choosing a function to model our data. We will also discuss techniques for finding functions when the data is not linear.

What does it determine? What it determines should help you remember how to calculate it. The coefficient of determination (r²) determines how much (what percent) of the original deviation from the mean line we have accounted for with our line of best fit. Subtracting the SS_res from the SS_dev tells you how much square area you have reduced the error by. Then by dividing by SS_dev will give your result as a percentage of the orignal deviation.

We did not discuss correlation today but you can handle that on your own in the reading. Suffice it to say that the (positive or negative) square root of the coefficient of determination is called the correlation coefficient and tells us how strongly the variables in the problem are associated.