# Math Help - coefficient of determination

1. ## coefficient of determination

Hi, I am trying to work out the coefficient of determination of r. I am able to compute it using the spreadsheet but I don’t know how to work it out manually. My data is as follows:
X – 0.01; 0.00; 0.01; 0.02; 0.03; 0.04; 0.05
Y - ; 200; 2000; 4100; 6200; 8300; 10,300

The coefficient of determination generated by excel was 1.

2. Originally Posted by cmgames
Hi, I am trying to work out the coefficient of determination of r. I am able to compute it using the spreadsheet but I don’t know how to work it out manually. My data is as follows:
X – 0.01; 0.00; 0.01; 0.02; 0.03; 0.04; 0.05
Y - ; 200; 2000; 4100; 6200; 8300; 10,300

The coefficient of determination generated by excel was 1.
$r = \frac{N \sum_{i = 1}^Nx_iy_i - \left ( \sum_{i = 1}^N x_i \right ) \left ( \sum_{i = 1}^N y_i \right )}{\sqrt{N \left ( \sum_{i = 1}^N x_i^2 \right ) - \left ( \sum_{i = 1}^N x_i \right )^2} \sqrt{N \left ( \sum_{i = 1}^N y_i^2 \right ) - \left ( \sum_{i = 1}^N y_i \right )^2}}$
where N is the number of data points.

It isn't hard to do, but rather time consuming. And make sure if you are looking for $r$ or $r^2$.

-Dan

3. Originally Posted by cmgames
Hi, I am trying to work out the coefficient of determination of r. I am able to compute it using the spreadsheet but I don’t know how to work it out manually. My data is as follows:
X – 0.01; 0.00; 0.01; 0.02; 0.03; 0.04; 0.05
Y - ; 200; 2000; 4100; 6200; 8300; 10,300

The coefficient of determination generated by excel was 1.
Why are there different numbers of x's and y's?

Also if you have equal increments in the x's (I assume tha x is the
independent variable) then if the increments in the y's is not equal then
r will not be 1.

RonL