Assignment #2
Understanding the various sum of squares
Obtain a regression line for you data by running the graphs program.
This is for understanding so you should estimate most of the numbers.  After you have obtained a printout with a regression draw lines from each data point to the regression line.  See the graphic below.

Estimat the length of each of the newly drawn lines.  Square each one and them add the square together.

For my data it looks like the first one is about .5.  The next about .25.   The next on is 0.  The next one looks about 1.25. and the last one about .85. 
So....
.5 X .5 = .25
.25 X .25 = .0625
0 X 0 =0
1.25 X 1.25 = 1.5625
.85 X .85 = .7225
When you add those numbers you get 2.285.  That is the sum of squares residual or error.

Now lets get the Total Sum of Squares.  In the graph above the lines are drawn from the mean of Y to the individual data points.  They are estimated to be.
2, 1, 0 2, and 1.  The are squared and summed.
2 X 2 =4
1 X 1 =1
0 X 0 =0
2 X 2 = 4
1 X 1 = 1
Those numbers added together are 10.  That is the Total Sum of Squares.
Now we need to get the Between Sum of Squares.  In the graph below lines are drawn from the mean of Y to the regression line for each person.  Notice that they are not drawn from the data points themselves.

These estimated lines are 1.9, 1.1, 0 .9 and 1.6 (estimated)
Soo......
1.9 X 1.9 = 3.61
1.1 X 1.1 = 1.21
0 X 0 = 0
.9 X .9 = .81
1.6 X 1.6 = 2.56
Those added together are 8.19.  That is the Between Sum of Squares

The correlation is obtained by dividing the Between-Sum-of-Squares by the Total-Sum-of-Squares and taking the square root of that result.  The correlation here is 8.19 (Between-Sum-of-Squares) divided by 10 (Total-Sum-of-Squares) = .819.  The square of that is .90.  Our correlation.