What is the total sum of squares?
The total sum of squares (also written
As written above, if we have
Sometimes we account for the average of all the data values (that is,
This version of total sum of squares is the corrected total sum of squares, and if we need to clarify that this is different than the uncorrected version, we can denote this something like
e.g. Suppose I tell you I have three numbers whose average is 4. How many of those numbers do I have to tell you in order for you to know all of them? The answer is "one less than all 3"; because you know the average, you can use the first two numbers I give you to figure out the third number by using
If the first two numbers are 3 and 4, you know the last number is 5. If I give you 2 and 4, you know the last number is 6. In this sense, one of the three data points is not free to vary. And since we are using the (fixed) average