How do you calculate r squared by hand?
Assuming this is a general question and not a reference to some undeclared statistical equation,
and assuming you know how to multiply two numbers together by hand,
For example if
However I suspect you had some specific statistical relationship in mind; please resubmit with explicit references if this is the case.
simply the square of the value of the residuals. The residual value is difference between the obtained y-value and the expected y-value. The expected y-value is the calculated value from the equation of line/plane.
For example, for a system with 1 unknown parameter/variable x, the calculated y-value would be the sum of
For a system with 2 unknown parameters/variables,
And in general,