# How do you calculate r squared by hand?

##### 2 Answers

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,

then

For example if

then

**However** I suspect you had some specific statistical relationship in mind; please resubmit with explicit references if this is the case.

#### Explanation:

The

or

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,

Furthermore, the