How do you calculate r squared by hand?

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jbaekk7q · Accepted Answer

Step 1Assuming 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 r squared (often written             r      2       is simply      r    ×    r   for whatever the value of r isFor example if       r    =    16  then r squared (or             r      2       )       =    16    ×    16    =    256  However I suspect you had some specific statistical relationship in mind; please resubmit with explicit references if this is the case.

Amira Serrano · Accepted Answer

Step 1The       S          S              E        r        r             or the sum of squares residuals is:      ∑                  y        i        2              -          B      0        ∑          y      i        -          B      1        ∑          x      i              y      i      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             B      0                    and                    B      1        x   (i.e.       Y    =          B      0        +          B      1        x   )For a system with 2 unknown parameters/variables,             x      1       and             x      2       , (i.e.       Y    =          B      0        +          B      1              x      1        +          B      2              x      2       ).And in general,       Y    =          B      0        +          B      1              x      1        +          B      2              x      2        +          B      3              x      3        +          B      4              x      4        +    ...    +          B      n              x      n      Furthermore, the       S          S              T        o        t              =    ∑                  y        i        2              -                                        (            ∑                          y              i                        )                    2                            n             where n is the number of observations or trials.

How do you calculate r squared by hand?

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