# d. The coefficient of determination is 83.0 %

#### karush

##### Well-known member
The coefficient of determination is 83.0 \%.
Provide an interpretation of this value.
$\begin{array}{rrrr} x & y \\ 12.17 & 1.88 \\ 11.70 & 1.82 \\ 11.63 & 1.77 \\ 12.27 & 1.93 \\ 12,03 & 1.83 \\ 11.60 & 1.77 \\ 12.15 & 1.83 \\ 11.72 & 1.83 \\ 11.30 & 1.70 \end{array}$

here is my desmos plot and I can see that R^2 is $83.0\%$
but after looking at some examples I don't see how it is derived

However, the interpretation of this is
of the variability in y is explained by the least-squares regression line.

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#### karush

##### Well-known member
ok I think we are supposed to use this
$r= \dfrac{SS_{xy}}{\sqrt{SS_{xx}SS_{yy}}}$

not sure what S is