-aux.05 coefficient of determination is 83.0 %

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Discussion Overview

The discussion revolves around the interpretation of the coefficient of determination, specifically a value of 83.0%. Participants are exploring how this value relates to the variability in a dataset represented by a set of x and y values, as well as the calculation methods involved.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant states that the coefficient of determination is 83.0% and provides a preliminary interpretation regarding the variability in y explained by the regression line.
  • Another participant suggests a formula for calculating the correlation coefficient, indicating uncertainty about the meaning of the symbols used in the formula.
  • A participant expresses a lack of clarity on how the coefficient of determination is derived from the provided data.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the derivation of the coefficient of determination or the interpretation of its value, and there are indications of uncertainty regarding the calculation methods.

Contextual Notes

There are unresolved questions about the definitions of terms used in the calculations and the steps required to derive the coefficient of determination from the dataset.

karush
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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.
nw5desmos.png
 
Last edited:
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ok I think we are supposed to use this
$r= \dfrac{SS_{xy}}{\sqrt{SS_{xx}SS_{yy}}}$

not sure what S is
 
.