MHB -aux.05 coefficient of determination is 83.0 %

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The coefficient of determination, R², is 83.0%, indicating that 83% of the variability in the dependent variable (y) can be explained by the independent variable (x) in the regression model. This suggests a strong correlation between x and y, meaning the regression line fits the data well. The discussion highlights confusion about how R² is calculated, specifically referencing the formula involving sums of squares (SS). Clarification on the meaning of "S" in this context is sought, indicating a need for further understanding of statistical concepts. Overall, the high R² value reflects a significant relationship between the variables analyzed.
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
 
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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
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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