MHB -aux.05 coefficient of determination is 83.0 %

AI Thread Summary
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
Gold Member
MHB
Messages
3,240
Reaction score
5
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:
Mathematics news on Phys.org
ok I think we are supposed to use this
$r= \dfrac{SS_{xy}}{\sqrt{SS_{xx}SS_{yy}}}$

not sure what S is
 
.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top