-aux.05 coefficient of determination is 83.0 %

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SUMMARY

The coefficient of determination, denoted as R², is calculated to be 83.0% based on the provided dataset. This indicates that 83.0% of the variability in the dependent variable (y) can be explained by the independent variable (x) using a least-squares regression line. The formula for calculating the correlation coefficient (r) is given as r = SS_xy / √(SS_xx * SS_yy), where SS represents the sum of squares. Understanding this relationship is crucial for interpreting regression analysis results effectively.

PREREQUISITES
  • Understanding of least-squares regression analysis
  • Familiarity with the concept of the coefficient of determination (R²)
  • Knowledge of statistical terms such as sum of squares (SS_xy, SS_xx, SS_yy)
  • Basic proficiency in using statistical software or tools for data analysis
NEXT STEPS
  • Learn how to calculate sum of squares in regression analysis
  • Explore the interpretation of R² in different contexts
  • Study the application of regression analysis using statistical software like R or Python
  • Investigate the assumptions and limitations of least-squares regression
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Data analysts, statisticians, and researchers interested in understanding regression analysis and its implications in data interpretation.

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
 
.