-aux.05 coefficient of determination is 83.0 %

In summary, the -aux.05 coefficient of determination is a statistical measure that represents the proportion of the variation in one variable that can be explained or predicted by another variable. It is calculated by taking the square of the Pearson correlation coefficient (r) between two variables, with values ranging from 0 to 1. A value above 0.7 is considered a strong relationship, while a value below 0.3 is considered a weak relationship. However, it should be interpreted in conjunction with other statistical tests and analyses. Factors such as sample size, type of relationship, and outliers can affect this measure. It is commonly used in research to assess the strength of relationships and predictive power of models, but should be used in conjunction with other
  • #1
karush
Gold Member
MHB
3,269
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:
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  • #2
ok I think we are supposed to use this
$r= \dfrac{SS_{xy}}{\sqrt{SS_{xx}SS_{yy}}}$

not sure what S is
 
  • #3
.
 
  • #4

1. What does the -aux.05 coefficient of determination represent?

The -aux.05 coefficient of determination, also known as R-squared, represents the proportion of variation in the dependent variable that is explained by the independent variable(s) in a statistical model. It is a measure of how well the model fits the data.

2. How is the -aux.05 coefficient of determination calculated?

The -aux.05 coefficient of determination is calculated by taking the sum of squared errors (SSE) and dividing it by the total sum of squares (SST). It is then subtracted from 1 to get the proportion of variation explained by the model.

3. What is considered a good -aux.05 coefficient of determination?

The -aux.05 coefficient of determination can range from 0 to 1, with a higher value indicating a better fit of the model to the data. Generally, a value above 0.7 is considered a good fit, but this can vary depending on the specific context and field of study.

4. Can the -aux.05 coefficient of determination be negative?

No, the -aux.05 coefficient of determination cannot be negative. It is always between 0 and 1, with 0 indicating that the model does not explain any of the variation in the data and 1 indicating that the model perfectly fits the data.

5. What are the limitations of using the -aux.05 coefficient of determination?

The -aux.05 coefficient of determination only measures the linear relationship between the independent and dependent variables and does not account for other factors that may influence the data. It can also be affected by outliers and can be misleading if used with a small sample size.

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