In a statistics study given that r=0.5 n =10 then £D power 2=??

In statistics, if you are given the correlation coefficient \( r = 0.5 \) and sample size \( n = 10 \), and if you're looking for \( R^2 \), this represents the **coefficient of determination**. The coefficient of determination is found by squaring the correlation coefficient \( r \).

\[
R^2 = r^2
\]

Given:
\[
r = 0.5
\]

Calculating \( R^2 \):
\[
R^2 = (0.5)^2 = 0.25
\]

Thus:
\[
R^2 = 0.25
\]

This means that 25% of the variability in the dependent variable is explained by the independent variable in this study.

Would you like further details, or do you have any additional questions?

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Here are some related questions for further exploration:

1. How is the coefficient of determination interpreted in regression analysis?
2. What does a higher or lower \( R^2 \) value imply about the strength of a relationship?
3. How do you test the significance of the correlation coefficient \( r \)?
4. How does the sample size \( n \) impact the reliability of \( r \) and \( R^2 \)?
5. What are the assumptions underlying the use of the correlation coefficient?

**Tip:** Remember, the \( R^2 \) value does not imply causation—only association strength between variables.

In a statistics study given that r=0.5 n =10 then £D power 2=?

Learn how to calculate the coefficient of determination (R^2) when the correlation coefficient (r) is 0.5 and the sample size (n) is 10. This solution explains the formula R^2 = r^2, and provides insights into interpreting R^2 in statistics. Suitable for students in Grades 10-12.

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