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To find the correlation coefficient \( r \) for this data set, we can use the fact that the correlation coefficient \( r \) is related to the coefficient of determination \( r^2 \) by the equation:

\[
r = \pm \sqrt{r^2}
\]

In the provided image, \( r^2 = 0.1681 \). Therefore, we take the square root of \( 0.1681 \) to calculate \( r \).

Let me do that now.The correlation coefficient \( r \) for this data set is approximately \( 0.41 \).

Would you like more details on this calculation or how it relates to the data set?

Here are 5 related questions:
1. What is the significance of the sign of \( r \) (positive or negative)?
2. How does the value of \( r^2 \) compare to \( r \) in terms of interpretation?
3. How would you interpret an \( r \) value of 0.41 in terms of strength of correlation?
4. How do you plot a trendline in Excel to find \( r^2 \)?
5. What would happen to \( r \) if \( r^2 \) were closer to 1?

**Tip:** The closer \( r^2 \) is to 1, the stronger the linear relationship between the variables.

You generate a scatter plot using Excel. You then have Excel plot the trend line and report the equation and the r^2 value. The regression equation is reported as y = -63.41x + 10.51 and the r^2 = 0.1681. What is the correlation coefficient for this data set?

Learn how to calculate the correlation coefficient (r) from the coefficient of determination (r^2) using the example where r^2 = 0.1681. Understand the relationship between r and r^2 in a linear regression equation. Suitable for high school students learning statistics.

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