Find the correlation coefficient, r, of the data described below.
A botanist at a university is studying oak trees and the acorns they produce. He collected several acorns from the same tree and measured them.
For each acorn, he recorded its volume (in cubic centimeters), x, and its weight (in grams), y.
Volume (in cubic centimeters)	Weight (in grams)
1.1	2.8
1.3	4.7
1.8	2.0
3.1	1.5
3.8	6.1
Round your answer to the nearest thousandth.
r=



To calculate the correlation coefficient \( r \), we need to use the formula:

\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n \sum x^2 - (\sum x)^2][n \sum y^2 - (\sum y)^2]}}
\]

Where:
- \( x \) is the volume of the acorns,
- \( y \) is the weight of the acorns,
- \( n \) is the number of data points.

The data is:
\[
x = [1.1, 1.3, 1.8, 3.1, 3.8]
\]
\[
y = [2.8, 4.7, 2.0, 1.5, 6.1]
\]

We will calculate the sums and sums of squares required for the formula:

- \( \sum x \)
- \( \sum y \)
- \( \sum xy \)
- \( \sum x^2 \)
- \( \sum y^2 \)

Let me perform the calculations.The correlation coefficient \( r \) for the given data is approximately 0.292 when rounded to the nearest thousandth.

Would you like further details on the steps, or do you have any other questions?

Here are 5 related questions:
1. What does a correlation coefficient of 0.292 indicate about the relationship between acorn volume and weight?
2. How do you interpret a positive versus a negative correlation coefficient?
3. How would the correlation change if the sample size were larger?
4. What are some limitations of using correlation to assess relationships in biological data?
5. How would you test for the statistical significance of this correlation?

**Tip:** A correlation coefficient near zero suggests a weak linear relationship, while values closer to -1 or 1 indicate stronger linear relationships.

Find the correlation coefficient, r, of the data described below.
A botanist at a university is studying oak trees and the acorns they produce. He collected several acorns from the same tree and measured them.
For each acorn, he recorded its volume (in cubic centimeters), x, and its weight (in grams), y.
Volume (in cubic centimeters)	Weight (in grams)
1.1	2.8
1.3	4.7
1.8	2.0
3.1	1.5
3.8	6.1
Round your answer to the nearest thousandth.
r=

Learn how to calculate the correlation coefficient (r) for acorn volume and weight data. This problem includes statistical analysis and the Pearson correlation coefficient formula, suitable for students in Grades 10-12.

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