https://file.aiquickdraw.com/mathbot/file/1730918865452cbc9gmfu.jpg

To find the correlation coefficient for the data in the table, we can use a statistical calculator or software to calculate the correlation coefficient (denoted as \( r \)) for the pairs of weight (\( x \)) and height (\( y \)) values.

The data pairs are:
- \( x \) (Weight): 8, 12, 18, 24, 30, 32, 35, 37, 40
- \( y \) (Height): 22, 23, 26, 30, 32, 33, 35, 36, 38

### Steps to Calculate the Correlation Coefficient \( r \):
1. Compute the mean of \( x \) values and the mean of \( y \) values.
2. Calculate the deviation of each \( x \) and \( y \) value from their respective means.
3. Find the product of these deviations for each data pair.
4. Calculate the square of each deviation for both \( x \) and \( y \).
5. Use the correlation formula:

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

After using technology or calculator to compute this, we get a correlation coefficient \( r \approx 0.997 \).

Thus, the correct answer is:
- **0.997**

Would you like a detailed breakdown of these calculations?

### Further Questions
1. What does a correlation coefficient close to 1 imply about the relationship between weight and height in this data?
2. How would you interpret a correlation coefficient of -0.503 in a similar context?
3. Can you identify any outliers in this data set based on the correlation coefficient?
4. How would the correlation coefficient change if there were an error in one of the data points?
5. Why is it important to verify the assumptions of linearity before relying on the correlation coefficient?

### Tip
Always interpret correlation in the context of the data. A high correlation does not imply causation but indicates a strong association between variables.

The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. Using technology, what is the correlation coefficient?

Learn how to calculate the correlation coefficient between weight and height measurements for a child over a two-year period. This statistical problem involves using the Pearson Correlation Coefficient formula to determine the strength and direction of the linear relationship between weight and height. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation