To find the correlation coefficient for the given data, we can use the formula for Pearson's correlation coefficient \( r \). However, since I can't compute it directly in this text, I can guide you through the interpretation based on typical calculations:
- Calculate the means of \( x \) and \( y \).
- Calculate the covariance of \( x \) and \( y \).
- Calculate the standard deviations of \( x \) and \( y \).
- Use the formula:
\[ r = \frac{\text{cov}(x, y)}{\sigma_x \sigma_y} \]
Given your data:
- In your example, it appears you've already been provided with a correlation coefficient (approximately -0.973) and the sign indicates a strong negative correlation.
A correlation coefficient close to -1 indicates a strong negative correlation, meaning as \( x \) increases, \( y \) tends to decrease. Conversely, a coefficient close to +1 indicates a strong positive correlation.
From the data provided:
- \( r = -0.97300135 \)
This indicates a strong negative correlation.
Therefore, the appropriate response is:
−0.97300135; strong negative