To determine the correlation coefficient of the given data, we first need to understand the relationship between the two variables, x and y. The correlation coefficient (often denoted as \( r \)) measures the strength and direction of a linear relationship between two variables. A value close to 1 or -1 indicates a strong linear relationship, while a value close to 0 indicates a weak linear relationship.
Based on the x and y values provided:
- \( x: 1, 3, 5, 7, 9 \)
- \( y: 13, 43, 51, 76, 81 \)
We can perform a calculation to find the correlation coefficient.
- The correlation coefficient \( r \) is calculated using the formula:
\[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} \]
- After calculating the required sums, we would get \( r \approx 0.97300135 \).
Since the correlation coefficient is approximately 0.973, it suggests a very strong positive linear relationship between the variables \( x \) and \( y \).
Thus, the correct response from the options provided is:
0.97300135; strong