To calculate the correlation coefficient for the given data points, we first need to have the pairs of \( x \) and \( y \) values. The values provided appear to be:
- \( x \): [1, 3, 5, 7, 9]
- \( y \): [13, 43, 51, 76, 81]
The correlation coefficient (typically denoted as \( r \)) measures the strength and direction of a linear relationship between two variables. The value of \( r \) ranges from -1 to 1, where:
- \( r = 1 \) indicates a perfect positive linear relationship,
- \( r = -1 \) indicates a perfect negative linear relationship,
- \( r = 0 \) indicates no linear correlation.
Given that you mentioned a positive correlation and a non-linear relationship, we should focus on the fact that the correlation coefficient calculated will help us determine how strong this correlation is.
Correlation Coefficient Calculation
Using a tool or formula to calculate the correlation coefficient between these two sets of numbers, you would get a coefficient around \( r \approx 0.973 \).
Interpretation
- A correlation of \( 0.973 \) indicates a strong positive correlation.
- Even if the relationship is non-linear, the strength of the correlation coefficient itself suggests that the values of \( x \) are strongly associated with the values of \( y \) in a positive sense.
Correct Answer
From the options you provided, the correct response is:
0.97300135; strong
This indicates a strong positive correlation.