To calculate the correlation coefficient (Pearson's r) for the provided data points, you can use the formula or a calculator. However, from your description and the responses given, it seems that you are primarily interested in identifying whether the correlation is strong or weak and whether it is positive or negative.
The data you provided correlates \( x \) values \( [1, 3, 5, 7, 9] \) with \( y \) values \( [13, 43, 51, 76, 81] \). Since you mentioned that there is a positive correlation, we can analyze the likely correlation coefficient given the context.
Interpretation of the Possible Responses:
- A correlation coefficient (r) close to 1 indicates a strong positive correlation.
- A correlation coefficient (r) close to -1 indicates a strong negative correlation.
- A correlation coefficient (r) around 0 indicates little to no correlation.
The value \( 0.97300135 \) suggests a strong positive correlation, which falls into the range of \( 0.9 \) to \( 1.0 \) for strong correlations.
Given this information, the correct response would be:
0.97300135; strong
If you are using statistical software or a calculator, you would calculate the value of r based on your data, but since you're asking about the correlation given the options, 0.97300135; strong accurately describes a robust positive correlation.