Question

What is the correlation coefficient of the following data? Is it a strong or weak correlation?

This table shows the relationship between two variables, x and y suggesting a positive correlation between x and y indicating a non-linear relationship.
x y
1 3 5 7 9
13 43 51 76 81
(1 point)
Responses

−0.97300135
; strong
negative 0.97300135 ; strong

−0.97300135
; weak
negative 0.97300135 ; weak

0.97300135; weak
0.97300135; weak

0.97300135; strong
0.97300135; strong
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Answer 1

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.