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; weak
0.97300135; weak

−0.97300135
−
0.97300135
; strong
negative 0.97300135 ; strong

−0.97300135
−
0.97300135
; weak
negative 0.97300135 ; weak

0.97300135; strong

Answer 1

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.

1. The correlation coefficient \( r \) is calculated using the formula:

\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}
\]

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**