Based on the data shown below, calculate the correlation coefficient (to three decimal places)



xy

5

78.2

6

86.2

7

85.2

8

88.4

9

90

10

99.8

r=

To calculate the correlation coefficient \( r \) for a set of data points, we can use the formula:

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

Where:
- \( n \) is the number of data points,
- \( x \) and \( y \) are the individual values of the variables.

Let’s calculate this step-by-step.

We have the following data points:
\[
(5, 78.2), (6, 86.2), (7, 85.2), (8, 88.4), (9, 90), (10, 99.8)
\]

First, I will calculate the required sums for \( x \), \( y \), \( xy \), \( x^2 \), and \( y^2 \). Let me handle that.The correlation coefficient \( r \) is approximately \( 0.926 \) (rounded to three decimal places).

Would you like further details or clarification?

Here are some related questions to consider:
1. What does a correlation coefficient of 0.926 indicate?
2. How does the value of \( r \) relate to the strength of the relationship between \( x \) and \( y \)?
3. What is the interpretation of \( r = 1 \) or \( r = -1 \)?
4. How can we visualize the relationship between \( x \) and \( y \)?
5. What are the limitations of using the correlation coefficient?

**Tip**: A correlation coefficient close to 1 indicates a strong positive linear relationship between the two variables.

Based on the data shown below, calculate the correlation coefficient (to three decimal places)

xy

5

78.2

6

86.2

7

85.2

8

88.4

9

90

10

99.8

r=

Learn how to calculate the correlation coefficient for the dataset: (5, 78.2), (6, 86.2), (7, 85.2), (8, 88.4), (9, 90), (10, 99.8). This statistical problem covers key concepts such as correlation and linear relationships, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation