Find the correlation coefficient, r, of the data described below.The design team at an electronics company is evaluating its new prototype for a miniature recording device. As part of this evaluation, designers at the company gathered data about competing devices already on the market.

Among other things, the designers recorded the thickness of each recording device (in millimeters), x, and its maximum recording length (in minutes), y.

To calculate the correlation coefficient \( r \), we need the data points for the thickness of each recording device (\( x \)) and the maximum recording length (\( y \)).

Here’s how we would calculate \( r \) if the data points were given:

### Formula for Correlation Coefficient \( r \):

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

Where:
- \( n \) is the number of data points
- \( x \) and \( y \) represent the individual values for thickness and recording length
- \( \sum xy \) is the sum of the products of corresponding \( x \) and \( y \) values
- \( \sum x^2 \) and \( \sum y^2 \) are the sums of the squares of the \( x \) and \( y \) values

If you provide the data set (values for \( x \) and \( y \)), I can compute the correlation coefficient \( r \).

### Please upload the data or provide the data points, and I will proceed with the calculation.

Would you like a breakdown of how each component in the formula works? Here are 5 related questions for further exploration:
1. What does the correlation coefficient tell us about the relationship between two variables?
2. How is the correlation coefficient interpreted in terms of strength and direction of a relationship?
3. What is the difference between a positive and negative correlation?
4. Can a correlation coefficient of zero mean there is no relationship at all?
5. How do outliers in the data affect the correlation coefficient?

**Tip:** The correlation coefficient \( r \) ranges from -1 to 1, where values closer to 1 or -1 indicate a strong linear relationship between the variables.

Find the correlation coefficient, r, of the data described below. The design team at an electronics company is evaluating its new prototype for a miniature recording device. As part of this evaluation, designers at the company gathered data about competing devices already on the market. Among other things, the designers recorded the thickness of each recording device (in millimeters), x, and its maximum recording length (in minutes), y.

Learn how to calculate the correlation coefficient (r) for the relationship between thickness and recording length of miniature recording devices. This statistical problem uses the Pearson correlation coefficient formula, 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