Find the correlation coefficient, r, of the data described below.
Max is a PR agent for an up-and-coming band. He wants to convince the band members that being active on social media is good for their careers. He claims that a large social media following typically translates into ticket sales. To prove his point, Max looked up information about several successful bands.
He compared the number of social media followers (in millions), x, to the average number of hours it takes these bands to sell out a concert, y.
Followers (in millions)	Hours
2.3	96
4.3	35
4.9	74
9.6	84
9.9	17
Round your answer to the nearest thousandth.
r=

To find the correlation coefficient, \( r \), between two sets of data, we 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,
- \( x \) is the independent variable (social media followers),
- \( y \) is the dependent variable (hours to sell out a concert).

Given the dataTo find the correlation coefficient, \( r \), between two sets of data, we 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,
- \( x \) is the independent variable (social media followers),
- \( y \) is the dependent variable (hours to sell out a concert).

Given the 

\[
x = [2.3, 4.3, 4.9, 9.6, 9.9]
\]
\[
y = [96, 35, 74, 84, 17]
\]

### Step-by-Step Calculations:

1. **Calculate \( \sum{x}, \sum{y}, \sum{x^2}, \sum{y^2}, \sum{xy} \):**

Let me compute that for you.The correlation coefficient \( r \) is approximately \(-0.414\), rounded to the nearest thousandth.

This suggests a moderate negative correlation, meaning that as the number of social media followers increases, the time it takes for a band to sell out a concert tends to decrease.

Would you like further details or have any questions?

Here are 5 related questions you might find useful:
1. What does a negative correlation coefficient indicate in this context?
2. How can you interpret different ranges of correlation coefficients (e.g., 0.8 to 1.0)?
3. Can a correlation coefficient of 0 mean no relationship between the variables?
4. What are the limitations of using correlation to prove causation?
5. How can we compute the coefficient of determination \(r^2\) from the correlation coefficient?

**Tip:** Always remember that correlation does not imply causation; a negative correlation only suggests an inverse relationship, not necessarily a direct cause.

Find the correlation coefficient, r, of the data described below. Max is a PR agent for an up-and-coming band. He wants to convince the band members that being active on social media is good for their careers. He claims that a large social media following typically translates into ticket sales. To prove his point, Max looked up information about several successful bands. He compared the number of social media followers (in millions), x, to the average number of hours it takes these bands to sell out a concert, y. Followers (in millions) Hours: 2.3 96, 4.3 35, 4.9 74, 9.6 84, 9.9 17. Round your answer to the nearest thousandth.

Learn how to calculate the correlation coefficient (r) between social media followers and concert ticket sales using the given followers in millions (2.3, 4.3, 4.9, 9.6, 9.9) and time to sell out (96, 35, 74, 84, 17 hours). Understand key statistical concepts like correlation and data analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation