1.2 Determine the correlation coefficient, 𝑟, for the data set.

The correlation coefficient \( r \) measures the strength and direction of the linear relationship between two variables. The formula to calculate \( r \) is:

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

Where:
- \( n \) is the number of data points
- \( \sum x \), \( \sum y \), \( \sum xy \), and \( \sum x^2 \) are as calculated previously
- \( \sum y^2 \) is the sum of the squares of the \( y \) values

We'll calculate \( \sum y^2 \) and then use it to find the correlation coefficient \( r \).The correlation coefficient \( r \) for the data set is approximately \(-0.773\).

This negative value indicates a strong inverse relationship between age and the amount of money spent on airtime. As age increases, the amount spent on airtime generally decreases.

Would you like more details or have any questions about this calculation?

Here are some related questions to consider:

1. What does the value of \( r \) imply about the strength of the relationship between the variables?
2. How does the value of \( r \) relate to the slope of the regression line?
3. What is the range of possible values for \( r \), and what do they signify?
4. How can we test if the correlation is statistically significant?
5. How would outliers in the data affect the value of \( r \)?

**Tip:** The closer the correlation coefficient \( r \) is to \(-1\) or \(1\), the stronger the linear relationship between the variables.

Learn how to calculate the correlation coefficient (r) for a given data set. Understand the formula and its application with an example problem. The correlation coefficient (r) for this data set is approximately -0.773, indicating a strong inverse relationship between age and money spent on airtime.

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