Data for a particular country on consumer debt (as a percentage of personal income) and mortgage debt (also as a percentage of personal income) for the 10 years from 2006 to 2015 are shown in the following table.
Consumer
Debt	Mortgage Debt
6.74 	5.98
7.07	    5.97
6.95 	5.88
6.69 	5.60
6.17	    5.15
5.58	    5.06
5.13	    4.96
4.95  	5.22
4.74	    5.30
4.59	    5.45
What is the value of the correlation coefficient for this data set? (Round your answer to four decimal places.)

To calculate the correlation coefficient between consumer debt and mortgage debt for the given data, we need to use the **Pearson correlation coefficient 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
- \( x \) represents consumer debt values
- \( y \) represents mortgage debt values

We'll apply this formula by computing the necessary sums and products of the data.

Let me compute that for you.The correlation coefficient for the given data set is \( r = 0.7288 \). This indicates a moderately strong positive relationship between consumer debt and mortgage debt as percentages of personal income.

Would you like further details or have any questions? Here are five related questions:

1. What does a correlation coefficient of 0.7288 imply about the relationship between two variables?
2. How would you interpret a negative correlation in this context?
3. Can you use this correlation coefficient to predict future consumer or mortgage debt levels?
4. How would outliers in the data affect the correlation coefficient?
5. What are the limitations of using the Pearson correlation coefficient in financial data?

**Tip:** A correlation coefficient close to 1 or -1 indicates a strong linear relationship, while a value close to 0 indicates little to no linear relationship.

Data for a particular country on consumer debt (as a percentage of personal income) and mortgage debt (also as a percentage of personal income) for the 10 years from 2006 to 2015 are shown in the following table. What is the value of the correlation coefficient for this data set? (Round your answer to four decimal places.)

Learn how to calculate the Pearson correlation coefficient for consumer debt and mortgage debt data over 10 years. This problem involves key statistical concepts, including correlation, and uses the Pearson formula. Suitable for students in Grades 11-12.

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