Math Problem Statement

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

x y 5 15.5 6 17.1 7 18.1 8 18.8 9 18.7 10 21.7 11 18.5 12 20.2 13 21.6 14 22.9 15 23.7 16 23.3 17 23.6 18 25.8

Solution

The correlation coefficient for the given data is 0.9500.950 (rounded to three decimal places).

This indicates a strong positive linear relationship between xx and yy.

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

Here are five related questions:

  1. What does a correlation coefficient of 0.950 suggest about the data?
  2. How is the correlation coefficient affected by changes in the data?
  3. Can a high correlation coefficient indicate causation between variables?
  4. How would you interpret a correlation coefficient of -0.950?
  5. What is the difference between correlation and regression analysis?

Tip: A correlation coefficient close to 1 indicates a strong positive relationship, while one close to -1 indicates a strong negative relationship.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Linear Relationship

Formulas

Pearson correlation coefficient formula

Theorems

Pearson's Correlation Theorem

Suitable Grade Level

Grades 9-12