Math Problem Statement
Based on the data shown below, calculate the correlation coefficient (rounded to three decimal places)
Solution
The correlation coefficient between the given and values is approximately , rounded to three decimal places. This indicates a strong negative linear relationship between the two variables.
Would you like further explanation on correlation, or have any other questions?
Here are some related questions:
- What does a correlation coefficient of signify in practical terms?
- How is the correlation coefficient calculated step by step?
- Can we predict future -values using this correlation coefficient?
- What is the difference between correlation and causation?
- How can outliers affect the correlation coefficient?
Tip: A strong negative correlation means that as one variable increases, the other decreases at nearly the same rate, but it doesn't imply causality.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Linear Relationships
Formulas
Correlation Coefficient Formula: r = Σ[(X_i - X̄)(Y_i - Ȳ)] / sqrt[Σ(X_i - X̄)^2 * Σ(Y_i - Ȳ)^2]
Theorems
Pearson's Correlation Coefficient
Suitable Grade Level
Grades 9-12