Math Problem Statement

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

x y 5 27.55 6 26 7 22.55 8 24.7 9 21.75 10 19 11 21.65 12 18.7

Solution

The correlation coefficient between the given xx and yy values is 0.896-0.896, rounded to three decimal places.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

  1. How is the correlation coefficient used in regression analysis?
  2. What does a negative correlation coefficient indicate about the relationship between variables?
  3. How do outliers affect the correlation coefficient?
  4. Can correlation imply causation in data analysis?
  5. What are the limitations of using the Pearson correlation coefficient?

Tip: A correlation coefficient close to -1 or 1 indicates a strong linear relationship, whereas a value near 0 suggests no linear relationship.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Linear Relationships

Formulas

Pearson Correlation Coefficient: r = Σ[(x_i - x̄)(y_i - ȳ)] / sqrt[Σ(x_i - x̄)^2 * Σ(y_i - ȳ)^2]

Theorems

Pearson Correlation Theorem

Suitable Grade Level

Grades 10-12