Math Problem Statement

Here is a bivariate data set. x y 33.6 98.9 42.7 86.9 22.2 56.4 42.4 -44 23.6 -108.5 40.8 21.1

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Find the correlation coefficient and report it accurate to three decimal places. r =

Solution

The correlation coefficient rr is approximately 0.2450.245.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

  1. What does the value of the correlation coefficient tell us about the relationship between xx and yy?
  2. How can you interpret a positive vs. negative correlation coefficient?
  3. What are the limitations of using the correlation coefficient for bivariate data?
  4. How would you calculate the coefficient of determination r2r^2 and what does it represent?
  5. How does the presence of outliers affect the correlation coefficient?

Tip: A correlation coefficient close to 0 suggests a weak linear relationship, while values closer to 1 or -1 indicate stronger positive or negative linear relationships, respectively.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficient
Bivariate Data

Formulas

Pearson's correlation coefficient formula: r = Σ[(x_i - mean(x))(y_i - mean(y))] / sqrt[Σ(x_i - mean(x))^2 Σ(y_i - mean(y))^2]

Theorems

Pearson's Correlation Theorem

Suitable Grade Level

Grades 10-12

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