Math Problem Statement

Here is a bivariate data set. x y 56.7 -71 69.9 46.2 66.4 19.1 63.4 48 83.2 -60.7 52.8 74.3 54 141 70.7 122.3

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

Solution

The correlation coefficient rr for the given bivariate data set is r=0.362r = -0.362, accurate to three decimal places.

Would you like further details or explanations?

Here are some related questions to expand your understanding:

  1. What does a negative correlation coefficient indicate about the relationship between two variables?
  2. How does the magnitude of the correlation coefficient affect the strength of the relationship?
  3. Can the correlation coefficient alone determine causality between variables?
  4. What other methods can be used to analyze the relationship between two variables, apart from correlation?
  5. How would the correlation coefficient change if the data had more outliers?

Tip: Always visualize the data (using scatter plots, for instance) to get a better sense of the relationship, especially when interpreting correlation coefficients.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Bivariate Data Analysis

Formulas

Pearson Correlation Coefficient Formula: r = Σ[(xi - x̄)(yi - ȳ)] / √[Σ(xi - x̄)^2 Σ(yi - ȳ)^2]

Theorems

Correlation and Covariance Theorem
Pearson's Correlation Theorem

Suitable Grade Level

Grades 10-12, College-level Statistics