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 for the given bivariate data set is , accurate to three decimal places.
Would you like further details or explanations?
Here are some related questions to expand your understanding:
- What does a negative correlation coefficient indicate about the relationship between two variables?
- How does the magnitude of the correlation coefficient affect the strength of the relationship?
- Can the correlation coefficient alone determine causality between variables?
- What other methods can be used to analyze the relationship between two variables, apart from correlation?
- 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