Math Problem Statement
Solution
The correct answer is "All of these."
Explanation:
The Pearson correlation coefficient, denoted as , measures the linear relationship between two variables. Its value ranges from -1 to 1, with interpretations as follows:
- : Indicates a strong positive correlation; as one variable increases, the other also tends to increase.
- : Indicates a strong negative correlation; as one variable increases, the other tends to decrease.
- : Indicates no linear correlation; the variables move independently of each other.
Thus, all the options listed describe specific cases of the Pearson correlation coefficient.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Linear Relationships
Formulas
Pearson correlation coefficient formula: r = Σ((xi - x̄)(yi - ȳ)) / (n * σx * σy)
Theorems
Properties of Pearson correlation
Suitable Grade Level
Grades 9-12
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