Math Problem Statement
The Pearson correlation coefficient between 2 variables is: Close to 1 if they tend to move in the same direction, Close to 0 if they move independently of each other, Close to -1 if they tend to move in the opposite direction, or All of these?
Solution
The correct answer to this question is:
"All of these".
Explanation:
The Pearson correlation coefficient measures the linear relationship between two variables:
- Close to 1: Indicates a strong positive correlation, meaning the variables move in the same direction.
- Close to -1: Indicates a strong negative correlation, meaning the variables move in opposite directions.
- Close to 0: Indicates no linear correlation, meaning the variables are largely independent of each other.
Would you like further clarification on the Pearson correlation coefficient or its applications?
Here are 5 related questions for further exploration:
- What is the formula for calculating the Pearson correlation coefficient?
- How does the Pearson correlation differ from Spearman's rank correlation?
- Can the Pearson correlation be used for non-linear relationships?
- How do outliers affect the Pearson correlation coefficient?
- What are common applications of the Pearson correlation coefficient in statistics?
Tip: When interpreting the Pearson correlation, always visualize the data with a scatterplot to confirm the linear relationship!
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation Analysis
Formulas
Pearson correlation coefficient formula: r = Σ((x - x̄)(y - ȳ)) / √(Σ(x - x̄)²Σ(y - ȳ)²)
Theorems
Properties of the Pearson correlation coefficient
Suitable Grade Level
Grades 9-12