Math Problem Statement
Solution
The scatter plot in the image shows a clear U-shaped pattern, indicating a nonlinear relationship between the variables. Despite this, the correlation coefficient suggests a strong linear relationship, which is misleading in this context due to the nonlinearity of the data.
Correct Answer: (c) It is affected by nonlinearity.
The correlation coefficient measures the strength of a linear relationship, and in the presence of nonlinearity, as in this case, it can give a distorted view of the relationship between the variables.
Would you like more details or have any other questions? Here are some related questions to consider:
- What does a correlation coefficient close to 1 or -1 indicate in a dataset?
- How can we detect nonlinearity in a dataset using visual methods?
- What are some statistical tests that can be used to check for nonlinearity?
- How do influential points affect the correlation coefficient?
- What alternative methods can be used to measure nonlinear relationships?
Tip: Always plot your data before relying solely on statistical measures like the correlation coefficient, especially when assessing linearity or nonlinearity.
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Math Problem Analysis
Mathematical Concepts
Correlation
Nonlinearity
Scatter Plot Analysis
Formulas
Correlation Coefficient Formula: r = Σ[(X - X̄)(Y - Ȳ)] / √[Σ(X - X̄)²Σ(Y - Ȳ)²]
Theorems
Linear Correlation and Nonlinear Patterns
Suitable Grade Level
College Level
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