Math Problem Statement
Solution
Looking at the scatter plot, there appears to be an outlier that does not follow the general trend of the other points.
Answers:
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Which point is an outlier?
- The point that is far from the linear trend of the other points is the outlier. From the image, it appears to be the point at the lower left.
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Estimated Correlation Coefficient (Ignoring the Outlier):
- The remaining points follow a strong positive linear trend, suggesting a high correlation coefficient close to 0.97.
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Effect of Including the Outlier on Correlation:
- Outliers typically decrease the correlation coefficient since they introduce variability that disrupts the linear trend.
- Correct answer: A. Including the outlier will decrease the correlation coefficient.
Would you like more details or a step-by-step explanation?
Here are 5 related questions to expand your understanding:
- What is the formula for the correlation coefficient?
- How do outliers affect the regression line?
- What are some methods to handle outliers in data analysis?
- What is the difference between a positive and negative correlation coefficient?
- Can the correlation coefficient ever be greater than 1 or less than -1?
Tip: When analyzing scatter plots, always check for outliers before interpreting correlation coefficients!
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation Coefficient
Outliers
Scatter Plots
Formulas
Correlation coefficient formula: r = Σ((xi - x̄)(yi - ȳ)) / sqrt(Σ(xi - x̄)² Σ(yi - ȳ)²)
Theorems
Impact of outliers on correlation coefficient
Suitable Grade Level
Grades 9-12
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