Math Problem Statement

Consider the scatter diagram in figure to the right. a. Which point is an outlier? Ignoring the outlier, estimate or compute the correlation coefficient for the remaining points. b. Now include the outlier. How does the outlier impact the correlation coefficient?

Solution

Looking at the scatter plot, there appears to be an outlier that does not follow the general trend of the other points.

Answers:

  1. 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.
  2. Estimated Correlation Coefficient (Ignoring the Outlier):

    • The remaining points follow a strong positive linear trend, suggesting a high correlation coefficient close to 0.97.
  3. 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:

  1. What is the formula for the correlation coefficient?
  2. How do outliers affect the regression line?
  3. What are some methods to handle outliers in data analysis?
  4. What is the difference between a positive and negative correlation coefficient?
  5. 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