Math Problem Statement

A graph shows the horizontal axis numbered 4 to 16 and the vertical axis numbered 4 to 12. Points and a line show a downward trend. Which is most likely the correlation coefficient for the set of data shown?

–0.91 –0.35 0.35 0.91

Solution

In the scenario described, where a graph shows a downward trend, the correlation coefficient is expected to be negative. The correlation coefficient (r) ranges from -1 to 1, with values closer to -1 indicating a strong negative correlation.

Given the options:

  • –0.91: Strong negative correlation
  • –0.35: Weak negative correlation
  • 0.35: Weak positive correlation
  • 0.91: Strong positive correlation

Since the graph shows a clear downward trend, the most likely correlation coefficient for the data is –0.91, indicating a strong negative correlation.

Would you like more details or have any questions about correlation coefficients? Here are some related questions:

  1. What does a correlation coefficient of 0 indicate?
  2. How can you visually determine the strength of a correlation from a graph?
  3. What are some factors that might influence the correlation between two variables?
  4. How is the correlation coefficient calculated?
  5. Can a correlation coefficient be misleading? If so, how?

Tip: Always visualize data before making assumptions about correlation!

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation

Formulas

Correlation coefficient formula r = (Σ(x - x̄)(y - ȳ)) / (√(Σ(x - x̄)² * Σ(y - ȳ)²))

Theorems

Properties of correlation coefficients

Suitable Grade Level

Grades 9-12