Math Problem Statement

Match the correlation coefficients (r values) of 0.996, -0.996, 0.678, 1, and 0.293 to their respective scatterplots.

Solution

Based on the uploaded scatterplots, let’s match the correlation coefficient rr values:

  1. Scatterplot 1: Displays a strong negative correlation (points tightly clustered in a downward slope). This corresponds to r=0.996r = -0.996.

  2. Scatterplot 2: Displays a strong positive correlation (points tightly clustered in an upward slope). This corresponds to r=0.996r = 0.996.

  3. Scatterplot 3: Displays no clear trend or pattern, indicating a very weak correlation. This corresponds to r=0.293r = 0.293.

  4. Scatterplot 4: Shows a moderate negative correlation (points loosely clustered in a downward slope). This corresponds to r=0.678r = -0.678.

  5. Scatterplot 5: Shows a perfect positive correlation (points form a straight upward line). This corresponds to r=1r = 1.

If you have further questions or would like clarifications, feel free to ask!

Here are 5 relative questions for expansion:

  1. What factors influence the strength of a correlation coefficient?
  2. How do we interpret the values of rr in terms of strength and direction?
  3. Can a scatterplot with a weak correlation still have significant patterns in the data?
  4. How is the correlation coefficient affected by outliers in the dataset?
  5. In real-world scenarios, what are examples of data that might produce perfect correlations?

Tip: When estimating rr, remember that tighter clustering of points along a line (positive or negative) indicates a stronger correlation.

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Math Problem Analysis

Mathematical Concepts

Correlation
Scatterplots
Statistics

Formulas

r = (Σ(xi - x̄)(yi - ȳ)) / √(Σ(xi - x̄)² * Σ(yi - ȳ)²)

Theorems

Correlation Coefficient Interpretation

Suitable Grade Level

Grades 10-12