Math Problem Statement

Correlation coefficient is the strength of the linear relationship between two quantitive variables. Sort the coefficients from strong to weak and make sure to put them from least to greatest in each column. Columns are strong correlation, moderate correlation and weak to no correlation. -0.45,1,-1,0.15,-0.85,0.63,0.52,0,-0.75

Solution

To sort the given correlation coefficients into columns based on the strength of their linear relationship (strong, moderate, and weak/no correlation), let's first define the ranges for each category:

  • Strong correlation: Coefficients close to -1 or 1, typically between -1 and -0.7 or 0.7 and 1.
  • Moderate correlation: Coefficients between -0.7 and -0.4 or 0.4 and 0.7.
  • Weak to no correlation: Coefficients between -0.4 and 0.4.

Sorted into categories:

Strong correlation:

  • Least to greatest: -1, -0.85, -0.75, 1

Moderate correlation:

  • Least to greatest: -0.45, 0.52, 0.63

Weak to no correlation:

  • Least to greatest: 0, 0.15

Final Table:

Strong correlationModerate correlationWeak to no correlation
-1-0.450
-0.850.520.15
-0.750.63
1

Would you like a detailed explanation on how these ranges are determined or have any questions?

Here are 5 questions for further exploration:

  1. What does a correlation coefficient of 0 signify in real-world scenarios?
  2. How do you calculate the correlation coefficient from data points?
  3. What is the difference between positive and negative correlations?
  4. How does the correlation coefficient relate to the slope in a linear regression?
  5. What limitations exist when interpreting the correlation coefficient?

Tip: Even a strong correlation does not necessarily imply causation; always consider the context of your data.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficient
Linear Relationships

Formulas

Correlation Coefficient Formula: r = Σ[(X_i - X̄)(Y_i - Ȳ)] / √[Σ(X_i - X̄)² Σ(Y_i - Ȳ)²]

Theorems

Properties of Correlation Coefficients
Range and Strength of Correlation

Suitable Grade Level

Grades 10-12