Math Problem Statement

A researcher fit a linear model to her data and calculated the correlation coefficient to be -0.29. Which statement about the correlation among the data is true?

Solution

The question asks about interpreting a correlation coefficient of 0.29-0.29.

Correlation coefficient:

  • A correlation coefficient (rr) measures the strength and direction of the linear relationship between two variables.
  • Values of rr range from 1-1 (perfect negative correlation) to +1+1 (perfect positive correlation).

Interpretation of r=0.29r = -0.29:

  • Since r=0.29r = -0.29 is negative, the relationship between the two variables is negative, meaning as one variable increases, the other tends to decrease.
  • The magnitude of 0.29-0.29 suggests a weak negative correlation, as values close to 0 represent weaker correlations.

Therefore, the correct answer is "There is a weak negative correlation.", which matches the option that has been selected.

Would you like more details on correlation or have any questions?

Here are 5 related questions:

  1. What is a strong negative correlation?
  2. How does a correlation of 0.7 differ from 0.3?
  3. Can a correlation coefficient be greater than 1?
  4. What is the significance of a correlation of 0?
  5. How is correlation different from causation?

Tip: Always check if the correlation is close to 1 or -1 for strong relationships, and near 0 for weak ones.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficient
Linear Models

Formulas

Correlation coefficient formula (r)
r = Σ((x_i - mean_x) * (y_i - mean_y)) / (n * std_x * std_y)

Theorems

Linear correlation theorem
Interpretation of correlation coefficients

Suitable Grade Level

Grades 9-12