Math Problem Statement
Solution
The question asks about interpreting a correlation coefficient of .
Correlation coefficient:
- A correlation coefficient () measures the strength and direction of the linear relationship between two variables.
- Values of range from (perfect negative correlation) to (perfect positive correlation).
Interpretation of :
- Since is negative, the relationship between the two variables is negative, meaning as one variable increases, the other tends to decrease.
- The magnitude of 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:
- What is a strong negative correlation?
- How does a correlation of 0.7 differ from 0.3?
- Can a correlation coefficient be greater than 1?
- What is the significance of a correlation of 0?
- 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
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