Correlation Coefficient r: Strength, Direction, and Thresholds
The correlation coefficient r in Algebra 1 (California Reveal Math, Grade 9) measures the strength and direction of a linear relationship between two quantitative variables, ranging from -1 to 1. r > 0 indicates positive correlation (both variables increase together); r < 0 indicates negative correlation (one increases as the other decreases). Common thresholds: |r| ≥ 0.8 is strong, 0.5 ≤ |r| < 0.8 is moderate, |r| < 0.5 is weak. r = 0 means no linear relationship. This statistic helps evaluate how well a linear model fits scatter plot data.
Key Concepts
The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. It always satisfies $ 1 \leq r \leq 1$.
Common Questions
What does the correlation coefficient r measure?
r measures the strength and direction of the linear relationship between two quantitative variables. Values range from -1 (perfect negative) to +1 (perfect positive), with 0 indicating no linear relationship.
What does a positive r value mean?
A positive r value (r > 0) indicates that as one variable increases, the other tends to increase as well — a positive linear association.
What does a negative r value mean?
A negative r value (r < 0) indicates that as one variable increases, the other tends to decrease — a negative or inverse linear association.
What value of r indicates a strong linear relationship?
Generally, |r| ≥ 0.8 indicates a strong linear relationship. |r| between 0.5 and 0.8 is moderate. |r| below 0.5 is weak. The exact thresholds may vary by context.
Where is the correlation coefficient covered in California Reveal Math Algebra 1?
r is taught in California Reveal Math, Algebra 1, as part of Grade 9 statistics and linear regression.
Does r = 0.9 prove causation between the variables?
No. A high r value shows strong linear association but does not establish that one variable causes the other. Causation requires controlled experimental evidence.
What is the difference between r and r²?
r is the correlation coefficient showing direction and strength. r² (coefficient of determination) shows the proportion of variance in y explained by the linear model — always between 0 and 1.