Association vs. Correlation
Association and correlation are related but distinct concepts in enVision Algebra 1 Chapter 3 for Grade 11. Association describes any general relationship between two variables — positive, negative, or none. Correlation specifically refers to linear relationships that can be modeled by y = mx + b. A scatter plot showing increasing test scores with more study time shows positive association; if the points follow a roughly straight line, that is also positive correlation. Data can show association (curved pattern) without linear correlation. Understanding this distinction prevents misapplying a line of best fit to non-linear relationships.
Key Concepts
Association describes the general relationship pattern between two variables (positive, negative, or no association), while correlation specifically refers to linear relationships that can be modeled with a straight line equation of the form $y = mx + b$.
Common Questions
What is the difference between association and correlation?
Association is any pattern between two variables (linear or nonlinear). Correlation specifically means a linear relationship that can be described by y = mx + b. All correlations are associations, but not all associations are correlations.
Can data show association but not correlation?
Yes. If a scatter plot shows a curved (parabolic or exponential) pattern, there is association but not linear correlation. A line of best fit would not describe the data well.
What does positive association look like on a scatter plot?
As one variable increases, the other tends to increase too. The points slope upward from left to right, though they need not follow a perfect line.
How does negative association differ from negative correlation?
Negative association means one variable tends to decrease as the other increases, in any pattern. Negative correlation specifically means this decrease follows a linear trend with a negative slope.
What does no association look like on a scatter plot?
No association means the points appear randomly scattered with no upward or downward trend. Knowing one variable's value gives no useful information about the other.