To determine the association from a scatterplot where points form a curved line, you can look for the following characteristics:
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Type of Association:
- A curved association typically indicates a non-linear relationship between the two variables. Depending on the curvature, it could be quadratic, exponential, logarithmic, etc.
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Direction:
- If the curve rises from left to right, it indicates a positive association—meaning as one variable increases, the other variable tends to also increase.
- If the curve falls from left to right, it shows a negative association—indicating that as one variable increases, the other tends to decrease.
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Strength:
- The strength of the association can be inferred from how closely the points adhere to the curved line. If the points are tightly clustered around the curve, the relationship is strong. If they are widely scattered, the relationship is weak.
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Form:
- Consider whether the points form a specific shape (like a U-shape or an S-shape), as this can indicate the nature of the relationship and may suggest that one variable affects another in a particular way.
In summary, if you observe a curved pattern in the scatterplot, you can conclude that there is a non-linear association between the variables, and you may want to further analyze the relationship using a curve-fitting technique or regression analysis to understand the nature and equation of the curve.