Question

which statement is true regarding the traits of scatterplots? the strength of a correlation is independent of whether the correlation of a scatterplot is positive or negative. a scatterplot with positive correlation can have either weak association or strong association. the slope of a line is independent of whether the correlation of a scatterplot has positive or negative correlation. a scatterplot with a negative slope can have either positive correlation or negative correlation. the nonlinear association of a scatterplot depends on whether it has a weak or strong correlation. a scatterplot with nonlinear association will have a strong correlation. the nonlinear association of a scatterplot depends on whether it has a positive or negative correlation. a scatterplot with nonlinear correlation will have a negative correlation.

Explanation:

• Option 1:
• The strength of a correlation (weak or strong) is indeed independent of whether the correlation is positive or negative. Positive correlation means as one variable increases, the other also increases; negative correlation means as one variable increases, the other decreases. But the "tightness" of the cluster of points (which determines strength) has nothing to do with the direction (positive or negative) of the relationship.
• Option 2:
• The slope of a line in a scatter - plot regression line is related to the direction of the correlation. A positive slope implies a positive correlation (as \(x\) increases, \(y\) increases) and a negative slope implies a negative correlation (as \(x\) increases, \(y\) decreases). So, the slope is not independent of the sign of the correlation.
• Option 3:
• Non - linear association has no relation to the strength of a linear correlation measure (like Pearson's \(r\)). A non - linear association can have a weak or strong non - linear relationship, but it is not measured in terms of the "strong" or "weak" of a linear correlation framework. Also, non - linear association is not about positive or negative linear correlation.
• Option 4:
• Non - linear association is not about positive or negative linear correlation. And a non - linear correlation does not imply a negative linear correlation.

Answer:

The first option: "The strength of a correlation is independent of whether the correlation of a scatterplot is positive or negative. A scatterplot with positive correlation can have either weak association or strong association."