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:

• Analyze Option A: The strength of correlation (weak/strong) is separate from its direction (positive/negative). A positive - correlated scatterplot can indeed have weak or strong association. This is correct.
• Analyze Option B: A negative slope implies a negative correlation (as slope sign relates to correlation direction), so a scatterplot with negative slope can't have positive correlation. This is wrong.
• Analyze Option C: Non - linear association doesn't depend on weak/strong correlation, and non - linear scatterplots usually have weak (or no) linear correlation. This is wrong.
• Analyze Option D: Non - linear association is not dependent on positive/negative correlation, and non - linear scatterplots don't necessarily have negative correlation. This is wrong.

Answer:

A. 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.