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 the first statement

Using the Scatterplot Analysis knowledge point

• The strength of a correlation (how closely the data points fit a trend) is measured by the absolute value of the correlation coefficient \(|r|\).
• This strength is completely independent of the direction (positive or negative sign of \(r\)).
• Therefore, a positive correlation can be either weak (points widely scattered) or strong (points tightly clustered). This statement is true.

Analyze the second statement

• The slope of a trend line and the correlation coefficient of a scatterplot always share the same sign.
• A negative slope must correspond to a negative correlation, not either positive or negative. Thus, this statement is false.

Analyze the third statement

• Nonlinear association refers to the shape of the relationship (e.g., quadratic or exponential), which is independent of whether the linear correlation coefficient is weak or strong. Thus, this statement is false.

Analyze the fourth statement

• A nonlinear association does not depend on or guarantee a positive or negative linear correlation. Thus, this statement is false.

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. (Correct answer)
• (B) 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.
• (C) 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.
• (D) 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.