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.

Answer 1

The first statement is true: "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."

To elaborate:

- The strength of the correlation (weak, moderate, or strong) refers to how closely the data points cluster around a line of best fit, regardless of whether the correlation is positive (upward slope) or negative (downward slope).
- A scatterplot with a positive correlation can display weak correlation if the points are widely spread out, or strong correlation if the points cluster tightly around the line.
- The other statements are incorrect for various reasons:
- The slope of a line indicates the direction of the relationship (positive or negative), but does not affect the nature of the correlation itself; thus, a negative slope indicates a negative correlation.
- Nonlinear correlations do not necessarily imply strong correlation; a scatterplot can exhibit a nonlinear association without showing a strong correlation.
- Nonlinear relationships can occur in both positive and negative correlations, and a scatterplot can exhibit nonlinear correlations regardless of the slope's direction.

Overall, the first statement captures an essential aspect of correlation accurately.