The correct statement is:
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 other statements are incorrect:
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 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.
The slope and shape of a scatterplot depends on the correlation (positive, negative or none), not vice versa. A negative slope can indicate either positive or negative correlation. Nonlinearity depends on the strength of correlation, not the sign.
So in summary, the key traits of scatterplots are:
1. The strength of correlation (weak, moderate, strong)
2. The direction of correlation (positive, negative, none)
3. The shape (linear, nonlinear)
The slope and nonlinearity are independent of the sign (positive vs negative) of correlation.