Given four scatterplots, each showing a different pattern of data points, which scatterplot shows the weakest negative linear correlation ($r$ closest to $0$ but less than $0$)?

• A. The scatterplot where the points form a tight cluster along a line sloping downward ($r$ close to $-1$).
• B. The scatterplot where the points form a tight cluster along a line sloping upward ($r$ close to $1$).
• C. The scatterplot where the points are widely scattered with no apparent trend ($r$ approximately $0$).
• D. The scatterplot where the points are widely scattered with a slight downward trend ($r$ is negative and close to $0$).

Answer: (D)

Verified step by step guidance

1. Understand that correlation measures the strength and direction of a linear relationship between two variables. A negative correlation means as one variable increases, the other decreases.
2. Identify that a 'tight cluster along a line sloping downward' indicates a strong negative linear correlation because points closely follow a downward trend.
3. Recognize that a 'tight cluster along a line sloping upward' indicates a strong positive linear correlation, which is not negative.
4. Note that points 'widely scattered with no apparent trend' suggest little to no correlation, meaning the correlation is weak or close to zero.
5. Conclude that among the options, the scatterplot with points 'widely scattered with a slight downward trend' shows the weakest negative linear correlation because the downward trend is weak and the points are spread out.