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Which scatterplot has a correlation coefficient closest to r = -1?

A) A scatterplot with points forming a straight line with a positive slope.
B) A scatterplot with points forming a straight line with a negative slope.
C) A scatterplot with points scattered randomly without any apparent pattern.
D) A scatterplot with points forming a curved line.

User Ggmathur
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1 Answer

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Final answer:

The scatterplot with points forming a straight line with a negative slope (Option B) has a correlation coefficient closest to r = -1, indicating a perfect negative correlation.

Step-by-step explanation:

The scatterplot that has a correlation coefficient closest to r = -1 is B) A scatterplot with points forming a straight line with a negative slope. The correlation coefficient (r) quantifies the strength and direction of the relationship between two variables. An r value of -1 signifies a perfect negative correlation, meaning as one variable increases, the other variable decreases in a perfectly linear relationship. Thus, a scatterplot showing a straight line with a negative slope would illustrate this relationship most accurately.

The other options do not demonstrate a correlation coefficient of -1. Option A shows a positive correlation (0 < r < 1), option C shows a zero correlation (r = 0), and option D might show a relationship, but not one that is linear, therefore not a perfect negative correlation.

User Shian
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