Which correlation best describes the strength of the linear association?

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Understand the Problem

The question is asking to identify the type of correlation that best describes the strength of a linear association based on the provided statistics, specifically the correlation coefficient r and the coefficient of determination r².

Answer

strong negative correlation because \( r = -0.9998 \)
Answer for screen readers

The best description of the correlation is: strong negative correlation because ( r = -0.9998 ).

Steps to Solve

  1. Identify the correlation coefficient ( r )

The provided correlation coefficient ( r ) is ( -0.9998 ). This value is negative, indicating a negative correlation.

  1. Understand the strength of the correlation

The absolute value of ( r ) is ( |r| = 0.9998 ). Values of ( r ) close to 1 or -1 indicate a strong relationship.

  1. Determine the strength category

Typically:

  • ( 0.70 \leq |r| < 1.00 ) indicates a strong correlation.
  • ( 0.30 \leq |r| < 0.70 ) indicates a moderate correlation.
  • ( |r| < 0.30 ) indicates a weak correlation.

Since ( |r| = 0.9998 ), this suggests a strong correlation.

  1. Decide on the type of correlation

Given that ( r ) is negative, this indicates that it is a strong negative correlation.

The best description of the correlation is: strong negative correlation because ( r = -0.9998 ).

More Information

The correlation coefficient ( r = -0.9998 ) indicates a very strong negative linear relationship between the two variables. This means that as one variable increases, the other decreases in a nearly perfect linear manner.

Tips

  • Misinterpreting the sign of the correlation coefficient. Remember that a negative ( r ) indicates an inverse relationship.
  • Confusing correlation strength with the direction of the relationship. High absolute values indicate strength, while the sign indicates the direction.
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