A strength coach is studying the relationship between an athlete’s maximum half-squat load (in kilograms) and their 1010-meter sprint time (in seconds). The data for 88 athletes is shown below:The correlation coefficient for this data is r=−0.99r=−0.99, indicating a strong negative linear relationship: higher squat strength is associated with faster sprint times. Now, the coach adds data for a new athlete who squats 210 kg210\text{ kg} and has a sprint time of 2.002.00 seconds. How will this affect the correlation coefficient rr?

The value of rr increases to 00, since the new data point overrides the existing trend.

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Problem 35Multiple Choice

A strength coach is studying the relationship between an athlete’s maximum half-squat load (in kilograms) and their $10$ -meter sprint time (in seconds). The data for $8$ athletes is shown below:

The correlation coefficient for this data is $r = - 0.99$ , indicating a strong negative linear relationship: higher squat strength is associated with faster sprint times. Now, the coach adds data for a new athlete who squats $210 kg$ and has a sprint time of $2.00$ seconds. How will this affect the correlation coefficient $r$ ?

The value of $r$ becomes more negative, because the new athlete is stronger than the others.

The value of $r$ becomes less negative, since the added point weakens the negative linear relationship.

The value of $r$ increases to $0$ , since the new data point overrides the existing trend.

The value of $r$ remains unchanged, because adding one point does not affect the correlation.

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