the-correlation-coefficient-for-this-data-is-r098r098-showing-a-strong-negative-

Question

The correlation coefficient for this data is $r = - 0.98$ , showing a strong negative linear relationship: higher body fat percentage tends to be associated with fewer push-ups.

Table showing body fat percentages and corresponding push-up counts, indicating a strong negative correlation.

Suppose the trainer removes the data for the client with $30 percent sign$ body fat and $22$ push-ups. How is the correlation coefficient $r$ likely to change?

Accepted Answer

The value of $r = - 0.98$ becomes slightly less negative, since a point that reinforced the linear trend was removed.

Answer

The value of $r = - 0.98$ remains unchanged, because removing one point doesn’t affect correlation.

Answer

The value of $r = - 0.98$ increases to $0$ , since fewer data points always weaken the correlation completely.

Answer

The value of $r = - 0.98$ becomes more negative because the point was an outlier.