A. Including the outlier will change the sign of the correlation coefficient.
B. Including the outlier will decrease the correlation coefficient.
C. Including the outlier will increase the correlation coefficient.
D. Including the outlier will have no affect on the correlation coefficient.
What is the correlation cretficient if the outlier is included?
A. 0.30
B. 0.59
C. -0.20
OD. -0.59

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UpStudy AI · Accepted Answer

1. We start by noting that an outlier can have a large influence on the linear relationship between two variables. In the given set of options, one statement is that "Including the outlier will change the sign of the correlation coefficient." This means that if the original (or “true”) correlation is positive, the addition of the influential outlier drives the calculation into the negative range.

2. The numeric responses provided suggest that without the outlier the correlation might have been approximately $$0.59$$ (a positive value). When the outlier is included, not only is the magnitude of the correlation affected but—according to one of the options—the sign is reversed.

3. Among the numerical options provided, the one that corresponds to a sign change from $$0.59$$ is $$-0.59$$. This tells us that the outlier not only affects the strength but also the sign of the linear relationship.

4. Thus, including the outlier:
   - Changes the sign of the correlation coefficient.
   - Produces a correlation coefficient of approximately $$-0.59$$.

The correct answers are:

- Statement: Including the outlier will change the sign of the correlation coefficient.
- Correlation coefficient (with the outlier included): $$-0.59$$.
Including the outlier changes the correlation coefficient to $$-0.59$$.

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