For a class project, you measure the weight in grams and the tail length in millimeters of a group of mice. The correlation is r = 0.7. The scatterplot shows one outlier of the relationship, falling clearly below the overall pattern of points. It turns out that this mouse was sick, and you decide to exclude it from the data set. With the outlier removed, do you expect the value of r to increase, decrease, or stay the same?

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12-09-2018
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For a class project, you measure the weight in grams and the tail length in millimeters of a group of mice. The correlation is r = 0.7. The scatterplot shows one outlier of the relationship, falling clearly below the overall pattern of points. It turns out that this mouse was sick, and you decide to exclude it from the data set. With the outlier removed, do you expect the value of r to increase, decrease, or stay the same?

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Rupicapra Rupicapra · Answer 1 · 2018-09-22T13:46:41+02:00

Answer: We can expect that the correlation coefficient will increase once the outlier is removed.

The Pearson's correlation coefficient is known to be sensitive to outliers. Outliers can inflate or deflate the correlation coefficient to the extent that it can lead to wrong conclusions.

An outlier that is mostly consistent with the trend will inflate the correlation coefficient; while an outlier that is not consistent with the trend will decrease the correlation coefficient.

In this case the weight and tail lengths of one mouse is inconsistent with the trend. When this data is removed from the sample, we can expect the value of r to increase.