Math  /  Data & Statistics

Question|The following bivariate data set contains an outlier. \begin{tabular}{|r|r|} \hline \multicolumn{1}{|c|}{xx} & \multicolumn{1}{c|}{yy} \\ \hline 17.7 & 345.8 \\ \hline 23.1 & -180.9 \\ \hline 31 & -615.6 \\ \hline-7.7 & 164.1 \\ \hline 47.6 & 304.4 \\ \hline 11.2 & 106 \\ \hline 22.1 & -362.4 \\ \hline 1.7 & -100.7 \\ \hline 32.9 & -296.7 \\ \hline 52.9 & 307.9 \\ \hline 37.8 & -902.3 \\ \hline 22.9 & -530.8 \\ \hline 48.6 & 420 \\ \hline 48.7 & -75.1 \\ \hline 234.7 & 4386.9 \\ \hline \end{tabular}
What is the correlation coefficient with the outlier? rw=r_{w}= \square [Round your answer to three decimal places.]
What is the correlation coefficient without the outlier? rwo=r_{w o}= \square [Round your answer to three decimal plades.]
Would inclusion of the outlier change the evidence for or against a linear correlation? Yes. Including the outlier changes the evidence regarding a linear correlation. No. Including the outlier does not change the evidence regarding a linear correlation.

Studdy Solution
Compare rw r_w and rwo r_{wo} to determine the effect of the outlier on the correlation.
The correlation coefficient with the outlier rw r_w is approximately 0.123 \boxed{-0.123} .
The correlation coefficient without the outlier rwo r_{wo} is approximately 0.876 \boxed{-0.876} .
Including the outlier changes the evidence regarding a linear correlation: Yes.

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