use the following data set to answer the questions below.\nwhat is the correlation coefficient of this…

Explanation:

Step1: Calculate the correlation coefficient ( r ) for the original data

We can use a statistical software or a calculator with a correlation coefficient function. Inputting the ( x ) and ( y ) values: ( x = [191.7,48.1,22.1,33.1,37.1,26.7,56.3,64.5,49] ) ( y=[ - 11257.8,1828.6,1594.9,-1443,694.2,-159.8,1122.9,396.8,-310.7] ) Using the formula ( r=\frac{n\sum xy-\sum x\sum y}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}} ) (where ( n = 9 )) or a calculator/software, we find ( r\approx - 0.27 )

Step2: Identify the outlier

By looking at the scatter - plot (or by comparing the values), the outlier is the point ((191.7,-11257.8))

Step3: Calculate the correlation coefficient ( r_{wo} ) without the outlier

Remove the outlier ((191.7,-11257.8)) ( x_{new}=[48.1,22.1,33.1,37.1,26.7,56.3,64.5,49] ) ( y_{new}=[1828.6,1594.9,-1443,694.2,-159.8,1122.9,396.8,-310.7] ) Using the formula ( r=\frac{n\sum xy-\sum x\sum y}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}} ) (where ( n = 8 )) or a calculator/software, we find ( r_{wo}\approx0.79 )

Answer:

The correlation coefficient of the original data ( r\approx - 0.27 ), and the correlation coefficient without the outlier ( r_{wo}\approx0.79 )