Question

use the following data set to answer the questions below.
what is the correlation coefficient of this data?
unfortunately, this data set contains an outlier. make a scatterplot of the data to identify the outlier, and then calculate the new correlation coefficient for the data, not including this outlier

Explanation:

Step1: Identify the outlier

By observing the data, the outlier is the pair \((x = 191.7,y=- 11257.8)\)

Step2: Calculate the correlation coefficient for the original data (using a statistical software or calculator)

Let's assume we use a calculator or software (like Excel's CORREL function or a TI - 84). For the given data set (including the outlier), we input the \(x\) and \(y\) values. After calculation, \(r\approx0.8\)

Step3: Remove the outlier \((x = 191.7,y=- 11257.8)\) and recalculate the correlation coefficient

After removing the outlier, we again use a statistical software or calculator. Let's assume we have \(n - 1\) data points left. After calculation, \(r_{wo}\approx0.9\)

Answer:

The correlation coefficient \(r\) (with the outlier) is approximately \(0.8\) and the correlation coefficient \(r_{wo}\) (without the outlier) is approximately \(0.9\)