Question

observing brain activity while subjects made their decisions pointed to specific brain regions. the table contains data for 16 subjects on behavioral loss aversion and
eural loss aversion,\ a measure of activity in one region of the brain.
find the correlation r between neural and behavioral loss aversion with the outlier. give your answer to four decimal places.
find the correlation r between neural and behavioral loss aversion without the outlier. give your answer to four decimal places.

Explanation:

Step1: Recall correlation - coefficient formula

The formula for the correlation coefficient \(r\) is \(r=\frac{n\sum xy-\sum x\sum y}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}\), where \(n\) is the number of data - points, \(x\) and \(y\) are the two variables. First, we need to identify the neural activity data as \(x\) and the behavioral loss aversion data as \(y\).

Step2: Calculate sums for all data (including outlier)

Let \(n = 16\). Calculate \(\sum x\), \(\sum y\), \(\sum xy\), \(\sum x^{2}\), and \(\sum y^{2}\) using the given data points. Then substitute these values into the correlation - coefficient formula to find \(r\) for all 16 data points.

Step3: Identify the outlier

Visually or using a statistical method (such as the z - score method or the inter - quartile range method), identify the outlier in the data set.

Step4: Recalculate sums without the outlier

Let \(n = 15\) (after removing the outlier). Recalculate \(\sum x\), \(\sum y\), \(\sum xy\), \(\sum x^{2}\), and \(\sum y^{2}\) using the 15 non - outlier data points. Then substitute these new values into the correlation - coefficient formula to find \(r\) without the outlier.

Since the actual data values from the table are not typed out and we don't have a way to perform the calculations directly, we assume you will use statistical software (like Excel, R, or Python's numpy and scipy.stats) or a calculator with statistical functions to perform the above steps.

Answer:

You need to perform the above - mentioned calculations using the data from the table to get the correlation coefficient \(r\) with and without the outlier. The final answers will be two values of \(r\) rounded to four decimal places.