The following data set was collected by Campus Life. They are investigating the possibility of a relationship between students' satisfaction with Penn State (on a scale of 1-10 where higher numbers indicate greater satisfaction) and how many activities they participate in on campus. In this table, each "ID" represents a single student.
1. Imagine that someone in campus life wants to convert the "Satisfaction" scale of 1-10 to a scale of 1-100. 2. Would the covariance get larger, smaller, or stay the same?
3. Would the correlation coefficient r become larger, smaller, or stay the same?
4. What would be an example of an impossible correlation coefficient? In other words, give a value of r that would lead you to suspect that the researcher made a mistake.
5. Imagine a study where all our data (x, y) falls perfectly on a flat and straight horizontal line. If we calculated the correlation coefficient r for this data, what would it be? What would that mean for our hypotheses?