Question

Mark and Elizabeth are creating a scatterplot of data, and calculating the LSRL. Since their evil teacher does not allow them to use calculators, this is a slow process. They decide to split the work up to save time. Mark decides to compute the correlation coefficient. "Done!" he quickly exclaims. "What?! No way you can be finished already," Elizabeth says. "Well, I am" replies Mark. "And here you go: r is 6.3." Should Elizabeth trust Mark and his work? Explain.

Answer 1

Elizabeth should not trust Mark's work. The reason for this is that the correlation coefficient, commonly denoted as r, has a possible range only from -1 to 1 inclusive. The correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. It will have a value of +1 in the case of a perfect direct or increasing linear relationship, a value of -1 in the case of a perfect decreasing linear relationship, and a value of 0 suggests that there is no linear relationship between the two variables.

In this context, Mark has calculated a correlation coefficient of 6.3. This value falls outside of the acceptable range for a correlation coefficient, because it is greater than 1. This suggests that there may have been an error in Mark's calculations, given that it's theoretically impossible to produce a correlation coefficient that exceeds 1 or is less than -1. Therefore, the result is incorrect, and Elizabeth should not trust it.

So, it's clear that Elizabeth should be skeptical of Mark's claim that the correlation coefficient (r) is 6.3. In statistical analysis, staying within the expected ranges for certain values is crucial for accurate interpretations and further calculations.