Exercise 4: Correlation Matrices (10 points)

In this next exercise we use correlation matrices to consider the correlations between some of the variables in our data. Once again, we've excluded the students who received an average of zero for their labs.

## pretest perusall labs tests ## pretest 1.00000000 0.1346194 0.07147391 0.1011485 ## perusall 0.13461936 1.0000000 0.69798568 0.5430982 ## labs 0.07147391 0.6979857 1.00000000 0.5975553 ## tests 0.10114845 0.5430982 0.59755528 1.0000000

1. What is the strongest association in the data (the biggest correlation)? What does it tell us?

2. Now find the correlation between lab scores and test scores. We visualized this relationship in the scatterplot, but now you can see the numbers behind it. How would you characterize the relationship between lab scores and test scores in terms of sign and size?

3. The r-squared value for the correlation between tests and labs is 0.36. What does this tell us?

4. Based on the correlations in the table, what advice might you give to students who want to succeed in this class?

5. Now imagine that there is a spurious correlation between Perusall scores and test scores: they are correlated with each other, but the relationship between them is entirely related to lab scores. How, if at all, would this new set of relationships change your advice if at all, and why?