Section 12.5: Correlation

1. State examples of paired data.
2. Construct a scatter plot by-hand for a (small) data set of paired data.
3. Construct a scatter plot in R using plot().
4. Define the sample covariance, and explain why it quantifies linear association between two outcomes.
5. Define the sample correlation, and relate the sample correlation to the sample covariance.
6. State the main properties of the sample correlation in terms of its range, invariance to affine transformations of the data, and symmetry in \(X\) and \(Y\).
7. Define the population covariance and population correlation.
8. State the assumptions made on the population used in constructing the hypothesis tests and confidence intervals presented in this section for the population correlation.
9. State the null and alternative hypotheses for a claim about a population correlation.
10. State a test statistic for testing a claim about a population correlation, including its sampling distribution under the null hypothesis when the population is bivariate Gaussian.
11. Test a claim about a population correlation by either constructing a rejection region or computing a \(P\)-value for an appropriate test statistic.
12. Use cor.test() and interpret its output to perform hypothesis tests or construct (approximate) confidence intervals / bounds for a population correlation.