5.4 Understanding correlations

Answer the following questions, referring to Fig. 5.8. The four correlation coefficients \(r\) are:

A: \(r = -0.95\) B: \(r = 0.12\) C: \(r = 0.75\) D: \(r = 0.94\)

For two plots, a correlation is not suitable.

  1. Determine which plot corresponds to which correlation coefficient (and for which two plots a correlation coefficient is not suitable).
  2. Think of an example of two quantitative variables that might produce a plot with a direction similar to Plot 1.
  3. Think of an example of two quantitative variables that might produce a plot with a direction similar to Plot 2.
  4. Compute the values of \(R^2\) for each plot identified in Part 1 of this question.
Six different scatterplots

FIGURE 5.8: Six different scatterplots