10.1 Understanding correlations and regression

Answer the following questions, referring to Fig. 10.1. 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.
  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.
  5. On each scatterplot in Fig. 10.1 for which a linear relationship is appropriate (there are four!):
    1. Draw the ‘best’ straight regression line (where appropriate).
    2. From the line you drew in Part 5a. above, estimate the slope for each line.
    3. From the line you drew in Part 5a. above, estimate the intercept for each line.
    4. Then write down an estimate of the regression line equation.
Six different scatterplots

FIGURE 10.1: Six different scatterplots