Selected answers are available in Sect. D.31.
Exercise 34.1 Draw a scatterplot with:
- A negative correlation coefficient, with the value of \(r\) very close to (but not equal to) \(-1\).
- A positive correlation coefficient, with the value of \(r\) very close to (but not equal to) \(+1\).
- A correlation coefficient very close to \(0\).
Exercise 34.2 A study (Myers (1990), p. 75) of American footballers measured the right-leg strengths \(x\) of 13 players (using a weight lifting test), and the distance \(y\) they punted a football (with their right leg) (Fig. 34.11).
- The value of the correlation coefficient is 0.881. Compute the value of \(R^2\), and explain what this means.
- jamovi was used to study the correlation (Fig. 34.12). Using this output, perform a hypothesis test to determine if a correlation exists between punting distance and right-leg strength.
- Using the plot, estimate the value of \(r\).
- The value of \(R^2\) is 99.29%. What is the value of \(r\)? (Hint: Be careful!)
- Would you expect the \(P\)-value testing \(H_0\): \(\rho=0\) to be small or large? Explain.
- Would the test be statistically valid?