Spearman's rank correlation and comparison with Pearson's r Problem set A Answers

\(r_s = 0.810\)

\(r_s = −0.607\)

\(r_s = −0.833\)

\(r_s = −0.715\)

B: \(r = 0.90\), \(r_s = 1\)

1. (a) 2, 4.5, 1, 7, 3, 8, 4.5, 6
2. (b) \(r_s = −0.994\)
3. (c) \(r_s = −0.994\): a strong negative association. As distance increases, monthly rent tends to decrease. This does not show that one causes the other.

1. (a) The points fall from left to right along a curve that flattens out.
2. (b) The points always fall as x increases but lie on a curve, not near a straight line.
3. (c) \(r_s = −1\), \(r = −0.928\)

1. (a) \(r = 0.965\), \(r_s = 0.929\)
2. (b) \(r_s = 0.929\): a strong positive association. As hours of sunshine increases, ice creams sold tends to increase. This does not show that one causes the other.

1. (a) \(r = 0.527\), \(r_s = 0.857\)
2. (b) \(r = 0.998\), \(r_s = 1\)
3. (c) Pearson's r changed more (by 0.472, against 0.143 for \(r_s\)). The outlier is one far-out value, which pulls r a long way. Its rank can only be 1 to 8, so it changes \(r_s\) less.