Scatter diagrams and correlation Problem set A Answers

1. (a) (6.71, 5.14)
2. (b) Points plotted, mean point (6.71, 5.14) marked, a line through it with the points about evenly on each side

1. (a) r = −0.948
2. (b) Strong negative linear correlation

1. (a) r = −0.873
2. (b) Yes: significant evidence of negative correlation

−0.95

1. (a) r = 0.988
2. (b) Correlation does not imply causation: hot, sunny weather (the lurking variable) increases both

1. (a) r = −0.807
2. (b) Firm 1: r = 0.940; Firm 2: r = 0.887
3. (c) The ten points hide two groups. Within each firm more experience means a higher salary, but the charity pays much less. The firm is the lurking variable

1. (a) (10, 24)
2. (b) y = −2x + 44
3. (c) 32 cm

1. (a) P: r = −0.959, mean 6.92; Q: r = −0.959, mean 6.92
2. (b) P scatters about a falling line. Q falls slowly then quickly, a curve. The same r and mean hide different patterns: r measures only linear correlation, so always plot the data

1. (a) r = 0
2. (b) No: y = 9 − x² exactly. The relationship is perfect but not linear, and r measures only linear correlation