Scatter diagrams and correlation Problem set B Answers

1. (a) (5.29, 14.5)
2. (b) Points plotted, mean point (5.29, 14.5) marked, a line through it with the points about evenly on each side

1. (a) r = −0.989
2. (b) Strong negative linear correlation

1. (a) r = 0.307
2. (b) No: not significant evidence of correlation

0.85

1. (a) r = 0.981
2. (b) Correlation does not imply causation: the size of the fire (the lurking variable) increases both

1. (a) r = −0.844
2. (b) Resort 1: r = 0.922; Resort 2: r = 0.933
3. (c) The ten points hide two groups. Within each resort a higher price goes with higher satisfaction, but Resort 2 is dearer and less liked. The resort is the lurking variable

1. (a) (12, 40)
2. (b) y = 3x + 4
3. (c) 31 litres

1. (a) P: r = 0.941, mean 4.93; Q: r = 0.941, mean 4.93
2. (b) P scatters about a rising line. Q grows faster and faster, 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 = x(16 − x) exactly. The relationship is perfect but not linear, and r measures only linear correlation