Correlation and scatter diagrams
Answers are for parents and teachers.
1
Say direct, inverse or none: (a) the hours a lamp stays on and the electricity it uses; (b) the age of a bicycle and its resale price; (c) a pupil’s height and his mark in Arabic.
(a) direct; (b) inverse; (c) none.
2
A bakery records the number of workers x on a shift and the minutes y needed to pack 100 loaves (table). Plot the six dots (the vertical axis from 15 to 55) and describe the correlation.
| Workers x | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|
| Minutes y | 48 | 41 | 33 | 30 | 24 | 22 |
The dots fall in a narrow strip from the upper left to the lower right: a strong inverse correlation (r is close to −1; the formula gives about −0.98).
3
Put these coefficients in order from the strongest correlation to the weakest: 0.35, −0.8, 0.6, −0.1.
−0.8, 0.6, 0.35, −0.1 (sizes 0.8 > 0.6 > 0.35 > 0.1).
4
A researcher notices that towns with more cafés also have more taxis. Does opening a café bring taxis? Suggest a third factor.
Not necessarily. A bigger population can explain both more cafés and more taxis.
5
The pairs (1, 12), (2, 9), (3, 6), (4, 3) lie on one straight line that falls. What is r? Explain.
r = −1: all the dots are on one falling line, a perfect inverse correlation.