As part of a statistics project, Gill collected data relating to the length of time, to the nearest minute, spent by shoppers in a supermarket and the amount of money they spent. Her data for a random sample of 10 shoppers are summarised in the table below, where t t\,t represents time and £m \pounds m\,£m the amount spent over £20.
| ttt (minutes) | £m\pounds m£m |
|---|---|
| 15 | -3 |
| 23 | 17 |
| 5 | -19 |
| 16 | 4 |
| 30 | 12 |
| 6 | -9 |
| 32 | 27 |
| 23 | 6 |
| 35 | 20 |
| 27 | 6 |
Write down the actual amount spent by the shopper who was in the supermarket for 15 minutes.
Calculate SttS_{tt}Stt, SmmS_{mm}Smm and StmS_{tm}Stm.
(You may use ∑t2=5478\sum t^2 = 5478∑t2=5478, ∑m2=2101\sum m^2 = 2101∑m2=2101, and ∑tm=2485\sum tm = 2485∑tm=2485)
Calculate the value of the product moment correlation coefficient between t t\,t and mmm.
Write down the value of the product moment correlation coefficient between t t\,t and the actual amount spent. Give a reason to justify your value.
Give an interpretation to both of these coefficients (0.914 and 0.178).
Suggest a practical reason why these two values are so different.
Practise Edexcel A Level Old Maths Correlation and Regression with exam-style questions for A Level Old Maths. 3 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.