A chemical engineer is investigating the relationship between the temperature of a solvent, TTT (in ∘C^\circ\text{C}∘C), and the mass of a specific solute that dissolves in it, ddd (in grams). A random sample of 15 trials was conducted, and the following summary statistics were recorded:
∑T=975∑T2=64125∑d=420Sdd=560∑Td=27930\sum T = 975 \quad \sum T^2 = 64125 \quad \sum d = 420 \quad S_{dd} = 560 \quad \sum Td = 27930∑T=975∑T2=64125∑d=420Sdd=560∑Td=27930
Find the values of STTS_{TT}STT and STdS_{Td}STd.
Calculate, to 3 significant figures, the product moment correlation coefficient between TTT and ddd.
The engineer also measured the viscosity of the solvent, vvv, during these 15 trials. The product moment correlation coefficient between TTT and vvv was found to be −0.552-0.552−0.552.
Describe, giving a reason, the nature of the correlation you would expect to find between vvv and ddd.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 100 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 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.