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=27930Find 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.
202 exam-style questions on Edexcel A Level Maths Regression, Correlation and Hypothesis Testing, covering 1.1 Exponential Models, 1.2 Measuring Correlation, and 1.3 Hypothesis Testing for Zero Correlation. Each one has a worked solution and a mark scheme showing where the marks go.