A chemical engineer is investigating the relationship between the reaction temperature TTT, in degrees Celsius, and the volume of byproduct VVV, in millilitres, produced in a specific industrial process. A sample of 50 reactions was monitored and the results were recorded.
The following summary statistics were calculated from these data:
∑T=1250,∑T2=32000,∑V=8000,∑TV=198400,SVV=4500 \sum T = 1250, \quad \sum T^2 = 32000, \quad \sum V = 8000, \quad \sum TV = 198400, \quad S_{VV} = 4500 ∑T=1250,∑T2=32000,∑V=8000,∑TV=198400,SVV=4500Find STTS_{TT}STT and STVS_{TV}STV.
Calculate, to 3 significant figures, the product moment correlation coefficient between TTT and VVV.
Give an interpretation of your coefficient in the context of the engineer's study.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.