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.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.