A chemical engineer monitors the efficiency of an industrial reactor. Each batch begins with 250 kg of a liquid solvent. Over n=10n=10n=10 trial runs, the engineer records the mean operating temperature, xxx ∘C^\circ\text{C}∘C, and the mass of solvent that evaporates, y kgy\text{ kg}y kg. The following summary statistics are obtained:
∑x=850,∑y=120,∑xy=10425,Sxx=650,Syy=115 \sum x = 850, \quad \sum y = 120, \quad \sum xy = 10425, \quad S_{xx} = 650, \quad S_{yy} = 115 ∑x=850,∑y=120,∑xy=10425,Sxx=650,Syy=115Calculate the product moment correlation coefficient between x x\,x and yyy.
The mass of liquid solvent remaining in the reactor at the end of each run is w kgw\text{ kg}w kg. (i) Write down an equation for w w\,w in terms of yyy. (ii) State the value of the product moment correlation coefficient between w w\,w and yyy.
State the value of the product moment correlation coefficient between x x\,x and www.
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.