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.
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.