A chemical engineer is investigating the relationship between the concentration of a specific catalyst, CCC (grams per liter), and the resulting reaction rate, RRR (moles per second). The least squares regression line of R R\,R on C C\,C is found to be:
R=18.00−0.750CR = 18.00 - 0.750CR=18.00−0.750C
The following summary statistics were recorded from a sample of 15 trials:
∑R=180.0,∑R2=2460,∑C2=1380,n=15\sum R = 180.0, \quad \sum R^2 = 2460, \quad \sum C^2 = 1380, \quad n = 15∑R=180.0,∑R2=2460,∑C2=1380,n=15
Show that SRR=300S_{RR} = 300SRR=300.
Find SCCS_{CC}SCC.
Find the product moment correlation coefficient between C C\,C and RRR.
One lab assistant claims that when the catalyst concentration is 20 g/L, the reaction rate will be under 4.0 mol/s.
Explain how the lab assistant could have reached this conclusion.
Another researcher uses the formula
range=mean±2.2×standard deviation\text{range} = \text{mean} \pm 2.2 \times \text{standard deviation}range=mean±2.2×standard deviation
to estimate the interval of typical values for CCC.
Find estimates for the minimum and maximum values of C C\,C in these data using this formula.
Comment, giving a reason, on the reliability of the lab assistant's claim in part (d).
The engineer suggests using the regression line R=18.00−0.750CR = 18.00 - 0.750CR=18.00−0.750C to estimate the catalyst concentration required to achieve a reaction rate of 5 mol/s. Comment on this suggestion.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 100 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.