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=18.00−0.750C R = 18.00 - 0.750C R=18.00−0.750CThe 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=15Show 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 deviationto 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.
202 exam-style questions on Edexcel A Level Maths Regression, Correlation and Hypothesis Testing, covering 1.1 Exponential Models, 1.2 Measuring Correlation, and 1.3 Hypothesis Testing for Zero Correlation. Each one has a worked solution and a mark scheme showing where the marks go.