A research scientist is investigating the relationship between the concentration of a new catalyst, c c\,c mg/L, and the resulting rate of a chemical reaction, R R\,R units/min. Data from 15 experiments were recorded and are summarised as follows:
∑c=150∑R=600∑c2=1625∑cR=6120SRR=250 \sum c = 150 \quad \sum R = 600 \quad \sum c^2 = 1625 \quad \sum cR = 6120 \quad S_{RR} = 250 ∑c=150∑R=600∑c2=1625∑cR=6120SRR=250Determine the values of SccS_{cc}Scc and ScRS_{cR}ScR for these experimental results.
Calculate, to 3 significant figures, the product moment correlation coefficient (PMCC) between the catalyst concentration and the reaction rate.
Determine the equation of the regression line of R R\,R on c c\,c in the form R=a+bcR = a + bcR=a+bc.
State, with a reason, which variable is the explanatory variable in this study.
Using the regression model from part (c), estimate: (i) the reaction rate when the catalyst concentration is 12 mg/L, (ii) the change in reaction rate associated with a 3 mg/L increase in concentration.
It was later discovered that the data point (c=12,R=50)(c=12, R=50)(c=12,R=50) was recorded incorrectly due to a sensor malfunction and is considered an outlier.
State, giving a reason, whether excluding this outlier would increase or decrease the value of the PMCC.
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.