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=60)(c=12, R=60)(c=12,R=60) 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.
