A biochemist is studying the effect of temperature, TTT in ∘C^\circ\text{C}∘C, on the rate of a catalytic reaction, VVV in units of 10−2 mol s−110^{-2} \text{ mol s}^{-1}10−2 mol s−1. Data from a random sample of 12 experiments are summarised as follows:
∑T=480∑T2=21200∑V=150∑V2=2025 \sum T = 480 \quad \sum T^2 = 21200 \quad \sum V = 150 \quad \sum V^2 = 2025 ∑T=480∑T2=21200∑V=150∑V2=2025and the regression line of VVV on TTT has the equation V=2.5+0.25TV = 2.5 + 0.25TV=2.5+0.25T.
Use the regression line to estimate the rate of reaction in mol s−1\text{mol s}^{-1}mol s−1 for an experiment conducted at 35∘C35^\circ\text{C}35∘C.
Find the values of STTS_{TT}STT and SVVS_{VV}SVV.
Calculate the product moment correlation coefficient between TTT and VVV.
A 13th experiment is performed. The temperature is recorded as 40∘C40^\circ\text{C}40∘C and the rate of reaction is measured as 0.125 mol s−10.125 \text{ mol s}^{-1}0.125 mol s−1.
Use the formula STV=∑(T−Tˉ)(V−Vˉ)S_{TV} = \sum (T - \bar{T})(V - \bar{V})STV=∑(T−Tˉ)(V−Vˉ) to demonstrate that the value of STVS_{TV}STV for the 13 experiments will be identical to its value for the original 12 experiments.
Determine the new equation of the regression line of VVV on TTT for the full set of 13 experiments.
Comment on the reliability of using the new regression line to estimate the rate of reaction for an experiment conducted at 120∘C120^\circ\text{C}120∘C, providing a justification for your answer.
