1 A biology student is carrying out an experiment to study the effect of a hormone on the growth of plant shoots. The student applies the hormone at various concentrations to a random sample of twelve shoots and measures the growth of each shoot. The data are illustrated on the scatter diagram below, together with the summary statistics for these data. The variables $x$ and $y$, measured in suitable units, represent concentration and growth respectively.\\
\includegraphics[max width=\textwidth, alt={}, center]{20fc4222-95c6-4b59-8e89-913dd988eb44-2_693_897_534_625}

$$n = 12 , \Sigma x = 30 , \Sigma y = 967.6 , \Sigma x ^ { 2 } = 90 , \Sigma y ^ { 2 } = 78926 , \Sigma x y = 2530.3 .$$
\begin{enumerate}[label=(\roman*)]
\item State which of the two variables $x$ and $y$ is the independent variable and which is the dependent variable. Briefly explain your answers.
\item Calculate the equation of the regression line of $y$ on $x$.
\item Use the equation of the regression line to calculate estimates of shoot growth for concentrations of\\
(A) 1.2,\\
(B) 4.3.

Comment on the reliability of each of these estimates.
\item Calculate the value of the residual for the data point where $x = 3$ and $y = 80$.
\item In further experiments, the student finds that using concentration $x = 6$ results in shoot growths of around $y = 20$. In the light of all the available information, what can be said about the relationship between $x$ and $y$ ?
\end{enumerate}

\hfill \mbox{\textit{OCR MEI S2 2008 Q1 [18]}}