7 An environmentalist measures the mean concentration, $c$ milligrams per litre, of a particular chemical in a group of rivers, and the mean mass, $m$ pounds, of fish of a certain species found in those rivers. The results are given in the table.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
$c$ & 1.94 & 1.78 & 1.62 & 1.51 & 1.52 & 1.4 \\
\hline
$m$ & 6.5 & 7.2 & 7.4 & 7.6 & 8.3 & 9.7 \\
\hline
\end{tabular}
\end{center}

(i) State which, if either, of $m$ and $c$ is an independent variable.\\
(ii) Calculate the equation of the least squares regression line of $c$ on $m$.\\
(iii) State what effect, if any, there would be on your answer to part (ii) if the masses of the fish had been recorded in kilograms rather than pounds. ( $1 \mathrm {~kg} \approx 2.2$ pounds.)\\
(iv) The data is illustrated in the scatter diagram. Explain what is meant by 'least squares', illustrating your answer using the copy of this diagram in the Printed Answer Booklet.\\
\begin{tikzpicture}[>=Stealth]
% Define scale: x-axis from 1 to 2.1, y-axis from 6 to 10
\def\xscale{8}
\def\yscale{1.5}

% Draw axes
\draw[->] (0,0) -- (8.8,0) node[right] {$c$};
\draw[->] (0,0) -- (0,6.3);

% x-axis: ranges from 1 to 2, with gridlines
% Map: c=1 -> x=0, c=2 -> x=8, so x = (c-1)*8
% y-axis: m=6 -> y=0, m=10 -> y=6, so y = (m-6)*1.5

% x-axis tick marks and labels
\foreach \c in {1, 1.2, 1.4, 1.6, 1.8, 2} {
  \pgfmathsetmacro{\xpos}{(\c - 1)*8}
  \draw (\xpos, -0.1) -- (\xpos, 0.1);
  \node[below] at (\xpos, -0.1) {$\c$};
}

% y-axis tick marks and labels
\foreach \m in {6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10} {
  \pgfmathsetmacro{\ypos}{(\m - 6)*1.5}
  \draw (-0.1, \ypos) -- (0.1, \ypos);
  \pgfmathsetmacro{\mval}{\m}
  \node[left] at (-0.1, \ypos) {$\pgfmathprintnumber[fixed,precision=1]{\mval}$};
}

% y-axis label
\node[left] at (-0.1, 6.3) {$m$};

% Grid lines (light gray)
\foreach \c in {1, 1.2, 1.4, 1.6, 1.8, 2} {
  \pgfmathsetmacro{\xpos}{(\c - 1)*8}
  \draw[gray!30] (\xpos, 0) -- (\xpos, 6);
}
\foreach \m in {6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10} {
  \pgfmathsetmacro{\ypos}{(\m - 6)*1.5}
  \draw[gray!30] (0, \ypos) -- (8, \ypos);
}

% Data points: (c, m)
% (1.94, 6.5) -> (7.52, 0.75)
\fill (7.52, 0.75) circle (3pt);
% (1.78, 7.2) -> (6.24, 1.8)
\fill (6.24, 1.8) circle (3pt);
% (1.62, 7.4) -> (4.96, 2.1)
\fill (4.96, 2.1) circle (3pt);
% (1.51, 7.6) -> (4.08, 2.4)
\fill (4.08, 2.4) circle (3pt);
% (1.52, 8.3) -> (4.16, 3.45)
\fill (4.16, 3.45) circle (3pt);
% (1.4, 9.7) -> (3.2, 5.55)
\fill (3.2, 5.55) circle (3pt);

\end{tikzpicture}

\hfill \mbox{\textit{OCR Further Statistics AS 2018 Q7 [8]}}