Moderate -0.8 This is a straightforward S1 linear regression question requiring standard calculations (Smt, Smm) from a small data table, finding the regression equation using formulas, and making a simple prediction. The data is clean, calculations are routine, and the interpretation questions are basic. Easier than average A-level as it's pure procedural application with no conceptual challenges.
An office has the heating switched on at 7.00 a.m. each morning. On a particular day, the temperature of the office, \(t { } ^ { \circ } \mathrm { C }\), was recorded \(m\) minutes after 7.00 a.m. The results are shown in the table below.
\(m\)
0
10
20
30
40
50
\(t\)
6.0
8.9
11.8
13.5
15.3
16.1
Calculate the exact values of \(S _ { m t }\) and \(S _ { m m }\).
Calculate the equation of the regression line of \(t\) on \(m\) in the form \(t = a + b m\).
Use your equation to estimate the value of \(t\) at 7.35 a.m.
State, giving a reason, whether or not you would use the regression equation in (b) to estimate the temperature
\begin{enumerate}
\item An office has the heating switched on at 7.00 a.m. each morning. On a particular day, the temperature of the office, $t { } ^ { \circ } \mathrm { C }$, was recorded $m$ minutes after 7.00 a.m. The results are shown in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
$m$ & 0 & 10 & 20 & 30 & 40 & 50 \\
\hline
$t$ & 6.0 & 8.9 & 11.8 & 13.5 & 15.3 & 16.1 \\
\hline
\end{tabular}
\end{center}
(a) Calculate the exact values of $S _ { m t }$ and $S _ { m m }$.\\
(b) Calculate the equation of the regression line of $t$ on $m$ in the form $t = a + b m$.\\
(c) Use your equation to estimate the value of $t$ at 7.35 a.m.\\
(d) State, giving a reason, whether or not you would use the regression equation in (b) to estimate the temperature\\
(i) at 9.00 a.m. that day,\\
(ii) at 7.15 a.m. one month later.\\
\hfill \mbox{\textit{Edexcel S1 2004 Q1 [13]}}