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