6 During a study of reaction times, each of a random sample of 12 people, aged between 40 and 80 years, was asked to react as quickly as possible to a stimulus displayed on a computer screen. Their ages, \(x\) years, and reaction times, \(y\) milliseconds, are shown in the table.

1. Calculate the equation of the least squares regression line of \(y\) on \(x\).
2. 1. Draw your regression line on the scatter diagram on page 16.
   2. Comment on what this reveals.
3. It was later discovered that the reaction times for persons E and H had been recorded incorrectly. The values should have been 820 and 590 respectively. After making these corrections, computations gave $$S _ { x x } = 1272 \quad S _ { x y } = 14760 \quad \bar { x } = 60 \quad \bar { y } = 720$$
   1. Using the symbol ⋅ , plot the correct values for persons E and H on the scatter diagram on page 16.
   2. Recalculate the equation of the least squares regression line of \(y\) on \(x\), and draw this regression line on the scatter diagram on page 16.
   3. Hence revise as necessary your comments in part (b)(ii).
      \includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-15_2484_1709_223_153}
      \section*{Reaction Times}
      \includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-16_1943_1301_351_292}
      \includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-17_2484_1707_223_155}