S1 June 2006 Q3

EdexcelOld spec18 marksCorrelation & Regression

3. A metallurgist measured the length, \(l\) mm, of a copper rod at various temperatures, \(t\,{}^\circ\mathrm{C}\), and recorded the following results.

\(t\)\(l\)
20.42461.12
27.32461.41
32.12461.73
39.02461.88
42.92462.03
49.72462.37
58.32462.69
67.42463.05

The results were then coded such that \(x = t\) and \(y = l - 2460.00\).

(a) Calculate \(S_{xy}\) and \(S_{xx}\).
(You may use \(\Sigma x^2 = 15965.01\)   and   \(\Sigma xy = 757.467\)) (5)
(b) Find the equation of the regression line of \(y\) on \(x\) in the form \(y = a + bx\). (5)
(c) Estimate the length of the rod at \(40\,{}^\circ\mathrm{C}\). (3)
(d) Find the equation of the regression line of \(l\) on \(t\). (2)
(e) Estimate the length of the rod at \(90\,{}^\circ\mathrm{C}\). (1)
(f) Comment on the reliability of your estimate in part (e). (2)
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