A metallurgist measured the length, l l\,l mm, of a copper rod at various temperatures, ttt °C, and recorded the following results.
| ttt | lll |
|---|---|
| 20.4 | 2461.12 |
| 27.3 | 2461.41 |
| 32.1 | 2461.73 |
| 39.0 | 2461.88 |
| 42.9 | 2462.03 |
| 49.7 | 2462.37 |
| 58.3 | 2462.69 |
| 67.4 | 2463.05 |
The results were then coded such that x=tx = tx=t and y=l−2460.00y = l - 2460.00y=l−2460.00.
Calculate SxyS_{xy}Sxy and SxxS_{xx}Sxx.
(You may use ∑x2=15965.01\sum x^2 = 15965.01∑x2=15965.01 and ∑xy=757.467\sum xy = 757.467∑xy=757.467)
Find the equation of the regression line of y y\,y on x x\,x in the form y=a+bxy = a + bxy=a+bx.
Estimate the length of the rod at 40 °C.
Find the equation of the regression line of l l\,l on ttt.
Estimate the length of the rod at 90 °C.
Comment on the reliability of your estimate in part (e).
Practise Edexcel A Level Old Maths Correlation and Regression with exam-style questions for A Level Old Maths. 3 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.