Actuarial Science, Linear models and forecasting

(a) Question (a) (10 marks) The results from an experiment in which different masses were placed on a spring and the resulting length of the spring measured, are shown below. Mass, x (kg) 20 40 60 80 100 Length, y (em) 48 55.1 56.3 61.2 68 a Calculate Sex and Say (You may use Ex = 300 Ex = 22000 X =60 Exy = 18238 > = 16879.14 Ly = 288.6 y = 57.72) b Calculate the regression line of y on x. c Use your equation to predict the length of the spring when the applied mass is: i 58kg ii 130kg d Comment on the reliability of your predictions. (b) Question (b) (10 marks) Eight samples of carbon steel were produced with different percentages, c%, of carbon in them. Each sample was heated in a furnace until it melted and the temperature, m in "C, at which it melted was recorded. The results were coded such that x = 10c and y = m - 700 5 The coded results are shown in the table. Percentage of carbon, x 2 3 4 5 6 7 8 Melting point, J 35 28 24 16 15 12 8 a Calculate S,, and Sex (You may use ) = 204 and _xy = 478) b Find the regression line of y on x. c Estimate the melting point of carbon steel which contains 0.25% carbon