Actuarial Science, linear models and forecasting

(a) Fit a second-order polynomial to the following data: X 1 2 3 4 5 6 7 8 9 10 Y 20.6 30.8 55 71.4 97.3 131.8 156.3 197.3 238.7 291.7 (7 marks) (b) A repair workshop finds that it is having a problem with a pressure gauge it uses. It decides to have the gauge checked by a specialist firm. The following data were obtained. Gauge reading, r (bars) 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 Correct reading, y (bars) 0.96 1.33 1.75 2.14 2.58 2.97 3.38 3.75 i. Show that Sry = 6.776 and find Ser. (2 marks) It is thought that a linear relationship of the form y = a + br could be used to describe these data. ii. Use linear regression to find the values of a and b, giving your answers to 3 signif- icant figures. (2 marks) iii. Draw a scatter diagram to represent these data and draw the regression line on your diagram. (2 marks) iv. The gauge shows a reading of 2 bars. Using the regression equation, work out what the correct reading should be. (2 marks)