Actuarial Science, linear models and forecasting

Location Pop. in thousands |Divorce rate per 100,000 Suicide rate per 100,000 A 679 30.4 11.6 B 1420 34.1 16.1 C 1349 17.2 9.3 D 296 26.8 9.1 E 6975 29.1 8.4 F 323 18.7 7.7 G 1200 32.6 11.3 H 633 32.5 8.4 (10 marks) (b) The following are the scores which 12 students obtained in the Internal and Final Examinations in a course in Linear Models. Internal Exam, x 71 49 80 73 93 85 58 82 64 32 89 80 Final Exam, y 83 62 76 77 74 48 78 76 51 73 389 i. Find the equation of the least squares line which will enable us predict the student's Final Examination score in this course on the basis of his or her score on the Internal Exam. (5 marks) ii. Predict the Final Exam score of a student who received an 84 in the Internal Exam. (2 marks) (c) The table below gives the experimental data for force (N) and velocity (m/s) for an object suspended in a wind tunnel. Veleocity, v (m/s) 10 20 30 40 50 60 70 80 Force F(N) 24 68 378 552 608 1218 831 1452 By taking velocity to be x and force to be y: i. Use the linear least-squares regression to determine the coefficients a and b in the function y = a + br that best fits the data. (5 marks) ii. Estimate the force when the velocity is 55 m/s. (1 mark) iii. calculate the standard deviation of errors, Se. ( marks) iv. find the error sum of squares, SSE. (2 marks) v. Find the total sum of squares, SST. (1 mark) vi. Find regression sum of squares, SSR. (2 marks) vii. Calculate the coefficient of determination. (2 marks)