Answer these questions. Step by step answers are recommended. Please ensure that your answers are precise.

A life assurance company is examining the force of mortality, /, , of a particular group of policyholders. It is thought that it is related to the age, x, of the policyholders by the formula: Hx = Bc* It is decided to analyse this assumption by using the linear regression model: Y, = a+ Bx; + &; where &; ~ N(0.') are independently distributed The summary results for eight ages were as follows: Age, x 30 32 34 36 38 40 42 44 Force of mortality. 5.84 6.10 6.48 7.05 7.87 Ux (x10*) 9.03 10.56 12.66 In 1 (3 s.f.) -7.45 -7.40 -7.34 -7.26 -7.15 -7.01 - 6.85 - 6.67 [x, = 296 Ex, =11,120 [In/x, =-57.129 [ (In #x, )? = 408.50 Ex, In My =-2,104.5 (i) (a) Apply a transformation to the original formula, My = Be*, to make it suitable for analysis by linear regression. Hence, write down expressions for Y, a and B in terms of Up , B and c. (b) Plot a graph of In /, against the age of the policyholder, x. Hence comment on the suitability of the regression model and state how this supports your transformation in part (a). [4] (ii) Use the data to obtain least squares estimates of B and c in the original formula. [3] (iii) (a) Calculate the coefficient of determination between In /, and x. Hence comment on the fit of the model to the data. (b) Complete the table of residuals and use them to comment on the fit. [5] Age, X 30 32 34 36 38 40 42 44 Residual, e; 0.08 -0.03 -0.06 0.02 0.09 (iv) Calculate a 95% confidence interval for the mean predicted response In //35 and hence obtain a 95% confidence interval for the mean predicted value of /35. [4] [Total 16]16 (a) Explain the implications for the weighted average cost of capital if a company's ordinary share price decreases. (b) Explain how this will affect the company's strategy for investing in capital projects. [5] 17 Explain the likely implications that will arise from a company preparing financial statements which do not comply with relevant accounting standards and the external auditor reporting that failure to comply in the audit report. [5] 18 Alpha is a quoted company. The company's directors consistently choose optimistic accounting policies in the belief that doing so increases their share price. Explain why it is unlikely that the share price will be overstated by this practice. [5]