S15QBUS5001 - Final Exam

I 2 marks write down the multiple linear regression

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(i) [2 marks] Write down the multiple linear regression model (“full model”) used by the business analyst and the model assumptions.

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QBUS5001 (2015 Semester 2) – Final Examination - 15 of 17 - (ii) [3 marks] Copy the ANOVA table to your answer booklet and complete the missing values. Correct your answers to four decimal places. (iii) [3 marks] From the parameter estimate tables, three independent variables, 6 X , 7 X and 8 X are identified to be potential unimportant variables. For each variable, explain why it may not be important in determining the salary. A senior business analyst uses the stepwise regression method and confirms that the three variables in (iii) can be removed from the model. Instruction: Go to Spreadsheet " Q4 " . Columns A to F contain the observed values of ,..., , , 2 1 X X Y and 5 X . Perform a multiple regression analysis on the data. Use α = 0.05 for all hypothesis tests. (iv) [1 mark] Write down the estimated linear regression equation of the new model (“reduced model”). (v) [2 marks] Find the coefficient of determination of this model and the correlation of the observed and predicted values of the log-salary. (vi) [2 marks] Comment briefly on the residual plot and draw a conclusion on the Chi- squared test for normality on the residuals. (vii) [4 marks] Perform a formal statistical test to show that the full model in (i) can be reduced to the model in (iv). You are given that 70 . 2 05 . 0 , 91 , 3 F . (viii) [3 marks] A 50-year-old male executive in a company has received 17 years of education and has 20 years of work experience. This company has an asset value of \$155 million and made a profit of 10 million in the previous year. This man is not a board member but he supervises 200 employees. Use the best multiple linear regression model to estimate his annual salary and construct a 95% prediction interval for his salary.
QBUS5001 (2015 Semester 2) – Final Examination - 16 of 17 - Question 5 (20 Marks) (a) [7 marks] A fund manager of ANZ bank in Hong Kong is interested in studying the linear relationships amongst four financial variables of the fifty constituent stocks of the Hang Seng Index (HSI). These four variables are Market - Market capitalisation of a stock; P/E Ratio - Price-to-earnings ratio of a stock; P/B Ratio - Price-to-book ratio of a stock; Yield - Yield (in %) of a stock. On a particular day, he collects the values of these four variables soon after the market closes. The correlation matrix is given below.

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