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A08ECMT3170-Exam

# A08ECMT3170-Exam - CODE 3926 Faculty of Economics Business...

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CODE 3926 Faculty of Economics & Business ECONOMETRICS & BUSINESS STATISTICS ECMT 3170 – Computational Econometrics Examination: Final Examination Semester/Year: Autumn Semester, 2008 Lecturer: Dr. Boris Choy Day/Date: Wednesday, 18 June, 2008 Time allowed: 3 hours plus 10 minutes reading time Start/End Time: 10:30am – 13:40pm Notes/Instructions to Candidates: Attempt all questions Each question is of equal value Answer each question on a new page Non-programmable calculators are permitted This examination requires the R and WinBUGS packages Computer files contain the R and WinBUGS codes are provided Page 1 of 19

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CODE 3926 Some Commonly Used Distributions 1. Uniform ) , ( ~ b a U Y 2 ] [ b a Y E + = 12 ) ( ] [ 2 a b Y V = a b b a y f = 1 ) , | ( b y a 2. Beta ) , ( ~ β α Be Y βα + = ] [ Y E ) 1 ( ) ( ] [ 2 + + + = αβ Y V 1 1 ) 1 ( ) , ( 1 ) , | ( = y y B y f 0 ; 0 ; 1 0 > > y 3. Normal ) , ( ~ 2 σθ N Y θ = ] [ Y E 2 ] [ σ = Y V 2 2 () 2 2 1 (|, ) 2 y fy e θσ πσ = 0 ; ; > < < < < y 4. Student- t ) , ( ~ t Y = ] [ Y E 2 [] (2 ) VY ασ for 2 > = 1 2 2 2 1( ) (|,,) 1 1 , 22 y B θσα σα + ⎛⎞ =+ ⎜⎟ ⎝⎠ 5. Gamma ) , ( ~ Ga Y = ] [ Y E 2 ] [ = Y V y e y y f Γ = 1 ) ( ) , | ( 0 ; 0 ; 0 > > > y 6. Inverse Gamma ) , ( ~ IG Y 1 ] [ = Y E ) 2 ( ) 1 ( ] [ 2 2 = αα Y V 1 1 (|,) y f ye y + = Γ 0 ; 0 ; 0 > > > y Scale Mixtures Distributions 1. Scale mixtures of normal form for the Student- t distribution ) , ( ~ , | μ t X i Î i i i N X λ μλ σμ 2 2 , ~ , , | and 2 , 2 ~ Ga i 2. Scale mixtures of uniform form the normal distribution ) , ( ~ , | 2 2 σμσ N X i Î ( ) i i i i u u U u X + , ~ , , | 2 and 2 , 2 ~ Ga u i Page 2 of 19
CODE 3926 Question 1 (20 marks) A group of students studied the relationship between the premium, Y , (in \$) of the motor vehicle comprehensive insurance in Sydney and a number of predictor variables. They obtained 30 quotations from the websites of three motor insurance companies and found that the following variables are significant in the linear regression analysis. = 1 X Insurance company (“1” = A, “2” = B, “3” = C) = 2 X Replacement value (\$) = 3 X Gender (“0” = Female, “1” = Male) The linear regression model adopted is i i i i i x x x y ε β + + + + = 3 3 2 2 1 1 0 , ) , 0 ( ~ 2 σε N i and the data are given in Table 1.1. (a) An ordinary least squares method is used in the regression analysis and the R output is given in Table 1.2. (i) [2 marks] Write down the estimated linear regression equation. How many percents of the total variation can be explained by this linear regression model? (ii) [1 mark] Given the same replacement value and same gender, which insurance company offers the least expensive comprehensive insurance? (iii) [1 mark] If a male driver and a female driver make a quote on the same vehicle replacement value at the same website, how much extra that the male driver is expected to pay? (iv) [1 mark] Standardized residual is used in the residual plot. How many outliers can be identified from this plot?

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A08ECMT3170-Exam - CODE 3926 Faculty of Economics Business...

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