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Contents 1 Introduction 1 2 Linear Regression Model 3 2.1 Method of moment estimate (MME) . . . . . . . . . . 3 2.2 Method of Least Squares Estimate . . . . . . . . . . . 5 3 Skew-Normal Distribution 7 3.1 The errors is correlated . . . . . . . . . . . . . . . . . 7 3.2 The errors is independent . . . . . . . . . . . . . . . . 9 4 Simulation study 11 4.1 Normal case . . . . . . . . . . . . . . . . . . . . . . . 11 4.2 Skew-normal case . . . . . . . . . . . . . . . . . . . . 13 4.3 Independent Skew-normal case . . . . . . . . . . . . . 15 5 Example 23 5.1 Example 1: House prices in Iowa . . . . . . . . . . . . 23 5.2 Example 2: University Admissions . . . . . . . . . . . 24 6 Conclusion 28 Reference 30
List of Figures 4.1 n = 50, ε ~iid N(0, 9), β= (1, 0.01)' . . . . . . . . . . . 13 4.2 n = 50, ε ~iid N(0, 9); β = (0.01, 0.01)' . . . . . . . . . 14 4.3 n = 100, ε~SN_100(0, 9 x I_100, 1), β = (1,2)' . . . . . 16 4.4 n = 100, ε~SN_100(0, 9 x I_100, 1), β = (1, 0.01)' . . . 17 4.5 n = 20, ε~iid SN(0, 3, 1), β = (0.01, 0.01)' . . . . . . . 18 4.6 n = 20, ε~iid SN(0, 3, 1), β = (1, 2)' . . . . . . . . . . 19 4.7 n = 50, ε~iid SN(0, 3, 1), β = (0.01, 0.01)' . . . . . . . 19 4.8 n = 50, ε~iid SN(0, 3, 1), β = (1, 2)' . . . . . . . . . . 20 4.9 n = 100, ε~iid SN(0, 3, 1), β = (0.01, 0.01)' . . . . . . 20 4.10 n = 100, ε~iid SN(0, 3, 1), β = (1, 2)' . . . . . . . . . . 21 4.11 n = 300, ε~iid SN(0, 3, 1), β = (0.01, 0.01)' . . . . . . 21 4.12 n = 300, ε~iid SN(0, 3, 1), β = (1, 2)' . . . . . . . . . . 22 5.1 Diagnostic for residuals at house data . . . . . . . . . 26 5.2 Diagnostic for residuals at GPA data . . . . . . . . . 27
List of Tables 4.1 ε ~iid N(0, 9), β = (1, 2)' . . . . . . . . . . . . . . . . . 12 4.2 ε ~iid N(0, 9), β = (1, 0.01)' . . . . . . . . . . . . . . . 12 4.3 ANOVA test on simulation data with ε ~iid N(0, 9), β = (1; 2)' , n = 300 . . . . . . . . . . . . . . . . . . . . . 12 4.4 ANOVA test on simulation data with ε ~iid N(0, 9), β = (1, 0.01)' , n = 300 . . . . . . . . . . . . . . . . . . . 13 4.5 ε ~ SN_100(0, 9 x I_100, 1), β = (1, 2)' . . . . . . . . . . 14 4.6 ε ~ SN_100(0, 9 x I_100, 1), β = (1, 0.01)' . . . . . . . . 15 4.7 ANOVA test on simulation data with ε ~ SN_100(0. 9 x I_100, 1), β = (1, 2)' , n = 300 . . . . . . . . . . . . . . 15 4.8 ANOVA test on simulation data with ε ~ SN_100(0, 9 x I_100, 1), β = (1, 0.01)' , n = 300 . . . . . . . . . . . . . 16 4.9 ε ~iid SN(0, 3, 1), β = (1, 2)' . . . . . . . . . . . . . . . 17 4.10 ε ~iid SN(0, 3, 1), β = (1, 0.01)' . . . . . . . . . . . . . 17 4.11 ANOVA test on simulation data with ε ~iid SN(0, 3, 1), β = (1; 2)' , n = 300 . . . . . . . . . . . . . . . . . . . . . 18 4.12 ANOVA test on simulation data with ε ~iid SN(0, 3, 1), β = (1, 0.01)' ; n = 300 . . . . . . . . . . . . . . . . . . . 18 5.1 Parameter estimates of house prices data. . . . . . . . 24 5.2 Parameter estimates of university admissions data. . . 26
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