a77a79a68a69a76a73a78a71 a84a72a69 a80a82a69a70a69a82a69a78a67a69 a79a70 a87a73a78a69 a81a85a65a76a73a84a89 a85a83a73a78a71 a76a79a71a73a83a84a73a67 a82a69a71a82a69a83a83a73a79a78 a84a69a67a72a78a73a81a85a69a83 a66a65a83a69a68 a79a78 a80a72a89a83a73a67a79a67a72a69a77a73a67a65a76 a80a82a79a80a69a82a84a73a69a83 a98a121 a80a101a114a112a101a116a117a97a108 a79a112a111a107a117 a65a103a121a101a109a97a110a103 a83a117a98a109a105a116a116a101a100 a105a110 a80a97a114a116a105a97a108 a70a117a108a28a108a108a109a101a110a116 a111a102 a116a104a101 a82a101a113a117a105a114a101a109a101a110a116a115 a102a111a114 a116a104a101 a68a101a103a114a101a101 a111a102 a77a65a83a84a69a82 a79a70 a83a67a73a69a78a67a69 a105a110 a77a97a116a104a101a109a97a116a105a99a115 a89a79a85a78a71a83a84a79a87a78 a83a84a65a84a69 a85a78a73a86a69a82a83a73a84a89 a68a101a99a101a109a98a101a114a44 a50a48a49a48 Modeling the Preference of Wine Quality Using Logistic Regression Techniques Based on Physicochemical Properties Perpetual Opoku Agyemang I hereby release this thesis to the public. I understand that this thesis will be made available from the OhioLINK ETD Center and the Maag Library Circulation Desk for public access. I also authorize the University or other individuals to make copies of this thesis as needed for scholarly research. Signature: Perpetual Opoku Agyemang, Student Date Approvals: Dr Thomas P. Wakefield, Thesis Advisor Date Dr. G. Andy Chang, Committee Member Date Dr. G. Jay Kerns, Committee Member Date Peter J. Kasvinsky, Dean of School of Graduate Studies and Research Date a65a66a83a84a82a65a67a84 a87a105a110a101 a113a117a97a108a105a116a121 a105a115 a97a116a116a114a105a98a117a116a101a100 a116a111 a109a97a110a121 a100a105a27a101a114a101a110a116 a102a97a99a116a111a114a115 a111a102 a116a104a101 a119a105a110a101 a119a111a114a107a105a110a103 a99a111a108a108a101a99a116a105a118a101a108a121 a116a111 a98a101a97a114 a97 a115a101a110a115a111a114a121 a101a120a112a101a114a105a101a110a99a101 a116a104a97a116 a105a115 a110a111a116 a97a112a112a97a114a101a110a116 a102a114a111a109 a99a111a110a115a105a100a101a114a105a110a103 a116a104a101a115a101 a99a111a109a112a111a110a101a110a116a115 a105a110 a105a115a111a108a97a45 a116a105a111a110a46 a84a104a101 a118a97a114a105a111a117a115 a99a104a101a109a105a99a97a108 a99a111a109a112a111a110a101a110a116a115 a105a110 a119a105a110a101 a103a105a118a101 a116a104a101 a119a105a110a101 a105a116a115 a100a105a115a116a105a110a99a116 a116a97a115a116a101 a97a110a100 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a116a104a101 a99a111a101a30a99a105a101a110a116a115 a102a111a114 a116a104a101 a118a97a114a105a97a98a108a101a115 a105a110 a116a104a101 a101a113a117a97a116a105a111a110a115 a100a111 a110a111a116 a100a105a27a101a114 a115a105a103a110a105a28a99a97a110a116a108a121 a105a102 a116a104a101a121 a119a101a114a101 a101a115a116a105a109a97a116a101a100 a105a110a100a105a118a105a100a117a97a108a108a121a46 a84a104a101 a105a110a116a101a114a99a101a112a116a115 a100a105a27a101a114a44 a98a117a116 a116a104a101 a115a108a111a112a101a115 a97a114a101 a102a117a110a100a97a109a101a110a116a97a108a108a121 a116a104a101 a115a97a109a101a46 a65a110 a111a114a100a105a110a97a108 a108a111a103a105a115a116a105a99 a114a101a103a114a101a115a115a105a111a110 a109a111a100a101a108 a105a115 a103a105a118a101a110 a98a121 ln P(a69a118a101a110a116) 1 P(a69a118a101a110a116) = 0 + 1X1 + 2X2 + 3X3 + + kXk a119a104a101a114a101 a116a104a101 a113a117a97a110a116a105a116a121 a116a111 a116a104a101 a108a101a102a116 a111a102 a116a104a101 a101a113a117a97a108 a115a105a103a110 a105a115 a99a97a108a108a101a100 a108a111a103a105a116 a114a101a112a114a101a115a101a110a116a105a110a103 a116a104a101 a100a101a112a101a110a100a101a110a116 a118a97a114a105a97a98a108a101a44P a105a115 a116a104a101 a112a114a111a98a97a98a105a108a105a116a121a44X1;X2;:::;Xk a97a114a101 a116a104a101 a105a110a100a101a112a101a110a100a101a110a116 a118a97a114a105a97a98a108a101a115a44 0 a105a115 a116a104a101 a105a110a116a101a114a99a101a112a116 a97a110a100 1; 2;:::; k a97a114a101 a116a104a101 a115a108a111a112a101a115a46 a76a111a103a105a116 a105a115 a116a104a101 a108a111a103 a111a102 a116a104a101 a111a100a100a115 a116a104a97a116 a97a110 a101a118a101a110a116 a111a99a99a117a114a115a46 a84a104a101 a111a100a100a115 a116a104a97a116 a97a110 a101a118a101a110a116 a111a99a99a117a114a115 a105a115 a116a104a101 a114a97a116a105a111 a111a102 a116a104a101 a112a114a111a98a97a98a105a108a105a116a121 a116a104a97a116 a116a104a101 a101a118a101a110a116 a111a99a99a117a114a115 a116a111 a116a104a101 a112a114a111a98a97a98a105a108a105a116a121 a116a104a97a116 a116a104a101 a101a118a101a110a116 a100a111a101a115 a110a111a116 a111a99a99a117a114a46 a84a104a101 a101a120a112a101a99a116a101a100 a118a97a108a117a101a115 a102a111a114 a116a104a101 a111a114a100a105a110a97a108 a108a111a103a105a116 a109a111a100a101a108 a97a114a101 a114a101a112a108a105a99a97a116a105a111a110a115 a111a102 a116a104a101 a112a114a101a100a105a99a116a101a100 a112a114a111a98a97a98a105a108a105a116a105a101a115 a102a111a114 a101a97a99a104 a99a97a116a101a103a111a114a121 a97a110a100 a103a105a118a101a110 a98a121 E(Y = j) = exp( j Xi )1 + exp( j Xi ) exp( j 1 Xi )1 + exp( j 1 Xi ) a119a104a101a114a101 j a114a101a112a114a101a115a101a110a116a115 a116a104a101 ja116a104 a99a97a116a101a103a111a114a121a46 a84a104a101 a112a114a101a100a105a99a116a101a100 a118a97a108a117a101 a105a115 a100a114a97a119a110 a102a114a111a109 a116a104a101 a108a111a103a105a116 a97a110a100 a111a98a115a101a114a118a101a100 a97a115 a111a110a101 a111a102 a116a104a101 J a100a105a115a99a114a101a116a101 a111a117a116a45 a99a111a109a101a115a46 a84a104a101 a100a105a27a101a114a101a110a99a101 a105a110 a101a97a99a104 a111a110a101 a111a102 a116a104a101 a112a114a101a100a105a99a116a101a100 a112a114a111a98a97a98a105a108a105a116a105a101a115 a105a115 a103a105a118a101a110 a98a121 P(Y = jjXi) P(Y = jjX) a49a48 a102a111a114 j = 1;2;:::Ja46 a65a115 a97 a99a111a110a116a114a97a115a116 a116a111 a115a105a109a112a108a101 a108a105a110a101a97a114 a114a101a103a114a101a115a115a105a111a110a44 a119a101 a100a105a100 a110a111a116 a117a115a101 a116a104a101 R a115a113a117a97a114a101 a105a110 a111a114a100a105a110a97a108 a114a101a103a114a101a115a45 a115a105a111a110 a98a101a99a97a117a115a101 R a115a113a117a97a114a101 a112a114a111a118a105a100a101a115 a105a110a102a111a114a109a97a116a105a111a110 a97a98a111a117a116 a104a111a119 a109a117a99a104 a118a97a114a105a97a110a99a101 a105a115 a101a120a112a108a97a105a110a101a100 a98a121 a116a104a101 a105a110a100a101a112a101a110a100a101a110a116 a118a97a114a105a97a98a108a101a46 a51a46a54 a65a115a115a117a109a112a116a105a111a110a115 a111a102 a79a114a100a105a110a97a108 a76a111a103a105a115a116a105a99 a82a101a103a114a101a115a115a105a111a110 a87a101 a119a105a108a108 a110a111a119 a105a116a101a109a105a122a101 a116a104a101 a97a115a115a117a109a112a116a105a111a110a115 a111a102 a111a114a100a105a110a97a108 a108a111a103a105a115a116a105a99 a114a101a103a114a101a115a115a105a111a110a46 a79a110a101 a100a101a112a101a110a100a101a110a116 a118a97a114a105a97a98a108a101 a84a104a101a114a101 a115a104a111a117a108a100 a98a101 a110a111 a109a117a108a116a105a112a108a101 a100a101a112a101a110a100a101a110a116 a118a97a114a105a97a98a108a101a115 a105a110 a111a114a100a105a110a97a108 a114a101a45 a103a114a101a115a115a105a111a110a46 a80a97a114a97a108a108a101a108 a108a105a110a101a115 a97a115a115a117a109a112a116a105a111a110 a84a104a101a114a101 a115a104a111a117a108a100 a98a101 a111a110a101 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a119a97a115 a99a104a101a99a107a101a100 a98a121 a101a120a97a109a105a110a105a110a103 a116a104a101 a115a116a97a110a100a97a114a100 a101a114a114a111a114a115 a102a111a114 a116a104a101 a101a115a116a105a109a97a116a101a100 a99a111a101a30a99a105a101a110a116a115a46 a65 a115a116a97a110a100a97a114a100 a101a114a114a111a114 a98a105a103a103a101a114 a116a104a97a110 2:0 a105a110a100a105a99a97a116a101a115 a110a117a109a101a114a105a99a97a108 a112a114a111a98a108a101a109a115a46 a84a97a98a108a101 a51 a99a111a110a116a97a105a110a115 a116a104a101 a87a97a108a100 a115a116a97a116a105a115a116a105a99a44 a116a104a101 a101a115a116a105a109a97a116a101a100 a99a111a101a30a99a105a101a110a116a115a44 a116a104a101 a115a116a97a110a100a97a114a100 a101a114a114a111a114a115 a102a111a114 a116a104a101 a99a111a101a30a99a105a101a110a116a115 a97a110a100 a97a115a115a111a99a105a97a116a101a100 pa45a118a97a108a117a101a115 a102a111a114 a116a104a101 a109a111a100a101a108a46 a84a104a101 a101a115a116a105a109a97a116a101a115 a108a97a98a101a108a101a100 a16a84a104a114a101a115a104a111a108a100a17 a97a114a101 ja44 a116a104a101 a105a110a116a101a114a99a101a112a116 a101a113a117a105a118a97a108a101a110a116 a116a101a114a109a115a46 a84a104a101 a101a115a116a105a109a97a116a101a115 a108a97a98a101a108a101a100 a16a76a111a99a97a116a105a111a110a17 a97a114a101 a111a102 a109a111a115a116 a105a110a116a101a114a101a115a116a46 a84a104a101a121 a97a114a101 a116a104a101 a99a111a101a30a99a105a101a110a116a115 a102a111a114 a116a104a101 a112a114a101a100a105a99a116a111a114 a118a97a114a105a97a98a108a101a115a46 a67a111a110a115a105a100a101a114a105a110a103 a97a108a108 a116a104a101 a105a110a100a101a112a101a110a100a101a110a116 a118a97a114a105a97a98a108a101a115 a97a116 95% a99a111a110a28a100a101a110a99a101 a105a110a116a101a114a118a97a108a44 a119a101 a114a101a97a108a105a122a101a100 a116a104a101a121 a97a114a101 a97a108a108 a115a116a97a116a105a115a116a105a99a97a108a108a121 a115a105a103a110a105a28a99a97a110a116 a115a105a110a99a101 a97a108a108 a116a104a101 pa45a118a97a108a117a101a115 a97a114a101 a108a101a115a115 a116a104a97a110 = :05a46 a77a111a114a101a111a118a101a114a44 a110a111a110a101 a111a102 a116a104a101 a115a116a97a110a100a97a114a100 a101a114a114a111a114a115 a101a120a99a101a101a100a101a100 2:0a44 a72a101a110a99a101a44 a116a104a101a114a101 a119a97a115 a110a111 a109a117a108a116a105a99a111a108a108a105a110a101a97a114a105a116a121 a112a114a111a98a108a101a109a46 a76a101a116 Aa61a65a108a99a111a104a111a108a44 Va61a86a111a108a97a116a105a108a101 a65a99a105a100a105a116a121a44 Sa61a83a117a108a112a104a97a116a101a44 Ta61a84a111a116a97a108 a83a117a108a102a117a114 a68a105a111a120a105a100a101a44 Fa61a70a114a101a101 a83a117a108a45 a102a117a114 a68a105a111a120a105a100a101a44 Ca61a67a104a108a111a114a105a100a101 a97a110a100 Pa61a112a72a46 a83a105a110a99a101 a113a117a97a108a105a116a105a101a115 3 a97a110a100 4 a97a114a101 a110a111a116 a115a116a97a116a105a115a116a105a99a97a108a108a121 a115a105a103a110a105a28a99a97a110a116a44 a116a104a101 a109a111a100a101a108 a102a111a114 a116a104a101 a28a102a116a104 a113a117a97a108a105a116a121 a105a115 a116a104a101a110 a119a114a105a116a116a101a110 a97a115 P(Y = a81a117a97a108a105a116a121 a53a124a88) = exp g(X) 1 + expg(X) a119a104a101a114a101 g(X) = 3:981 +:884A 3:070V + 2:784S :012T 5:778C 1:312P +:017F: a49a57 a69a115a116a105a109a97a116a101 a83a116a97a110a100a97a114a100 a69a114a114a111a114 a87a97a108a100 a83a105a103 a84a104a114a101a115a104a111a108a100 a113a117a97a108a105a116a121= 3 1:638 a49a46a54a52a48 a46a50a48a48 a113a117a97a108a105a116a121= 4 a46a50a55a57 a46a48a53a48 a46a56a50a51 a113a117a97a108a105a116a121= 5 a51a46a57a56a49 a49a48a46a50a51a54 a46a48a48a49 a113a117a97a108a105a116a121= 6 a54a46a56a51a48 a50a57a46a54a52a57 a46a48a48a48 a113a117a97a108a105a116a121= 7 a57a46a56a51a52 a53a56a46a55a54a55 a46a48a48a48 a76a111a99a97a116a105a111a110 a65a108a99a111a104a111a108 a46a56a56a52 a46a48a52a53 a50a52a53a46a52a49a54 a46a48a48a48 a86a111a108a97a116a105a108a101 a65a99a105a100a105a116a121 3:070 a46a52a53a54 a56a57a46a56a49a54 a46a48a48a48 a83a117a108a112a104a97a116a101 a50a46a55a56a52 a49a46a55a53 a54a54a46a49a57a52 a46a48a48a48 a84a111a116a97a108 a83a117a108a102a117a114 a68a105a111a120a105a100a101 :012 a49a46a57a55a52 a51a49a46a50a48a51 a46a48a48a48 a67a104a108a111a114a105a100a101 5:778 a46a48a57a55 a50a49a46a49a50a54 a46a48a48a48 a112a72 1:312 a49a46a50a53a54 a49a50a46a57a53a50 a46a48a48a48 a70a114a101a101 a83a117a108a102a117a114 a68a105a111a120a105a100a101 a46a48a49a55 a46a57a55a53 a54a46a56a52a54 a46a48a48a57 a84a97a98a108a101 a51a58 a80a97a114a97a109a101a116a101a114 a69a115a116a105a109a97a116a101a115 a102a111a114 a82a101a100 a87a105a110a101 a84a104a101a114a101a102a111a114a101a44 P(Y = a81a117a97a108a105a116a121 a53a124a88) = exp 3:981+:884A 3:070V +2:784S :012T 5:778C 1:312P+:017F 1 + exp3:981+:884A 3:070V +2:784S :012T 5:778C 1:312P+:017F: a84a104a101 a115a105a120a116a104 a113a117a97a108a105a116a121 a104a97a115 a116a104a101 a109a111a100a101a108 P(Y = a81a117a97a108a105a116a121 a54a124a88) = exp g(X) 1 + expg(X) a119a104a101a114a101 g(X) = 6:830 +:884A 3:070V + 2:784S :012T 5:778C 1:312P +:017F: a72a101a110a99a101a44 P(Y = a81a117a97a108a105a116a121 a54a124a88) = exp 6:830+:884A 3:070V +2:784S :012T 5:778C 1:312P+:017F 1 + exp6:830+:884A 3:070V +2:784S :012T 5:778C 1:312P+:017F: a84a104a101 a115a101a118a101a110a116a104 a113a117a97a108a105a116a121 a104a97a115 a116a104a101 a115a97a109a101 a109a111a100a101a108 a98a117a116 a119a105a116a104 a97 a100a105a27a101a114a101a110a116 a105a110a116a101a114a99a101a112a116a46 a65a115 a97a110 a105a110a116a101a114a112a114a101a116a97a116a105a111a110 a111a102 a116a104a101 a99a111a101a30a99a105a101a110a116a115 a105a110 a116a104a101 a109a111a100a101a108a44 a102a111a114 a101a118a101a114a121 a105a110a99a114a101a97a115a101 a111a102 q a103a114a97a109a115 a111a102 a112a111a116a97a115a115a105a117a109 a115a117a108a112a104a97a116a101 a112a101a114 a99a117a98a105a99 a100a101a99a105a109a101a116a101a114 a111a102 a115a117a108a112a104a97a116a101 a99a111a110a116a101a110a116 a111a102 a114a101a100 a119a105a110a101a44 a116a104a101 a108a111a103 a111a102 a111a100a100a115 a40a99a104a97a110a99a101a41 a111a102 a98a101a105a110a103 a105a110 a116a104a101 a28a102a116a104 a113a117a97a108a105a116a121 a108a101a118a101a108 a105a110a99a114a101a97a115a101a115 a98a121 2:784qa46 a84a104a101 a108a111a103 a111a100a100a115 a99a104a97a110a103a101 a105a115 q a97a110a100 a116a104a101 a97a115a115a111a99a105a97a116a101a100 a111a100a100a115 a114a97a116a105a111 a105a115 exp (q )a44 a119a104a101a114a101 a105a115 a116a104a101 a101a115a116a105a109a97a116a101a100 a99a111a101a30a99a105a101a110a116 a102a111a114 a116a104a101 a112a114a101a100a105a99a116a111a114 a118a97a114a105a97a98a108a101 a115a117a108a112a104a97a116a101a46 a50a48 a67a104a105a45a115a113a117a97a114a101 a83a105a103 a80a101a97a114a115a111a110 a55a50a56a55a46a50a51a56 a46a48a48a48 a68a101a118a105a97a110a99a101 a51a48a56a48a46a56a52a56 a49a46a48a48a48 a84a97a98a108a101 a52a58 a71a111a111a100a110a101a115a115a45a111a102a45a70a105a116 a102a111a114 a82a101a100 a87a105a110a101 a52a46a49a46a54 a71a111a111a100a110a101a115a115a45a111a102a45a70a105a116 a83a116a97a116a105a115a116a105a99a115 a102a111a114 a82a101a100 a87a105a110a101 a85a115a105a110a103 a116a104a101 a111a98a115a101a114a118a101a100 a97a110a100 a101a120a112a101a99a116a101a100 a102a114a101a113a117a101a110a99a105a101a115a44 a119a101 a99a111a109a112a117a116a101a100 a116a104a101 a80a101a97a114a115a111a110 a97a110a100 a68a101a118a105a97a110a99a101 a103a111a111a100a110a101a115a115a45a111a102a45a28a116 a109a101a97a115a117a114a101a115a46 a84a104a101 a80a101a97a114a115a111a110 a103a111a111a100a110a101a115a115a45a111a102a45a28a116 a115a116a97a116a105a115a116a105a99 a105a115 X2HL = gX i=1 (Oi Ni i)2 Ni i(1 i) a119a104a101a114a101 Ni a105a115 a116a104a101 a116a111a116a97a108 a102a114a101a113a117a101a110a99a121 a111a102 a115a117a98a106a101a99a116a115 a105a110 a116a104a101 ia116a104 a103a114a111a117a112a44 Oi a105a115 a116a104a101 a111a98a115a101a114a118a101a100 a110a117a109a98a101a114 a111a102 a99a97a115a101a115 a105a110 a116a104a101ia116a104 a103a114a111a117a112a44 a97a110a100 i a105a115 a116a104a101 a97a118a101a114a97a103a101 a101a115a116a105a109a97a116a101a100 a112a114a111a98a97a98a105a108a105a116a121 a111a102 a97a110 a101a118a101a110a116 a111a117a116a99a111a109a101 a102a111a114 a116a104a101 ia116a104 a103a114a111a117a112a46 a76a97a114a103a101 a118a97a108a117a101a115 a111a102 X2HL a115a104a111a119 a97 a108a97a99a107 a111a102 a28a116 a111a102 a116a104a101 a109a111a100a101a108a46 a73a116 a105a115 a97 a99a104a105a45a115a113a117a97a114a101 a100a105a115a116a114a105a98a117a116a105a111a110 a119a105a116a104 (n g) a100a101a103a114a101a101a115 a111a102 a102a114a101a101a100a111a109a44 a119a104a101a114a101 n a105a115 a116a104a101 a115a97a109a112a108a101 a115a105a122a101 a97a110a100 g a105a115 a116a104a101 a110a117a109a98a101a114 a111a102 a99a97a116a101a103a111a114a105a101a115a46 a84a104a101 a100a101a118a105a97a110a99a101 a103a111a111a100a110a101a115a115a45a111a102a45a28a116 a115a116a97a116a105a115a116a105a99 a105a115 D = 2 nX i=1 nX j=1 Oij ln O ij Eij a119a104a101a114a101 Oij a105a115 a116a104a101 a111a98a115a101a114a118a101a100 a118a97a108a117a101 a102a111a114 a116a104a101 a118a97a114a105a111a117a115 a99a97a116a101a103a111a114a105a101a115 a97a110a100 Eij a105a115 a116a104a101 a101a120a112a101a99a116a101a100 a118a97a108a117a101a46 a84a104a101a115a101 a116a119a111 a103a111a111a100a110a101a115a115a45a111a102a45a28a116 a115a116a97a116a105a115a116a105a99a115 a97a114a101 a117a115a101a100 a111a110a108a121 a102a111a114 a109a111a100a101a108a115 a116a104a97a116 a104a97a118a101 a114a101a108a97a116a105a118a101a108a121 a108a97a114a103a101 a101a120a112a101a99a116a101a100 a118a97a108a117a101a115 a105a110 a101a97a99a104 a99a101a108a108a46 a83a105a110a99a101 a119a101 a104a97a100 a109a97a110a121 a99a111a110a116a105a110a117a111a117a115 a105a110a100a101a112a101a110a100a101a110a116 a118a97a114a105a97a98a108a101a115a44 a119a101 a104a97a100 a109a97a110a121 a99a101a108a108a115 a119a105a116a104 a115a109a97a108a108 a101a120a112a101a99a116a101a100 a118a97a108a117a101a115a46 a84a97a98a108a101 a52 a115a104a111a119a115 a116a104a97a116 a116a104a101 a111a98a115a101a114a118a101a100 a115a105a103a110a105a28a99a97a110a116 a108a101a118a101a108 a102a111a114 a80a101a97a114a115a111a110 a105a115:000 a97a110a100 a68a101a118a105a97a110a99a101 a105a115 a49a46a48a48a48 a119a104a105a99a104 a105a115 a109a111a114a101 a116a104a97a110 :05a44 a104a101a110a99a101 a116a104a101 a109a111a100a101a108 a28a116a115 a116a104a101 a100a97a116a97 a119a101a108a108a46 a52a46a49a46a55 a73a110a100a101a112a101a110a100a101a110a99a101 a84a101a115a116 a102a111a114 a82a101a100 a87a105a110a101 a84a111 a99a104a101a99a107 a105a102 a116a104a101a114a101 a119a97a115 a108a105a116a116a108a101 a111a114 a110a111 a97a117a116a111a99a111a114a114a101a108a97a116a105a111a110 a105a110 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a118a97a114a105a97a98a108a101 a105a115 a109a111a114a101 a116a104a97a110 10a44 a116a104a97a116 a112a114a101a100a105a99a116a111a114 a118a97a114a105a97a98a108a101 a105a115 a111a109a105a116a116a101a100 a102a114a111a109 a111a117a114 a109a111a100a101a108 a115a105a110a99a101 a105a116 a105a115 a110a111a116 a115a105a103a110a105a28a99a97a110a116a46 a84a111a108a101a114a97a110a99a101 a105a115 a116a104a101 a114a101a99a105a112a114a111a99a97a108 a111a102 a116a104a101 a118a97a114a105a97a110a99a101 a105a110a29a97a116a105a111a110 a102a97a99a116a111a114a46 a50a52 a70a105a103a117a114a101 a54a58 a83a99a97a116a116a101a114a112a108a111a116 a111a102 a82a101a103a114a101a115a115a105a111a110 a83a116a97a110a100a97a114a100a105a122a101a100 a82a101a115a105a100a117a97a108 a102a111a114 a87a104a105a116a101 a87a105a110a101 a118a115a46 a82a101a103a114a101a115a115a105a111a110 a83a116a97a110a100a97a114a100a105a122a101a100 a80a114a101a100a105a99a116a101a100 a86a97a108a117a101 a77a111a100a101a108 a84a111a108a101a114a97a110a99a101 a86a73a70 a81a117a97a108a105a116a121 a65a108a99a111a104a111a108 a46a49a51a49 a55a46a54a50a51 a86a111a108a97a116a105a108a101 a65a99a105a100a105a116a121 a46a57a52a54 a49a46a48a53a55 a67a105a116a114a105a99 a65a99a105a100 a46a48a56a53 a49a49a46a56a50a56 a82a101a115a105a100a117a97a108 a83a117a103a97a114 a46a49a50a57 a55a46a54a49a50 a67a104a108a111a114a105a100a101 a46a48a55a57 a49a50a46a53a55a57 a70a114a101a101 a83a117a108a102a117a114 a68a105a111a120a105a100a101 a46a56a55a48 a49a46a49a52a57 a68a101a110a115a105a116a121 a46a50a51a56 a56a46a49a50a51 a112a72 a46a52a55a51 a50a46a49a49a52 a83a117a108a112a104a97a116a101a115 a46a56a56a53 a49a46a49a51a48 a70a105a120a101a100 a65a99a105a100a105a116a121 a46a51a51a56 a50a46a53a56a48 a84a111a116a97a108 a83a117a108a102a117a114 a68a105a111a120a105a100a101 a46a48a51a56 a50a54a46a49a50a51 a84a97a98a108a101 a55a58 a83a116a101a112a119a105a115a101 a82a101a103a114a101a115a115a105a111a110 a102a111a114 a87a104a105a116a101 a87a105a110a101 a50a53 a69a115a116a105a109a97a116a101 a83a116a97a110a100a97a114a100 a69a114a114a111a114 a87a97a108a100 a83a105a103 a84a104a114a101a115a104a111a108a100 a113a117a97a108a105a116a121= 3 467:769 a55a51a46a54a50a53 a46a48a48a48 a113a117a97a108a105a116a121= 4 465:407 a55a50a46a56a57a53 a46a48a48a48 a113a117a97a108a105a116a121= 5 462:367 a55a49a46a57a53a57 a46a48a48a48 a113a117a97a108a105a116a121= 6 459:780 a55a49a46a49a54a57 a46a48a48a48 a113a117a97a108a105a116a121= 7 457:527 a55a48a46a52a55a55 a46a48a48a48 a113a117a97a108a105a116a121= 8 453:847 a54a57a46a51a52a52 a46a48a48a48 a76a111a99a97a116a105a111a110 a65a108a99a111a104a111a108 a46a52a50a50 a49a46a49a48a48 a51a52a46a54a57a57 a46a48a48a48 a86a111a108a97a116a105a108a101 a65a99a105a100a105a116a121 5:073 a46a48a50a52 a51a48a48a46a53a50a48 a46a48a48a48 a82a101a115a105a100a117a97a108 a83a117a103a97a114 a46a50a51a54 a46a49a49a48 a49a50a54a46a48a56a48 a46a48a48a48 a70a114a101a101 a83a117a108a102a117a114 a68a105a111a120a105a100a101 a46a48a49a49 a46a48a48a55 a51a56a46a50a57a56 a46a48a48a48 a68a101a110a115a105a116a121 478:478 a46a48a48a49 a55a53a46a49a48a53 a46a48a48a48 a112a72 a50a46a48a57a53 a49a46a51a52a52 a53a54a46a50a53a51 a46a48a48a48 a83a117a108a112a104a97a116a101a115 a49a46a56a49a54 a46a49a48a51 a52a57a46a51a57a53 a46a48a48a48 a70a105a120a101a100 a65a99a105a100a105a116a121 a46a50a52a52 a46a49a48a48 a49a56a46a53a51a55 a46a48a48a48 a84a97a98a108a101 a56a58 a80a97a114a97a109a101a116a101a114 a69a115a116a105a109a97a116a101a115 a102a111a114 a87a104a105a116a101 a87a105a110a101 a52a46a50a46a53 a80a97a114a97a109a101a116a101a114 a69a115a116a105a109a97a116a101a115 a102a111a114 a87a104a105a116a101 a87a105a110a101 a87a101 a117a115a101a100 a116a104a101 a101a115a116a105a109a97a116a101a100 a99a111a101a30a99a105a101a110a116a115 a116a111 a28a116 a116a104a101 a118a97a114a105a111a117a115 a109a111a100a101a108a115 a102a111a114 a119a104a105a116a101 a119a105a110a101a46 a87a101 a99a104a101a99a107a101a100 a109a117a108a116a105a99a111a108a108a105a110a101a97a114a105a116a121 a105a110 a116a104a101 a109a111a100a101a108 a98a121 a101a120a97a109a105a110a105a110a103 a116a104a101 a115a116a97a110a100a97a114a100 a101a114a114a111a114a115 a102a111a114 a116a104a101 a101a115a116a105a109a97a116a101a100 a99a111a101a30a99a105a101a110a116a115a46 a65 a115a116a97a110a100a97a114a100 a101a114a114a111a114 a98a105a103a103a101a114 a116a104a97a110 2:0 a105a110a100a105a99a97a116a101a115 a110a117a109a101a114a105a99a97a108 a112a114a111a98a108a101a109a115a46 a84a97a98a108a101 a56 a99a111a110a116a97a105a110a115 a116a104a101 a101a115a116a105a109a97a116a101a100 a99a111a101a30a99a105a101a110a116a115a44 a116a104a101 a115a116a97a110a100a97a114a100 a101a114a114a111a114a115 a102a111a114 a116a104a101 a99a111a101a30a99a105a101a110a116a115a44 a116a104a101 a87a97a108a100 a116a101a115a116 a97a110a100 a97a115a115a111a99a105a97a116a101a100 pa45a118a97a108a117a101a115 a102a111a114 a116a104a101 a109a111a100a101a108a46 a84a104a101 a101a115a116a105a109a97a116a101a115 a108a97a98a101a108a101a100 a16a84a104a114a101a115a104a111a108a100a17 a97a114a101 a116a104a101 ja46 a84a104a101 a101a115a116a105a109a97a116a101a115 a108a97a98a101a108a101a100 a16a76a111a99a97a116a105a111a110a17 a97a114a101 a116a104a101 a99a111a101a30a99a105a101a110a116a115 a102a111a114 a116a104a101 a112a114a101a100a105a99a116a111a114 a118a97a114a105a97a98a108a101a115a46 a65a116 95% a99a111a110a28a100a101a110a99a101 a105a110a116a101a114a118a97a108a44 a119a101 a114a101a97a108a105a122a101a100 a97a108a108 a116a104a101 a105a110a100a101a112a101a110a100a101a110a116 a118a97a114a105a97a98a108a101a115 a97a114a101 a115a116a97a116a105a115a116a105a99a97a108a108a121 a115a105a103a110a105a28a99a97a110a116 a115a105a110a99a101 a97a108a108 a116a104a101 pa45a118a97a108a117a101a115 a97a114a101 a108a101a115a115 a116a104a97a110 = :05a46 a70a117a114a116a104a101a114a109a111a114a101a44 a110a111a110a101 a111a102 a116a104a101 a115a116a97a110a100a97a114a100 a101a114a114a111a114a115 a101a120a99a101a101a100a101a100 2:0a44 a72a101a110a99a101a44 a110a111a110a101 a111a102 a116a104a101 a105a110a100a101a112a101a110a100a101a110a116 a118a97a114a105a97a98a108a101a115 a100a101a112a101a110a100a101a100 a111a110 a101a97a99a104 a111a116a104a101a114a46 a65a103a97a105a110a44 a108a101a116 Aa61a65a108a99a111a104a111a108a44 Va61a86a111a108a97a116a105a108a101 a65a99a105a100a105a116a121a44 Ra61a82a101a115a105a100a117a97a108 a83a117a103a97a114a44 Fa61a70a114a101a101 a83a117a108a102a117a114 a68a105a111a120a105a100a101a44 Da61a68a101a110a115a105a116a121a44 Pa61a112a72a44 Sa61a83a117a108a112a104a97a116a101 a97a110a100 FAa61a70a105a120a101a100 a65a99a105a100a105a116a121a46 a65a108a108 a116a104a101 a113a117a97a108a105a116a121 a108a101a118a101a108a115 a97a114a101 a115a105a103a110a105a28a99a97a110a116 a97a110a100 a115a111 a116a104a101 a109a111a100a101a108 a102a111a114 a116a104a101 a116a104a105a114a100 a113a117a97a108a105a116a121 a105a115 a116a104a101a110 a119a114a105a116a116a101a110 a97a115 P(Y = a81a117a97a108a105a116a121 a51a124a88) = exp g(X) 1 + expg(X) a119a104a101a114a101 g(X) = 467:769+:422A 5:073V +:236R+:011F 478:478D+2:095P+1:8165S+:244FA: a50a54 a67a104a105a45a115a113a117a97a114a101 a83a105a103 a80a101a97a114a115a111a110 a53a54a56a52a56a46a51a53a55 a46a48a48a48 a68a101a118a105a97a110a99a101 a49a48a57a48a50a46a49a48a54 a49a46a48a48a48 a84a97a98a108a101 a57a58 a71a111a111a100a110a101a115a115a45a111a102a45a70a105a116 a102a111a114 a87a104a105a116a101 a87a105a110a101 a72a101a110a99a101a44 P(Y = a81a117a97a108a105a116a121 a51a124a88) = exp 467:769+:422A 5:073V +:236R+:011F 478:478D+2:095P+1:8165S+:244FA 1 + exp 467:769+:422A 5:073V +:236R+:011F 478:478D+2:095P+1:8165S+:244FA: a84a104a101 a109a111a100a101a108 a102a111a114 a116a104a101 a102a111a117a114a116a104 a113a117a97a108a105a116a121 a105a115 P(Y = a81a117a97a108a105a116a121 a52a124a88) = exp g(X) 1 + expg(X) a119a104a101a114a101 g(X) = 465:407+:422A 5:073V +:236R+:011F 478:478D+2:095P+1:8165S+:244FA: a84a104a101a114a101a102a111a114a101a44 P(Y = a81a117a97a108a105a116a121 a52a124a88) = exp 465:407+:422A 5:073V +:236R+:011F 478:478D+2:095P+1:8165S+:244FA 1 + exp 465:407+:422A 5:073V +:236R+:011F 478:478D+2:095P+1:8165S+:244FA: a84a104a101 a109a111a100a101a108 a102a111a114 a116a104a101 a111a116a104a101a114 a113a117a97a108a105a116a121 a108a101a118a101a108a115 a102a111a108a108a111a119 a116a104a101 a115a97a109a101 a101a113a117a97a116a105a111a110 a119a105a116a104 a100a105a27a101a114a101a110a116 a105a110a116a101a114a99a101a112a116a115a44 a97a108a116a104a111a117a103a104 a116a104a101 a99a111a101a30a99a105a101a110a116a115 a97a99a114a111a115a115 a116a104a101a115a101 a101a113a117a97a116a105a111a110a115 a100a111 a110a111a116 a118a97a114a121a46 a84a104a101 a99a111a101a30a99a105a101a110a116a115 a105a110 a116a104a101 a109a111a100a101a108 a97a114a101 a105a110a116a101a114a112a114a101a116a101a100 a97a115a44 a102a111a114 a101a97a99a104 a105a110a99a114a101a97a115a101 a111a102 c a103a114a97a109a115 a112a101a114 a99a117a98a105a99 a100a101a99a105a109a101a116a101a114 a111a102 a114a101a115a105a100a117a97a108 a115a117a103a97a114 a99a111a110a116a101a110a116 a111a102 a119a104a105a116a101 a119a105a110a101a44 a116a104a101 a108a111a103 a111a102 a111a100a100a115 a40a99a104a97a110a99a101a41 a111a102 a98a101a105a110a103 a105a110 a116a104a101 a116a104a105a114a100 a113a117a97a108a105a116a121 a108a101a118a101a108 a105a110a99a114a101a97a115a101a115 a98a121 :236ca46 a84a104a101a110 a116a104a101 a108a111a103 a111a100a100a115 a99a104a97a110a103a101 a105a115 c a97a110a100 a116a104a101 a97a115a115a111a99a105a97a116a101 a111a100a100a115 a114a97a116a105a111 a105a115 exp (c )a44 a119a104a101a114a101 a105a115 a116a104a101 a101a115a116a105a109a97a116a101a100 a99a111a101a30a99a105a101a110a116 a102a111a114 a114a101a115a105a100a117a97a108 a115a117a103a97a114a46 a52a46a50a46a54 a71a111a111a100a110a101a115a115a45a111a102a45a70a105a116 a83a116a97a116a105a115a116a105a99a115 a102a111a114 a87a104a105a116a101 a87a105a110a101 a84a104a101 a103a111a111a100a110a101a115a115a45a111a102a45a28a116 a116a101a115a116 a119a97a115 a117a115a101a100 a116a111 a99a104a101a99a107 a104a111a119 a119a101a108a108 a116a104a101 a109a111a100a101a108 a97a99a116a117a97a108a108a121 a114a101a29a101a99a116a101a100 a116a104a101 a100a97a116a97a46 a73a116 a118a101a114a105a28a101a115 a104a111a119 a99a108a111a115a101 a116a104a101 a111a98a115a101a114a118a101a100 a118a97a108a117a101a115 a109a97a116a99a104 a116a104a101 a101a120a112a101a99a116a101a100 a117a110a100a101a114 a116a104a101 a28a116a116a101a100 a109a111a100a101a108a46 a84a97a98a108a101 a57 a115a104a111a119a115 a116a104a101 a99a111a108a117a109a110 a108a97a98a101a108a101a100 a16a68a101a118a105a97a110a99a101a17 a119a104a105a99a104 a105a115 a116a104a101 a100a105a27a101a114a101a110a99a101 a98a101a116a119a101a101a110 a116a104a101 a111a98a115a101a114a118a101a100 a118a97a108a117a101a115 a97a110a100 a116a104a101 a101a120a112a101a99a116a101a100 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