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4141 ISDS INTRODUCTION TO DATA MINING
Final Exam
Problem 1. (1) True ( X ); False ( ) (2) True ( ); False ( X ) (3) True ( X ); False ( ) (4) True ( X ); False ( ) (5) True ( X ); False ( ) (6) True ( ); False ( X ) (7) True ( ); False ( X ) (8) True ( X ); False ( ) (9) True ( ); False ( X ) (10) True ( X ); False ( ) (11) True ( ); False ( X )(12) True ( ); False ( X ) (13) True ( X ); False ( )(14) True ( X ); False ( ) (15) True ( ); False ( X ) Problem 2. (a) P[Peanut Butter, Bread] = 10/100 = 0.1 (b) P[Bread | Peanut Butter] = 10/40 = 0.25 (c) P[Peanut Butter, Bread ] / (P[Peanut Butter ] P[Bread ]) = 0.1/(0.2*0.4) = 1.25 (d) (10*50 10*30)^2 / (20 * 80 * 60 * 40) * 100 =1.0417 Problem 3. (a) y-bar = b0 + b1 * x-bar x-bar = (y-bar b0) / b1 = 600 (b) E[Y-hat] = -395 + 1.825 * 700 = $882.5 (c) 1- SSE/(n-k-1) / SSTO/(n-1) = 0.7926 (d) Alternatives H0: 1 = 0 H1: 1 0 Decision rules If |t*| t8, 0.025 ( = 2.306 ), conclude Ho Test statistic t* = 5.94969 Conclusion Conclude H1. Problem 4. (a) = exp(bx)/[1+ exp(bx)] where bx = -9.6 + 0.1*X1 + 0.8*X2 (b) bx = -9.6 + 0.1*50 + 0.8*5 = -0.6 = exp(bx) / [1+ exp(bx)] = 35.43% (c) -9.6 + 0.1*X1 + 0.8*X2 = 0 or 1 X1 + 8 X2 = 96 Problem 5. (a) Minimax rule Bayes rule Reject a2 with E[L] = $110 Accept a1 E[L] ith = $44
ISDS 4141
Dr. Chun
ISDS 4141
2/2
(b)
If x2 (Good), then a1 (Accept). E[L] = $60
Problem 6. (a) P[Yes | Child] = 57/109 = 52.29% (b) P[Yes, No] = 57/109 * 52/109 * 2 = 49.89% (c) P[Yes | Adult Female] => P[Adult | Yes] P[Female | Yes] P[Yes] = 654/711 * 344/711 * 711/2201 = 0.14376 P[No | Adult Female] => P[Adult | No] P[Female | No] P[No] = 1438/1490 * 126/1490 * 1490/2201 = 0.05524 Since P[Yes | Adult Female] > P[No | Adult Female], classify it as Yes (d) He(Y) = 0.6291 H(Y) = He(Y) / ln(2) = 0.9077 He(Y|X) = He(X, Y) - He(X) = 0.8218 0.1971 = 0.6247 H(Y|X) = He(Y|X) / ln(2) = 0.9012 H(Y) H(Y|X) = 0.9077 0.9012 = 0.0065 (d) Classification Yes No Yes 57 654 True class No 52 1438 Total 109 2092 Error rate = (52 + 654)/1438 = 32.076% Problem 7. (a) r = 24 / sqrt(32 * 72) = 0.5 (b) d(A, B) = 4 + 6 + 0.1 = 10.1 (c) d(A, B) = sqrt(16 + 36 + 0.01) = 7.2118 (d) d(A, B) = SQRT(1 + 1 + 1) = 1.732 Problem 8. Multicorrelinearity problem! Expensive to maintain the model Hard to analyze and understand
Total 711 1490 2201
Problem 9. Nave Bayesian classifiers assume that the effect of an attribute value on a given class is independent of the values of the other attributes. This assumption is called class conditional independence.

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