Suppose a logistic regression analysis of some data for restaurants gave the following result, in terms of L, which here represents the logit, that is, the log odds, lnOdds. L(x1, x2) = .3 − .2x1 + .1x2, where Y = 1 denotes closing within one year of startup, Y = 0 denotes staying in business more than one year , X1 = 1 if franchised, 0 if not, X2 = 1 if a fast-food restaurant, 0 if not, Px = Pr{Y = 1|x1,x2}, Qx = Pr{Y = 0|x1,x2}, L(x1, x2) = ln(Px1,x2 /Qx1,x2 ) = logit(Px1,x2 ) 1. What is the value of L(0, 1) ? (A) .1 (B) .2 (C) .3 (D) .4 (E) .5 2. The number P(Y = 1|X1 = 0,X2 = 1) is the probability that (A) a franchised fast-food restaurant is bankrupt within one year. (B) a franchised non-fast food restaurant is not bankrupt within one year. (C) a non-franchised fast-food restaurant is bankrupt within one year. (D) a non-franchised non-fast food restaurant is bankrupt within one year. (E) a fast-food restaurant is franchised. 3. (continuation) What is the value of this probability ? (A).401 (B) .450 (C) .550 (D) .599 (E) .67 4. What is the value of L(0, 0)? (A) β0 (B) 0 (C) β0 + β12 (D) β12 (E) 1 5. What is the value of L(0, 1)? (A) β0 (B)0 (C) β0 + β12 (D)β12 (E)1 6. What is the value of L(1, 0)? (A) β0 (B)0 (C) β0 + β12 (D)β12 (E)1 7. What is the value of L(1, 1)? (A) β0 (B)0 (C) β0 + β12 (D)β12 (E)1 8. Given a binary (0,1) variable Y , let Px = Pr{Y = 1| x}. Then the regression function E[Y |x] = (1)Px.+(0)Qx =? (A) Px (B)Qx (C)0 (D)1 (E)½ 9. If P = 1/2, what is the value of the logit function, ln(P/Q), where Q = 1 − P? (A) 0 (B) 1/2 (C) 1 (D) 3/2 (E) 2 10. Forx>0,eln(x) =? (A)ex (B) ln(x) (C) x (D) 0 (E) 1 11. ln(ex) = ? (A) ex (B) ln(x) (C) x (D) 0 (E) 1 12. ln(2e) = (A)1/2 (B) 1 (C) 2 (D) 3 (E) 1+ln(2) 13. Which of the following is closest to the value of the number e ? (A) 2.7 (B) 2.72 (C) 2.718280 (D) 2.7182818280 (E) 2.71828182846 14. Which of the following is closest to the value of the number 1/e ? (A) 1/3 (B) 0.368 (C) 1/2 (D) 3 (E) 3.14159 15. If z = 0, what is the value of the logistic function, 1/(1 + e−z ) ? (A) -1 (B) -1/2 (C) 0 (D) 1/2 (E) 1
Suppose a logistic
L(x1, x2) = .3 − .2x1 + .1x2,
where
Y = 1 denotes closing within one year of startup,
Y = 0 denotes staying in business more than one year , X1 = 1 if franchised, 0 if not,
X2 = 1 if a fast-food restaurant, 0 if not,
Px = Pr{Y = 1|x1,x2}, Qx = Pr{Y = 0|x1,x2},
L(x1, x2) = ln(Px1,x2 /Qx1,x2 ) = logit(Px1,x2 )
1. What is the value of L(0, 1) ?
(A) .1 (B) .2 (C) .3 (D) .4 (E) .5
2. The number P(Y = 1|X1 = 0,X2 = 1) is the probability that
- (A) a franchised fast-food restaurant is bankrupt within one year.
- (B) a franchised non-fast food restaurant is not bankrupt within one year.
- (C) a non-franchised fast-food restaurant is bankrupt within one year.
- (D) a non-franchised non-fast food restaurant is bankrupt within one year.
- (E) a fast-food restaurant is franchised.
3. (continuation) What is the value of this probability ?
(A).401 (B) .450 (C) .550 (D) .599 (E) .67
4. What is the value of L(0, 0)?
(A) β0 (B) 0 (C) β0 + β12 (D) β12 (E) 1
5. What is the value of L(0, 1)?
(A) β0 (B)0 (C) β0 + β12 (D)β12 (E)1
6. What is the value of L(1, 0)?
(A) β0 (B)0 (C) β0 + β12 (D)β12 (E)1
7. What is the value of L(1, 1)?
(A) β0 (B)0 (C) β0 + β12 (D)β12 (E)1
8. Given a binary (0,1) variable Y , let Px = Pr{Y = 1| x}. Then the regression
(A) Px (B)Qx (C)0 (D)1 (E)½
9. If P = 1/2, what is the value of the logit function, ln(P/Q), where Q = 1 − P?
(A) 0 (B) 1/2 (C) 1 (D) 3/2 (E) 2
10. Forx>0,eln(x) =?
(A)ex (B) ln(x) (C) x (D) 0 (E) 1
11. ln(ex) = ?
(A) ex (B) ln(x) (C) x (D) 0 (E) 1
12. ln(2e) =
(A)1/2 (B) 1 (C) 2 (D) 3 (E) 1+ln(2)
13. Which of the following is closest to the value of the number e ?
(A) 2.7 (B) 2.72 (C) 2.718280 (D) 2.7182818280 (E) 2.71828182846
14. Which of the following is closest to the value of the number 1/e ?
(A) 1/3 (B) 0.368 (C) 1/2 (D) 3 (E) 3.14159
15. If z = 0, what is the value of the logistic function, 1/(1 + e−z ) ?
(A) -1 (B) -1/2 (C) 0 (D) 1/2 (E) 1
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