IDS 371 Business Statistics II Examination No. 2 of 2 Topics: 0 Multiple Regression o The Market Model: Beta in Bull and Bear Markets 0 Minimizing a Quadratic 0 Stable Seasonal Pattern 0 Portfolio Mean and Variance o Categorical Datal 0 Order Statistics Due online by 11:59 p.m. on Thursday, April 29. Twenty-seven (27) questions. Table 1: Cumulative distribution function of the standard Normal distribution 2: 0 1 2 3 Probability to the left of z: .5000 .84134 .97725 .99865 Probability to the right of z: .5000 .15866 .022?5 .00135 Probability between -2. and z: .6827 .9544 .99730 Table 2: Inverse of the cumulative distribution function of the standard Normal distribution Probability to the left of z: .90 .92 .95 .975 .9990 2: 1.282 1.405 1.645 1.960 3.09 1 Correlation Coefcients The formula for computing t from :r' is t : Suppose that r = .6. 1. What is the value of r2? (A) .2 (B) .36 (C) .6 (D) .64 (E) .99 2. What is the value of 1 r2? (A) .2 (B) .36 (C) .6 (D) .64 (E) .99 3. What is the value of 1 6\"? (A) .2 (B) .36 (C) .6 (D) .64 (E) .8 4. What is the value of r/ 1 r2? (A) .2 (B) .36 (C) .6 (D) .75 (E) none of these 5. What is the value of x/N 2 when N = 27? (A) 1 {B} 2 (C) 3 (D) 4 (E) 5 6. What is the value oft when N = 27 and r = .6? (A) 1.0 (B) 1.80 (C) 3.0 (D) 3.75 (E) none of these 7. If the correlation coefcient is .6, what percentage of the variability of Y is explained by X ? (A) 20% (B) 36% (C) 50% (D) 54% {399% 8. Adjusted Rsquare. If MST = 24 and MSE = 12, what is the value of Big? (A) .2 (B) .36 (C) .5 (D) .64 (E) .99 2 Multiple Regression: The \"Market Model\": \"Beta\" in Bull and Bear Markets Monthly rates of return (%) of a mutual fund, the Cheetah Fund, were regressed on those of the 336F500. The tted equation was predicted value on = 0.3 + 0.5 L + 0.6 X + 0.7 X L (*) where Y 2 rate of return (%) of Cheetah Fund X 2 rate of return of S&P500 and L = 1 if Bull market, 0 if Bear market. 9. What is equation (*) in a Bear Market 'E' (A) predicted value of Y = 0.3 + 0.5 = 0.8 (B) predicted value of Y = 0.3 + 0.6 X (C) predicted value of Y = 0.8 + 0.6 X (D) predicted value of Y = 0.3 + 1.3 X (E) predicted value of Y = 0.8 + 1.3 X 10. What is equation (*) in a Bull Market ? (A) predicted value of Y = 0.3 + 0.5 = 0.8 (B) predicted value of Y = 0.3 + 0.6 X (C) predicted value of Y = 0.8 + 0.6 X (D) predicted value of Y = 0.3 + 1.3 X 11. 12. 13. 14. 15. 16. 17. (E) predicted value of Y = 0.8 + 1.3 X What is the Cheetah Fund's \"beta\" in a Bear market? (A) 0.3 (B) 0.5 (C) 0.6 (D) 1.3 (E) 1.4 What is the Cheetah Fund's \"beta\" in a Bull market ? (A) 0.3 (B) 0.5 (C) 0.5 (D) 1.3 (E) 1.4 3 Minimizing a Quadratic If 20.36 + b = 0, what is :c in terms of a and b? (A) -b/a {13) -b/2a {cm/2 (D) -b (E) b/2a Suppose that the COST {53) per unit as a function of the level x of input (for a suitable range of 3:) is Predicted COST per unit 2 22 0.158 + 0.002.162. What is the predicted COST per unit if x = 10 ? (A) $22 (B) $10 (C) $ 0.20 (D) $ 12 (E) $ 21.20 What is x'"1 the optimal value of x, that is, the value that minimizes the value of predicted COST per unit? (A) 22 (B) 10 (C) 25 (D) 12 (E) 12.20 units . What is the corresponding minimum COST per unit '3' (A) $22 (B) $10 (C) $0.20 (D) $ 2 (E) none of these 4 Time Series Analysis 4.1 Stable Seasonal Pattern Suppose that sales last year were 80.0 B95, and there is a stable seasonal pattern across quarters, namely 15%, 20%, 25%, and 40% for the rst, second, third, and fourth quarters, respectively. Using the predictor that total sales for this year will be ten percent higher than sales were for last year, what is the forecast of total sales for this year 'E' (A) 3.0 (B) 80.0 (C) 88.0 (D) 90.0 (E) 100 13$ 18. Using this forecast of annual sales and stable seasonal pattern, forecast the sales for the second quarter of this year. (man (B) 16.0 (C) 17.5 (D) 90.0 (E) 100 13$ 19. (continuation) Nowcasting. Using the new information that sales for Q1, the rst quarter of this year, were 12.0 B$, forecast the sales for Q2, the second quarter of this year. Reason that now the predicted total for this year is given by 12 = .15 x total, or total = 12/.15 = 4/.05 2 4(20) = 80, and that the sales in Q2 will be 20% of that, or (A) 8.0 (B) 16.0 (C) 80.0 (D) 90.0 (E) 100 B$ 4.2 Time Series Analysis 20. If a series is Y1 = 1, Y9 = 4, and Y3 = Q, what are the values of the two rst differences? YzY1=? 1313:? (A)3and5 (B)3and6 {C)1and2 {D)1and3 (E)1and4 21. (continuation) What is the value of the second difference, Y3 21/72 + Y1 ? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 22. In general, the second difference, that is, the difference of the rst difference, is (A) YtYzi (B) YtYis (C) Y: 2YE1'l' Yaz (D) YtYz1+ Yisa (E) Ya+ 2y11+ Yia- 5 Portfolio Mean and Variance Table 3: Annual ROR {rate of return) of two stocks. Stock: A B Variable representing ROB X Y mean of ROB 15% 9 % std dexr of ROB. 10% 3% Corer,Y) = -.5 Consider a portfolio with weights 11),, = .6 and w), = .4 for Stocks A and B. Refer to the table above. 23. What is the mean ROB for this portfolio? (A) 9 % (B) 12.5% (C) 13.2 % (D) 15 % (E) 16 % 24. What is the variance of ROR for this portfolio? (A) 9 (B) 64 (C) 13.2 (D) 30.24 (E) none of these 25. What is the standard deviation of ROR for this portfolio? (A) 3 % (B) 10% (C) 4 % (D) 5.5 % (E) 16 % 6 Order Statistics 26. If Pr{X > x} = e-2, what is the probability that X exceeds 1/2 ? (A) e-2 (B) 1/2 (C) e-1/2 (D) 1 -e-2 (E) el 27. (continuation) If you have a random sample X1, X2, ..., Xn, with Pr(Xi > x} = e-2x what is the probability that the sample minimum exceeds 1/2 ? (A) e-2 (B) (1/2)" (C) en (D) 1 -en (E) e-2n Copyright @ 2020, 2021 Stanley Louis Sclove latest editions: 2015: Nov. 9 and 2020: April 12; 2021: April 22