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ID : Quiz section or time: ____________________________ 3?qu :12 Stat/Math 390, Spring, Test 2, May 8, 2009; Marzban Suppose that :r and y are positive variables and that a sample of 71 pairs results in r m 1. If the sample
correlation coefﬁcient is compu)ted for the (m, y2) pairs, the resulting value will be
w a < 5 larger d) none of the above.
“Se same c) -
bl "13114 W l\ MVL Os MW \‘m‘f Y‘JCMQM .
l’ following 1s a printout from a simple linear regression analysis, predicting concrete strength from 1ts modulus of elasticity. What’s the typical value of the error from the line? Circle the answer.
Predictor Coef Stdev t—ratio p Constant 3.2925 0.6008 5.48 0.000
mod elas 0.10748 0.01280 8.40 0.000
s = 0. 8657 , R—sq = 73.8%, R—sq (adj) = 72.8%. \Uﬁ-u/IL In the absence of collinearity, in multiple linear regression with an interaction term a) the interaction creates collinearity between the predictors. @inique OLS estimate of all the regression coefﬁcients can be obtained )regression coefﬁcients convey how much the response changes as a result of changes in predictors
d All of the above. “does not” in the following two blanks _ “L o compute the accuracy of a device one ElEL‘Eé- need to know the truth. A'CC“V°‘-‘ N \I ‘fT/ug To compute the precision of a device, one dﬂﬁiﬂjneed to know the truth. Prams“ 9“ N 8 1 ‘L , 2} NJ; 2 (‘1. "I )
'D" A factory uses three production lines to manufacture cans of certain type. The accompanying table 1‘ gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the three
lines. Denote “Ll” the event when a random nonconforming can comes from Line 1; etc. Denote “B” the
event when a random nonconforming can has a Blemish; etc. In this notation, the element in the table which reads 20% is the probability of what event (conditional or otherwise)?
Line 1 Line 2 Line 3 Blemish w 10% 3v. : P (B l L L) Crack 30'0 60% 30% Other 50% 30% 40% , A11 [10% 100% E‘ja‘j ' (B ““3 100% Inn» 0
1¢IINM+__ . : ose the best regression ﬁt to a data set has been determined to be of the form log(y )— — a + 6:10, nd the OLS estimates have been computed. Suppose you are interested in the OLS estimates one obtains @Y:d+ﬂlx =7 dz/egaxl—ﬁ?
7k—> (.1, => off—a (c )_ "“ A K ’ap—Y 6" 0L ——9 —vl‘—_i’,,e.%CcY‘r)’- >¢ 3 7‘mid—page, the book states “One of the nice features of the proportional allocation is that
the resulting data is ‘self—weighing’; in other words, instead of calculating the stratiﬁed estimate we can simply combine the data from all the strata and calculate the ordinar sam le mean of t e combined data, which only in this case [i. e., for proportional allocation] will exactly equal TS”. Show that the book s
statement is true P/DP. Mo 5. IX . S $\' =21 3f
:3 Q a NY
2 5108. For any collection of events A1, A2,. .. ,Ak, it can be shown that P(A1 ﬂ A2 ﬂ. .
( g)... — 13(142.) always holds. Suppose that a system consists of k: components is connected in series, which means that all k: components must operate correctly for the whole system to operate correctly. Also,
suppose that the probability of each component operating correctly is q. What lower bound can you place
on the probability that the whole system operates correctly? L—X‘Af: L/W'Q‘ when COMFDMQMT; wwlI-s- =3 WAN—’1
arrive? mm M- '> = Format-unit) fﬂHZﬂM-u HAW] = V— kCL—aﬂl l—- 4y LI '1,
3 @‘ large farming area is divided into four parcels of land: 15, 20, 25, and 10 acres each. Suppose the a obability that a randomly sampled tree from the farm comes from a particular parcel is proportional to
the size of the parcel. We are interested in the probability that a randomly chosen tree comes from one of
the ﬁrst two parcels of land. a) Let Bl, i— — 1,2,3, 4, be the event when randomly selected tree comes from parcel 2'. In this notation,
what 1s the event of interest? (8 U 9 L5 b) Compute the probability of plaining any rules or assumptions used at every step. PCB,UE,): P(Q,)+ Wm— (48108,) 13141.1. EJL.
H l‘ M ['3’ 20 0k EMMA 3;. are much «Q. Q 35/10 =
3 5:810 Consider a factory (different from that in question 5) which also has three lines of production (Lines , 2, and 3), and three types of nonconforming cans (Blemish, Crack, and Other). Suppose the following
probabilities are given: P(B|L1) = 0.15,P(B|L2) = 0.12,P(B|L3) = 0.20. Now, suppose Line 1 produces
500 nonconforming cans, Line 2 produces 400 such cans, and Line 3 makes 600 nonforming cans. If one of these 1500 cans is randomly selected, what is the probability that the reason for nonconformance is a
Blemish? Show work, don t just multiply and add numbers! Jmt/ﬁzB% P(BﬂL1) $13 BﬂL2)+P(BﬂL3)
“N W) = MAL) a. ?(%AL,,)+ 91%,) $0131), 5’ mum 10.9 +- PCBlLv)PCL—1’) + WW4) “”3) a, finial 9.1;. 543 ,_ 9.12. “£3 + 9.7492 40.16;) 1569 ‘5‘“ [gm H ...
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