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Unformatted text preview: 12.1.1 (a) 4.2 + (1.7 x 10) = 21.2
(b) 3 x 1.7 = 5.1
(c) P(N(4.2 + (1.7 x 513.22): 12) = 0.587
(d) P(N(4.2 + (1.7 x 8),3.22) 3 17) = 0.401 (e) P(N(4.2 + (1.7 x 6),,322) 2 N(4.2+ (1.7 x 71322)) = 0.354 12.1.4 Since the model minimizes the sum of squares of residuals (vertical differences) the
model will change if the :1: and y variables are exchanged. If there is a reason to consider that one variable can be naturally thought of as being
“determined” by the choice of the other variable, then that indicates the appropriate
choice of the a: and 3; variables (the y variable should be the “determined” variable). In addition, if the model is to be used to predict one variable for given values of the other variable, then that also indicates the appropriate choice of the :1: and 9
variables (the y variable should be the variable that is being predicted). 12.28 (a) 30 = _1.911
Bl = 1.6191 (b) 1.6191 x 1: 1.6191
The expert is underestimating the times. 41.911 + (1.6191 x 7) = 9.42 (c) If the model is used then it would be extrapolation,
so the prediction may be inaccurate. (d) 62 = 12.56
12.3.7 (a) 3.6.(51)=0.2829 (b) (1.619 4 (2.042 x 0.2829),1.619 + (2.042 x 02829)) = (1041,2197) (c) If 61 = 1 then the actual times are equal to the estimated times except for a
constant diﬁerence of 50.
The t—statistic is 1.619—1.000 _
0.2829 _ 2‘19 and the pvalue is 0.036. 12.4.7 (—oo,10.63) 12.4.8 (68.07, 70.37) 12.4.9 21:14:. 2 122.6 §=152 — 1939.24 1i— 3 = % = 15.325 SXX = 1939.24 — 12152 = 60.395 12.5.6 (—55,15.59) 12.7.5 The variability of the actual times increases as the estimated time increases. 13.12 (a) 132:0.23 (b) Source df SS MS F p—vaiue
Regression 6 2.67 0.445 1.89 0.108
Error 38 8.95 0.2355
Total 44 11.62 (c) 62 = 0.2355
(d) The p—value is 0.108. (e) (1.05 — (2.024 x 0.91),1.05 + (2.024 x 0.91)) (—0.79, 2.39) 13.2.3 (a) 6.] = —3,233.6 61 = 0.9615
82 = 0.732
63 = 2.889
64 = 3899 (b) The variable geology has a p—value of 0.737 and is not needed in the model. The sample correlation coefﬁcient between the cost and geology is “r = 0.89. (C) The sample correlation coefﬁcient between the depth and geology is 'r = 0.92.
The variable geology is not needed in the model because it is highly correlated with the variable depth which is in the model. The variable rigindex can also be removed from the model. A ﬁnal model
cost = —3011 + (1.04 X depth) + (2.67 X downtime) can be recommended. 13.4.2 (a) The residual plots do not indicate any problems. (1)) If it were beneﬁcial to add the variable geology to the model, then there would
be some pattern in this residual plot. ((1) The observation with a cost of 8089.5 has a standardized residual of 2.01. ...
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 Spring '08
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