Business Analytics, Loose-leaf Edition (3rd Edition)
3rd Edition
ISBN: 9780135231692
Author: James R. Evans
Publisher: PEARSON
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Chapter 1, Problem 11PE
In this chapter, we noted the importance of defining and analyzing a problem prior to attempting to find a solution. Consider this example: One of the earliest operations research groups during World War II was conducting a study on the optimum utilization of Spitfire and Hurricane aircraft during the Battle of Britain. Whenever one of these planes returned from battle, the locations of the bullet holes on it were carefully plotted. By repeatedly recording these data over time, and studying the clusters of data, the group was able to estimate the regions of the aircraft most likely to be hit by enemy gunfire, with the objective of reinforcing these regions with special armor. What difficulties do you see here?
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2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model
below:
1
y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €.
See Question 2, Tutorial 3 for the meaning of the variables in the above model.
The following results are obtained:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.302e+03 4.320e+02 3.015 0.00307
x4
x6
x8
x4:x8
x6:x8
-1.442e+02
2.056e+01 -7.013 1.02e-10
6.340e-01 6.099e+00 0.104 0.91737
-9.455e-02 5.802e-02 -1.630
0.10550
2.882e-02 2.589e-03 11.132
1.673e-03 7.215e-04 2.319
F)
x4
1
3486722
3486722
17.9286 4.214e-05
x6
1
14595537
x8
x4:x8
x6:x8
1
132.4836 < 2.2e-16
1045693
194478
5.3769 0.02191
1 1198603043 1198603043 6163.1900 < 2.2e-16
1 25765100 25765100
1045693
Residuals 135 26254490
Estimated variance matrix
(Intercept)
x4
x6
x8
x4:x8
x6:x8
(Intercept)
x4
x6
x8
x4:x8
x6:x8
0.18875694
1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953
-5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013
-2.322825e+03…
In some applications the distribution of a discrete RV, X resembles the Poisson distribution except that 0 is not a possible value of X. Consider such a RV with PMF
where 1 > 0 is a parameter, and c is a constant.
(a) Find the expression of c in terms of 1.
(b) Find E(X).
(Hint: You can use the fact that, if Y ~ Poisson(1), the E(Y) = 1.)
Suppose that X ~Bin(n,p). Show that
E[(1 - p)] = (1-p²)".
Chapter 1 Solutions
Business Analytics, Loose-leaf Edition (3rd Edition)
Ch. 1 - Discuss how you might use business analytics in...Ch. 1 - How might analytics be used in the following...Ch. 1 - A supermarket has been experiencing long lines...Ch. 1 - For each of the following scenarios, state whether...Ch. 1 - Suppose that a manufacturer can produce a part for...Ch. 1 - A bank developed a model for predicting the...Ch. 1 - Four key marketing decision options are price P,...Ch. 1 - Total marketing effort is a term used to describe...Ch. 1 - A manufacturer of headphones is preparing to set...Ch. 1 - In this chapter, we noted the importance of...
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