Index

Note: Page numbers followed by f indicate figures, t indicate tables, and b indicate boxes.

A

Absolute average deviation  See Average deviation
Absolute frequency 22, 32–33, 33f
Absolute nesting data structure 990
Adaptive quadrature process 1005
Advanced Integrated Multidimensional Modeling Software (AIMMS) 774
Agglomeration schedules 311–312, 324, 326f
hierarchicals 325 See also Hierarchical agglomeration schedules
k-means procedure 325
linkage methods 325
nonhierarchicals 325 See also Nonhierarchical k-means agglomeration schedule
Aggregated planning problem 734–736b, 734t
binary programming (BP) 733
decision variables 733
general formulation 733
integer programming (IP) model 734–736
mixed-integer programming (MIP) problem 734–736
model parameters 733
nonlinear programming (NLP) 733
resources 732
Akaike information criterion (AIC) 695
Allocation/attribution problem  See Job assignment problem
A Mathematical Programming Language (AMPL) 774
Analysis of variance (ANOVA) 525, 527f
assumptions 232
linear regression models 457, 458f
multiple interactions 246
one-way ANOVA 234–236b, 234f, 235–236t
calculations 233, 233t
null hypothesis 232
observations 232, 232t
residual sum of squares 233
SPSS Software 236–237, 237–238f
Stata Software 237–238, 238f
two-way ANOVA 241–242b, 242t
calculations 241, 241t
factors 240
observations 239, 239t
residual sum of squares (RSS) 240
SPSS Software 242–244, 243–246f
Stata Software 244–245, 246f
sum of squares of factor 240
sum of total squares 240
Anti-Dice similarity coefficient 323
Arbitrary weighting procedure 314
Arithmetic mean 
continuous data 41–42, 41t, 41–42b
grouped discrete data 40–41, 40–41b, 40–41t
ungrouped discrete and continuous data 
simple arithmetic mean 38–39, 38t, 38–39b
weighted arithmetic mean 39–40, 39–40t, 39–40b
Autocorrelation 
Breusch-Godfrey test 493–494
causes 492, 492f
consequences 493
data time evolution 491
Durbin-Watson test 493, 493f
first-order autocorrelation 492
generalized least squares method 494
residuals problem 492, 492f
Average deviation 
continuous data 56, 56b, 56t
grouped discrete data 54–55, 55t, 55b
modulus/absolute deviation 54
ungrouped discrete and continuous data 54, 54t, 54b

B

Bacon algorithm 533
Balanced nested data structure 988
Balanced transportation model 839, 846, 846b
Bar charts 21, 26–27, 26t, 26–27b, 27f
Bartlett’s χ2 test 210–212, 211–212b, 211t
Bartlett’s test of sphericity 387, 389–390, 413, 413f, 423, 424f
Basic solution (BS) 755
Basic variables (BV) 755, 755b
Bayesian (Schwarz) information criterion (BIC) 695
Bayes’ theorem 132–133, 132–133b
Bernoulli distribution 142–144, 143–144b, 143f, 609, 691
Best linear unbiased predictions (BLUPS) 1005
Between-groups/average-linkage method 328, 335–338, 337t, 338f
Big Data 983, 984f
Binary logistic regression model 539
confidence intervals 556–557, 556–557t, 557b
cutoff 558, 559–560t
dichotomic form 540
event nonoccurrence 541
event occurrence 540–542, 541t
explanatory variables 540
graph 541–542, 541f
logit 540
maximum likelihood 542–547, 542–544t, 545–547f
overall model efficiency (OME) 560
pi values 558, 558t
probability model 557–558
ROC curve 561–562, 562f
sensitivity analysis 559–560, 561f
specificity 560
SPSS  See IBM SPSS Statistics Software
Stata  See Stata Software
statistical significance 
chi-square test 548–550, 550f
degrees of freedom 550
Hosmer-Lemeshow test 554
Insert Function 551, 552f
likelihood-ratio test 552, 553f
linear and logistic adjustments 547–548, 548f
logistic probability adjustment 555, 555f
McFadden pseudo R2 548
null model 548, 549f
parameter estimation 551, 556
Solver 547–548, 549f, 553f
Wald z test 550–551
Binary programming (BP) 733
capital budgeting problem 894t, 894b
attributes 895b
decision variables 895, 897f
Excel spreadsheet 894, 895b, 895f
investment projects 894
linear programming model 894
Net Present Value (NPV) 894
optimal solution 895, 897f
Solver Parameters dialog box 895, 896f
Traveling Salesman Problem (TSP) 898–899t, 898–900b, 899f
Excel Solver 901f, 902, 902b, 903–904f
formulations 896–901
Hamiltonian problem 896, 898f
network programming 896
Binomial distribution 144–145, 144f, 145b, 1169–1176t
Binomial test 250–254, 251–253b, 252t, 253f
SPSS Software 253, 254–255f
Stata Software 253–254, 255f
Bivariate descriptive statistics 93, 94f
perceptual maps 93
qualitative variables, measures of association 
chi-square statistic 102–110, 102–110b, 102–103t, 104–106f, 107t, 109–110f
joint frequency distribution tables  See Joint frequency distribution tables
Spearman’s coefficient 110–113, 110f, 111–113b, 111t, 112–113f
quantitative variable, measures of correlation 
covariance 118, 118b
Pearson’s correlation coefficient 119–121, 119–121b, 119–121f
scatter plot 114–118, 114–118f, 115–116b
Blending/mixing problem 717–719, 717–719b, 718t
Blocked Adaptive Computationally Efficient Outlier Nominators (BACON) algorithm 52
Bowley’s coefficient of skewness 63–64, 64b
Box-Cox transformations 
IBM SPSS Statistics Software 527
nonlinear regression models 497–498, 497b
ordinary least squares (OLS) method 480–481
Stata, regression models estimation 511, 512f
results 513, 515f
Boxplots 21, 37–38, 37f
position/location measures 53–54, 53f
Breusch-Godfrey test 493–494, 516, 517f
Breusch-Pagan/Cook-Weisberg test 489–490, 505, 506t, 506f
Business Analytics 983

C

Canberra distance 319
Capital budgeting problem 721–724, 722–723t, 722–724b, 894t, 894b
attributes 895b
decision variables 895, 897f
Excel spreadsheet 894, 895b, 895f
investment projects 894
linear programming model 894
Net Present Value (NPV) 894
optimal solution 895, 897f
Solver Parameters dialog box 895, 896f
C chart 966–967, 966–968f
Chebyshev distance 319, 320t
Chi-square statistic measures 
binary logistic regression model 548–550, 550f
contingency coefficient 107, 108b, 109f
Cramer’s V coefficient 108, 108–110b, 109–110f
definition 102
distribution 158–160, 159–160f, 160b, 196, 196f, 490, 1166–1167t
example 102–106b, 102–103t, 104–106f
K independent samples 295–299, 296f, 296b, 296t
SPSS Software 297, 297–299f
Stata Software 297–299, 299f
one sample 255–257, 255–256f, 256b, 256t
SPSS Software 256–257, 257–258f
Stata Software 257, 259f
Phi coefficient 106, 106–108b, 107t, 109–110f
two independent samples 276–280, 277–278f, 277–278t, 277–278b
SPSS Software 279, 279–280f
Stata Software 279–280, 280f
Cluster analysis 
agglomeration schedules 311–312, 324, 326f
hierarchicals 325 See also Hierarchical agglomeration schedules
k-means procedure 325
linkage methods 325
nonhierarchicals 325 See also Nonhierarchical k-means agglomeration schedule
arbitrary weighting procedure 314
creation 312, 313f
definition 311
discriminant analysis 311
distance measures 314, 319, 320–321t
Canberra distance 319
Chebyshev distance 319, 320t
data standardization procedure 318
Euclidean squared distance 318, 320t
Manhattan distance 319
metric variables, dataset 315, 316t, 318, 318t
Minkowski distance 318
Pearson’s correlation coefficient 315
Pythagorean distance formula 316, 317f
three-dimensional scatter plot 315, 316–317f
Z-scores procedure 321
internal homogeneity 313
Likert scale 314
logic 311, 312f
multinomial logistic regression 311
multivariate outliers 379–382, 380–382f
rearrangement 314, 314f
scatter plot 312, 312f
similarity measures 314, 325t
absolute frequencies 322, 322t, 324, 324t
anti-Dice similarity coefficient 323
arbitrary weighting problems 321
binary variable 321
dataset 321, 322t
Dice similarity coefficient (DSC) 323
Euclidean distance 322
Hamann similarity coefficient 324
Jaccard index 323
Ochiai similarity coefficient 323
Rogers and Tanimoto similarity coefficient 323
Russel and Rao similarity coefficient 323
simple matching coefficient (SMC) 322
Sneath and Sokal similarity coefficient 324
Yule similarity coefficient 323
static procedures 314
variability 312, 313f
Cochran’s C statistics 212–213, 213b, 1191t
K paired samples 286–290, 287–288b, 287t, 288–290f
Coefficient of determination 453–456, 455t, 455–456f
Coefficient of kurtosis 65, 66f
on Stata 66–68, 67–68b, 67t
Coefficient of skewness on Stata 64–65
Coefficient of variation 61, 61b
Combinations 134, 134b
Combinatorial analysis 
arrangement 133–134, 133–134b
combinations 134, 134b
definition 133
permutations 135, 135b
Communalities 394, 415, 415f
Complementary events 128, 128f, 130
Completely randomized design (CRD) 936–937, 937f
Conditional probability 131
multiplication rule 131–132, 131–132b, 132t
Confidence intervals 
binary logistic regression model 556–557, 556–557t, 557b
negative binomial regression model 644, 644t
Poisson regression model 630–632, 631t, 632b
population mean 192
known population variance 193–194, 193–194b, 193f
unknown population variance 194–195, 194f, 194–195b
population variance 196–197, 196f, 197b
proportions 195–196, 196b
Confirmatory factor analysis 383
Confirmatory techniques 405
Contingency coefficient 107, 108b, 109f
Contingency tables creation 
chi-square statistic measures 102–106b, 102–103t, 104–106f
IBM SPSS Statistics Software 
Cell Display dialog box 97, 100f
cross tabulation 97, 99–100f
labels 97, 98f
variables selection 96, 97f
Stata Software 101, 101f
Continuous random variable 139f
cumulative distribution function (CDF) 140–141, 141b
definition 139
expected/average value 140
probability density function 139
probability distributions 
chi-square distribution 159–160, 159–160f, 160b
exponential distribution 156–157, 156f, 157b
gamma distribution 157–158, 158f
normal distribution  See Gaussian distribution
Snedecor’s F distribution 162–164, 163b, 163f, 164t
Student’s t distribution 160–162, 161f, 162b
uniform distribution 151–152, 151t, 152b, 152f
variance 140, 140b
Continuous variables 8, 16
Control chart 1194t
Convenience sampling 175, 175b
Convex and nonconvex sets 748, 748f
Correlation coefficients 383
Correlation matrix 391
Covariance 118, 118b
CPLEX 774
Cramer’s V coefficient 108, 108–110b, 109–110f
Cronbach’s alpha 
calculation 435t, 436
internal consistency 434
reliability level 434
SPSS 436, 436–437f
Stata 437–438, 438f
variance 434
Crossindustry standard process of data mining (CRISP-DM) 984–985, 986f
Cumulative distribution function (CDF) 
continuous random variable 140–141, 141b
discrete random variable 138–139, 139b
Cumulative frequency 22
Czuber’s method 46, 46–47b, 46t

D

Data, information, and knowledge logic 3, 4f
Data mining 
Big Data 983, 984f
Business Analytics 983
complexity 983
crossindustry standard process of data mining (CRISP-DM) 984–985, 986f
HLM  See Hierarchical linear models (HLM)
IBM SPSS Modeler 986, 986f
knowledge discovery in databases (KDD) 984, 985f
multilevel modeling 987–988
nested data structures 988–991, 989–990f, 989–990t
predictive capacity 983
standard recognition 983
tasks 985–986
tools and software packages 986
variety and variability 983
volume and velocity 983
Deciles 48
continuous data 50–52, 51–52b, 51t
grouped discrete data 50, 50b
ungrouped discrete and continuous data 48–50, 49–50b
Decision-making process 3, 5
Descriptive statistics 7
Design of experiments (DOE) 935
blocking 936
completely randomized design (CRD) 936–937, 937f
control 936
data analysis 936
factorial ANOVA 938
factorial design (FD) 937
factors and levels 935
one-way analysis of variance (one-way ANOVA) 938
problem definition 935
randomization 936
randomized block design (RBD) 937, 937f
replication 936
response variable 935
results and conclusions 936
type 936
Dice similarity coefficient (DSC) 323
Dichotomous/binary variable (dummy) 16, 17t
Diet problem 720–721, 720–721b, 720t
Excel Solver 788–790, 789b, 789–791f
Directed network 836–837, 837f
Direct Oblimin methods 398
Discrete random variable 
cumulative distribution function (CDF) 138–139, 139b
definition 137
expected/average value 137–138
probability distributions 
Bernoulli distribution 142–144, 143–144b, 143f
binomial distribution 144–145, 144f, 145b
discrete uniform distribution 141–142, 141f, 142t, 142b
geometric distribution 145–147, 146–147b, 146f
hypergeometric distribution 148–149, 148f, 149b
negative binomial distribution 147–148, 147f, 148b
Poisson distribution 149–151, 150f, 150–151b
variance 138, 138b, 138t
Discrete uniform distribution 141–142, 141f, 142t, 142b
Discrete variables 8, 16
Dispersion/variability measures 
average deviation 
continuous data 56, 56b, 56t
grouped discrete data 54–55, 55t, 55b
modulus/absolute deviation 54
ungrouped discrete and continuous data 54, 54t, 54b
coefficient of variation 61, 61b
range 54
standard deviation 59–60, 59–60b
standard error 60–61, 60–61b, 60t
variance 
continuous data 58–59, 58–59b, 59t
definition 57
grouped discrete data 57–58, 58t, 58b
ungrouped discrete and continuous data 57, 57b
Durbin-Watson test 1164–1165t
autocorrelation 493, 493f
IBM SPSS Statistics Software 528, 528f
result 529, 529f
Stata, regression models estimation 515, 516f

E

Eigenvalues 391, 408, 408t, 424, 424f
Eigenvectors 391–392, 401–402, 424, 424f
Empty set 129
Erlang distribution 158
Estimation 
interval estimation 190, 190b See also Confidence intervals
parameter, definition 189
point estimation 189, 189b
maximum likelihood estimation 192
method of moments 190–191, 191t, 191b
ordinary least squares (OLS) 191–192
population parameters 189
Euclidean squared distance 318, 320t
Events 127, 129b
independent 128, 130
mutually excluding/exclusive 128, 128f, 130
Excel Solver 775–779, 775–779f
classic transportation problem 856–860, 856f, 857b, 858–861f
diet problem 788–790, 789b, 789–791f
facility location problem 907–908, 907–909f, 907–908b
farmer’s problem 790–792, 791b, 791–793f
job assignment problem 870, 871–872f, 871b
knapsack problem 891–893, 891–893f, 892b
Lifestyle Natural Juices Manufacturer 798, 802b, 802–804f
maximum flow problem 879–881, 880–881f, 880b
Naturelat Dairy 784–786, 785b, 785–787f
Oil-South Refinery 787–788, 787b, 788–789f
portfolio selection 793–797, 793–797f, 794b, 796b
production and inventory problem, Fenix&Furniture 798, 799–801f, 800b
sensitivity analysis 818–822, 818–823f
shortest path problem 875, 876b, 876–877f
transhipment problem (TSP) 866–868, 866–867b, 866–868f
Venix Toys 779–783, 780b, 780–784f, 784b
Experimental unit 935
Explanatory variables 935
Exploratory factor analysis 383
Exploratory multivariate technique 383
Exponential distribution 156–158, 156f, 157b
Extrapolations 449–450

F

Facility location problem 905–906b, 905f, 906t
candidate locations 902
Excel Solver 907–908, 907–909f, 907–908b
modeling 902–906
network programming problem 902
Factor extraction method 411–412, 411f
Factorial analysis of variance 239–246
Factorial ANOVA 938
Factorial design (FD) 937
Failure rate 157
Farmer’s problem 790–792, 791b, 791–793f
Feasible basic solution (FBS) 755
First-order correlation coefficients 387–389, 399, 399t
Fisher’s coefficient 
kurtosis 66
skewness 64
Fisher’s distribution  See Snedecor’s F distribution
Fixed effects parameters 988
Friedman’s test 1189t
K paired samples 290–295, 291–292t, 291–293b, 293–295f
F-test 456, 474
Furthest-neighbor/complete-linkage method 327, 332–335, 334t, 335–336f

G

Gamma distribution 157–158, 158f, 634, 635t, 635f
Gaussian distribution 
binomial approximation 155
cumulative distribution function 154, 154f
Poisson approximation 155–156
probability density function 152, 153f
standard deviations 153, 153f
standard normal distribution 153–154, 154–155f
Zscores 153–154
Gauss-Jordan elimination method 769, 769t, 772, 772t
General Algebraic Modeling System (GAMS) 774
Generalized linear latent and mixed model (GLLAMM) 1005
Geometric distribution 145–147, 146–147b, 146f
Geometric propagation/snowball sampling 177, 177b
Graph 835, 836f

H

Hamann similarity coefficient 324
Hamiltonian path 837
Hampered analysis 326, 327f
Hartley’s Fmax test 213–214, 213–214b, 1193t
Hierarchical agglomeration schedules 
between-groups/average-linkage method 328, 335–338, 337t, 338f
dendrogram 327
Euclidian distance 328, 329f
furthest-neighbor/complete-linkage method 327, 332–335, 334t, 335–336f
Hampered analysis 326, 327f
linkage methods 325, 326t
nearest-neighbor/single-linkage method 327–332, 331t, 331f, 333f
phenogram 327
SPSS  See IBM SPSS Statistics Software
Stata  See Stata Software
Hierarchical crossclassified models (HCM) 990
Hierarchical linear models (HLM) 988
count data 1056–1057, 1058–1063f, 1058t, 1059–1062
generalized linear latent and mixed models (GLLAMM) 1052, 1052f
hierarchical logistic models 
ceteris paribus 1055
chart of 1056, 1057f
dataset 1053, 1054f, 1054t
mixed effects logistic regression models 1052–1053
odds ratios 1055
outputs 1053, 1054f, 1056, 1056f
SPSS  See IBM SPSS Statistics Software
Stata  See Stata Software
three-level hierarchical linear models, repeated measures (HLM3) 998
individual models 996, 996f
intercepts and slopes randomness 996–997
intraclass correlation 997
temporal evolution 995
variance-covariance matrix 995
two-level hierarchical linear models, clustered data (HLM2) 
first-level model 991
individual models 991, 992f
intercepts 992
intraclass correlation 993
likelihood-ratio tests 993, 995
logarithmic likelihood function 994–995
maximum likelihood estimation (MLE) 994
multiple linear regression model 991
multivariate normal distribution 993
random intercepts model 993
random slopes model 993
reduced maximum likelihood 994
restricted maximum likelihood (REML) 994
slopes 992
statistical significance 993
Higher-order correlation coefficients 387–389
Histogram 21, 32–34, 32–33b, 32–33t, 33–34f
absolute frequency 32–33, 33f
analysis tools 32–33
continuous data 33, 34f
definition 32
discrete data 33, 34f
Monte Carlo method 921–922, 922f, 924f
Horizontal bar charts 26, 27f
Hosmer-Lemeshow test 579, 579f
binary logistic regression model 554
Huber-White robust standard error estimation 491
Stata, regression models estimation 507
Hypergeometric distribution 148–149, 148f, 149b
Hypotheses tests 
bilateral test 199
critical region (CR) 199, 199f
nonparametric tests 201 See also Nonparametric tests
parametric tests 201 See also Parametric tests
P-value 201
statistical hypothesis 199
type I error 200, 200t
type II error 200, 200t
unilateral test 199
left-tailed test 199, 200f
right-tailed test 200, 200f

I

IBM SPSS Statistics Software 
ANOVA 525, 527f
binary logistic regression model 591–601, 592–597f, 600–601f
Box-Cox transformations 527
C chart 967, 967–968f
confidence levels and intercept exclusion 519, 519f
Cp, Cpk, Cpm and Cpmk indexes 975–976, 975–976f
Cronbach’s alpha 436, 436–437f
Dependent box 516–518, 518f
Descriptives Option 74–76, 77f
Descriptives dialog box 76, 77f
Options dialog box 76, 78f
Options, summary measures 76, 78f
Durbin-Watson test 528, 528f
result 529, 529f
estimation 516, 517f
excluded variables 519–523
Explore Option 77–78, 79f
boxplot 79, 82f, 83
Descriptives Option, results 78, 81f
Explore dialog box 78, 79f
histogram 79, 82f, 83
Outliers option results 79, 81f
Percentiles option, results 78–79, 81f
Plots dialog box 78, 80f
Statistics dialog box 78, 80f
stem-and-leaf chart 79, 82f, 83
Frequencies Option 73f
Charts 74, 76f
Charts dialog box 74, 75f
Frequencies dialog box 73, 73f
frequency distribution table 74, 76f
qualitative and quantitative variables 72
Statistics dialog box 73, 74f
Statistics, summary measures 74, 75f
heteroskedasticity problem 524
hierarchical agglomeration schedules 350, 351f
allocation 356, 357f
clustering stage 354, 354f
dendrogram 350, 352f, 354, 355f
distance measure 361, 362f
Euclidian distance 350–351, 353, 353f, 360, 361f
linkage method 353, 353f
matrix 350, 352f
means 358, 360–361f
multidimensional scaling 360–361, 362f
nominal (qualitative) classification 356, 358f
Number of clusters 356, 356–357f
one-way analysis of variance 358, 358–359f
two-dimensional chart 361, 363f
variables selection 350, 351f
HLM2  See Two-level hierarchical linear model, clustered data
HLM3  See Three-level hierarchical linear model, repeated measures
Independent(s) box 516–518, 518f
lndist variable 527, 528f
multicollinearity diagnostic 523, 524f
multinomial logistic regression model 602–606, 602–604f
negative binomial regression model 676–685, 680–685f
nonhierarchical k-means agglomeration schedule 364–367, 364–368f
nonparametric tests 
binomial test 253, 254–255f
chi-square test 256–257, 257–258f, 279, 279–280f, 297, 297–299f
Cochran’s Q test 288, 289–290f
Friedman’s test 293, 294–295f
Kruskal-Wallis test 302, 302–303f
Mann-Whitney U test 284, 284–285f
McNemar test 264, 265–266f
sign test 260, 260–261f, 268–269, 269–270f
Wilcoxon test 274, 274–275f
normality plots with tests 523, 523f
np chart 960–963, 963b, 964f
outputs 519, 520f, 522f
parameter and confidence intervals selection 518–519, 518f
parametric tests 
one-way ANOVA 236–237, 237–238f
Student’s t-test 221, 222–223f, 225–226, 226–227f, 229–230, 230–231f
two-way ANOVA 242–244, 243–246f
P chart (defective fraction) 959–960, 960–963f
Poisson regression model 664–675, 665–679f
predicted values 519, 521f
principal components factor analysis 
algebraic solution 410
communalities 415, 415f
dataset 418, 419f
Display factor score coefficient matrix 412, 412f
eigenvalues and variance 413, 413f, 416, 418f
factor analysis 410, 410f
factor extraction method 411–412, 411f
factor loadings 414, 414f
factor scores 414, 414f
initial options 411, 411f
KMO statistic and Bartlett’s test of sphericity 413, 413f
loading plot 415–416, 415f, 417f
Pearson’s correlation coefficients 413, 413f, 418–419, 420f
ranking 420, 422f
rotated factor loadings 416, 417f
rotated factor scores 416, 418f
rotation angle 416, 418f
rotation method 412, 412f
Save as variables option 416, 416f
sorting 421, 422f
variable creation 420, 421f
variables selection 410, 410f
Varimax orthogonal rotation method 416, 416f
R chart 948–952f, 949
residuals behavior 524, 525f
residual sum of squares 524, 526f
RESUP variable 525, 527f
Shapiro-Wilk normality test result 523, 523f
square of the residuals 524, 526f
stepwise procedure selection 519, 521f
U chart 970, 971f
univariate tests for normality 
normality test selection 206, 207f
procedure 206, 207f
tests results 207–208, 208f
variable selection 206, 207f
VIF and Tolerance statistics 523, 524f
Independent events 128, 130
Integer programming (IP) 714–717, 731, 734–736
binary integer programming (BIP) 887 See also Binary programming (BP)
characteristics 887, 888b
facility location problem 905–906b, 905f, 906t
candidate locations 902
Excel Solver 907–908, 907–909f, 907–908b
modeling 902–906
network programming problem 902
heuristic procedure 887
knapsack problem 890–891b, 890t
decision variables 890
Excel Solver 891–893, 891–893f, 892b
mathematical formulation 890
model parameters 890
linear relaxation 888, 889b, 889f
metaheuristic procedure 887
mixed binary programming (MBP) 887
mixed integer programming (MIP) 887
rounding 888–890
staff scheduling problem 908–912, 909–912b, 911f, 913–914f
Interpolations 449–450
Interquartile range/interquartile interval (IQR/IQI) 37, 52
Intersection 128, 128f
Interval estimation 190, 190b See also Confidence intervals
Intraclass correlation 993, 997

J

Jaccard index 323
Job assignment problem 868, 868f
Excel Solver 870, 871–872f, 871b
mathematical formulation 869–870, 869–870b, 869t
Joint frequency distribution tables 
qualitative variables 
contingency/crossed classification/correspondence table 93
example 94–101b, 94–95t, 96–101f
marginal totals 94–101
quantitative variables 114
Judgmental/purposive sampling 175, 175b

K

Kaiser criterion 393
Kaiser-Meyer-Olkin (KMO) statistic 387, 389, 389t, 399, 413, 413f, 423, 424f
Karhunen-Loève transformation 384
Kernel density estimate 503, 503f
Stata, regression models estimation 511–513, 514f
King’s method 46–47, 47b
Knapsack problem 890–891b, 890t
decision variables 890
Excel Solver 891–893, 891–893f, 892b
mathematical formulation 890
model parameters 890
Knowledge discovery in databases (KDD) 984, 985f
Kolmogorov-Smirnov (K-S) test 1177t
univariate tests for normality 201–203, 202–203t, 202–203b
Kruskal-Wallis test 1190t
K independent samples 299–304, 300–302b, 301t, 301–304f

L

Lagrange multiplier (LM) 489–490
Latent root criterion 393
Levene’s F-Test 214–216, 214–216b, 215–216t
SPSS Software 
procedure 216, 217–218f
results 216, 218, 218f
variables selection 216, 217f
Stata Software 218–219, 219f
Lifestyle Natural Juices Manufacturer 798, 802–804f, 802b
Lifetime 157
Likelihood-ratio tests 993, 995
Likert scale 17, 314, 384
Linear Interactive and Discrete Optimizer (LINDO) Systems 773–774
Linear mixed models (LMM) 988
Linear programming (LP) problems 
additivity assumption 713
Advanced Integrated Multidimensional Modeling Software (AIMMS) 774
aggregated planning problem 734–736b, 734t
binary programming (BP) 733
decision variables 733
general formulation 733
integer programming (IP) model 734–736
mixed-integer programming (MIP) problem 734–736
model parameters 733
nonlinear programming (NLP) 733
resources 732
basic solution (BS) 755
basic variables (BV) 755, 755b
blending/mixing problem 717–719, 717–719b, 718t
canonical form 710, 712b
capital budget problems 721–724, 722–724b, 722–723t
certainty 713
continuous function 709
convex and nonconvex sets 748, 748f
CPLEX 774
degenerate optimal solution 753–754, 754f, 754b
diet problem 720–721, 720t, 720–721b
divisibility and non-negativity 713
equality constraint 711
Excel Solver 775–779, 775–779f
diet problem 788–790, 789–791f, 789b
farmer’s problem 790–792, 791b, 791–793f
Lifestyle Natural Juices Manufacturer 798, 802–804f, 802b
Naturelat Dairy 784–786, 785b, 785–787f
Oil-South Refinery 787–788, 787b, 788–789f
portfolio selection 793–797, 793–797f, 794b, 796b
production and inventory problem, Fenix&Furniture 798, 799–801f, 800b
Venix Toys 779–783, 780b, 780–784f, 784b
feasible basic solution (FBS) 755
feasible solutions 709
free variable 711
General Algebraic Modeling System (GAMS) 774
inequality constraint 711
linear function and constraints 709
Linear Interactive and Discrete Optimizer (LINDO) Systems 773–774
A Mathematical Programming Language (AMPL) 774
MINOS 774
multiple optimal solutions 751–752, 751–752b, 752f
nonbasic variables (NBV) 755, 755b
no optimal solution 753, 753b
optimal solution 709, 747
maximization problem 748–750, 748–750b, 749f
minimization problem 750–751, 750–751f, 750–751b
Optimization Subroutine Library (OSL) 774
portfolio selection problem 726–728b, 726–728t
financial investments 724
investment portfolio risk minimization 725–728
investment portfolio’s expected return 724–725
Markowitz’s model 724
production and inventory problem 
costs and capacity 730t
decision variables 729
demand per product and period 730t
general formulation 729
integer programming (IP) problem 731
inventory balance equations 731
maximum inventory capacity 732
maximum production capacity 731
model parameters 729
non-negativity constraints 729–732
optimal solution 732t
production mix problem 713–717, 714–717b, 715–716t
proportionality assumption 712–713, 713f
resource optimization problems 713
sensitivity analysis 747, 807–808b
Excel Solver 818–822, 818–823f
independent constraints terms 807
objective function coefficients 808–812, 808–809f, 810–811b
reduced cost 816–818, 817–818b
shadow price 812–816, 813–816b
Simplex method  See Simplex method
slack variable 711
software packages 773
Solver error messages, unlimited and infeasible solutions 
no optimal solution 800, 805f
Solver Results dialog box 798
unlimited objective function z 798–799, 804–805f
Solver results 
Answer Report 802–806, 806f
Excel spreadsheets 800
Limits Report 806–807, 806f
standard form 709–710, 711–712b
standard maximization problem 711
surplus variable 711
unlimited objective function z 752–753, 752–753b, 753f
viable/feasible solution 747
XPRESS 774
Linear regression models 
analysis of variance (ANOVA) 457, 458f
confidence levels 
dataset 465, 466t
dispersion of points 463, 464f
inclusion/exclusion criteria 464–465, 465b
null hypothesis rejection 464–465
for parameters 462–463, 463–464f
predicted time vs. distance traveled 465–466, 466–467f
degrees of freedom 457
dummy variables 
ceteris paribus condition 474
confidence interval amplitudes 479
criteria 476, 476t
dataset 473, 473t
driving style variable 474, 476, 476t
F-test 474
GDP growth 472
joint selection 473, 475f, 477, 477f
outputs 473, 475f, 477–478, 478–479f
qualitative explanatory variable 472–473, 474t
random weighting 472
substitution of 476, 477t
t-test 474
explanatory power 453, 454f
coefficient of determination 453–456, 455t, 455–456f
residual sum of squares (RSS) 451
sum of squares due to regression (SSR) 451
total sum of squares (TSS) 451
explanatory variables 443
F significance level 457, 458f
F statistic 457
F-test 456
functional form 480
metric/quantitative variable 443
multiple models 443–444 See also Multiple linear regression models
null hypothesis, nonrejection 460, 462, 462f
OLS method  See Ordinary least squares (OLS) method
predicted value and parameters 444
P-values 459–460
quantitative dependent variable 443
residual error 444
simple linear regression model 443–444, 444f
SPSS  See IBM SPSS Statistics Software
standard error 459, 460f
statistical tests 443
t statistic 457–459
t-test 457–459
coefficients and significance 459, 461f
significance levels 460, 461f
Linear specification 988
Linear trend model 
random intercepts 1020–1023, 1021–1023f
random intercepts and slopes 1023–1027, 1024–1025f, 1027–1028f
Line chart 920, 922, 922–923f
Line graphs 21, 30–31, 30t, 30–31b, 31f
Logarithmic likelihood function 994–995

M

Mahalanobis distance 379
Manhattan distance 319
Mann-Whitney U test 1185–1188t
two independent samples 281–286, 282–283t, 282–284b, 284–286f
Markowitz’s model 724
Maximum flow problem 
destination node 876–877
Excel Solver 879–881, 880–881f, 880b
mathematical formulation 878–879, 878–879b, 878f
Maximum likelihood estimation (MLE) 192, 994, 1005
binary logistic regression model 542–547, 542–544t, 545–547f
multinomial logistic regression model 564–570, 565–566t, 567–568f, 569–570t, 570f
negative binomial regression model 
dataset 636, 637t
histogram 637, 638f
mean and variance 637, 637t
parameters estimation 639, 640f
results 638, 640t
Solver window 638, 639f
Poisson regression model 621t
dependent variable mean and variance 621, 621t, 622f
Excel Solver tool 622, 624, 624f
log-linear model 625
non-negative and discrete values 620
overdispersion 621–622
parameters estimation 625, 626f
rate of incidence 622–623, 623t, 623f
results 624, 625t
Stata, regression models estimation 500
McFadden pseudo R2 548
McNemar test 262–264, 263t, 263–264b, 265–266f
Mean absolute deviation (MAD) 725
Mean arrivals rate 157
Measurement, definition 9
Median 
continuous data 44–45, 44t, 44–45b
grouped discrete data 43–44, 43t, 43–44b
ungrouped discrete and continuous data 42–43, 42t, 42–43b
Method of moments 190–191, 191b, 191t
Minimum cost method 849, 850–851t, 850–852b
Minimum path problem  See Shortest path problem
Minimum spanning tree 837, 838f
Minkowski distance 318
MINOS 774
Mixed binary programming (MBP) 887
Mixed effects logistic regression models 1052–1053
Mixed-integer programming (MIP) problem 734–736, 887
Mode 
continuous data 46–47, 46–47b, 46t
grouped qualitative/discrete data 45–46, 45–46b, 46t
ungrouped data 45, 45t, 45b
Monte Carlo method 
application 920
Excel 
Data Analysis 920
histogram 921–922, 922f, 924f
line chart 920, 922, 922–923f
profit and loss forecast 926–928, 928–931f
random number generation and probability distributions 920–921, 921f, 923f
red wine consumption 923–925, 924–928f
frequency distribution 920
histogram 920
Manhattan project 919
probability density functions (PDF) 920
risks and uncertainties 920
Multilevel modeling 987–988
Multilevel negative binomial regression model 1059
Multilevel Poisson regression model 1059
Multinomial logistic regression model 311, 539
confidence intervals 574–575, 574–575t
event 563
logits 563
maximum likelihood 564–570, 565–566t, 567–568f, 569–570t, 570f
occurrence probabilities 563
SPSS  See IBM SPSS Statistics Software
Stata  See Stata Software
statistical significance 570–574, 571–572f
Multiple linear regression models 393, 443–444, 991
ceteris paribus concept 467
dataset 468, 468t
explanatory variables 470, 471f
multicollinearity 472
null hypothesis, nonrejection 472
outputs 470, 471f
parameters calculation 469–470, 469–470t
residual sum of squares 468
Stata  See Stata, regression models estimation
time equation 470
Multivariate normal distribution 394, 993
Mutually excluding/exclusive events 128, 128f, 130

N

Naturelat Dairy 784–786, 785b, 785–787f
Nearest-neighbor/single-linkage method 327–332, 331f, 331t, 333f
Negative binomial distribution 147–148, 147f, 148b
Negative binomial regression model 
confidence intervals 644, 644t
Gamma distribution 634, 635f, 635t
maximum likelihood 
dataset 636, 637t
histogram 637, 638f
mean and variance 637, 637t
parameters estimation 639, 640f
results 638, 640t
Solver window 638, 639f
mean 636
negative binomial type 1 (NB1) regression model 636
negative binomial type 2 (NB2) regression model 636
occurrence probability 634
overdispersion 634
Poisson distribution 634
probability distribution function 634
quantitative variable 633
SPSS  See IBM SPSS Statistics Software
Stata  See Stata Software
statistical significance 641–643, 641–642f
variance 636
Nested data structures 987–991, 989–990f, 989–990t
Network programming 
classic transportation problem 838f, 839–841b, 840t, 840f
algorithm  See Transportation algorithm
balanced transportation problem 839
decision variables 838
Excel Solver 856–860, 856f, 857b, 858–861f
general formulation 839
model parameters 838
Simplex method 839
supply chain 838
total supply capacity and total demand 841–845, 841f, 841–845b, 842t, 843f, 844t, 845f
demand nodes 835
directed and undirected arc 836, 836f
directed and undirected cycle 837
directed and undirected path 837
directed network 836–837, 837f
graph 835, 836f
Hamiltonian path 837
job assignment problem 868, 868f
Excel Solver 870, 871–872f, 871b
mathematical formulation 869–870, 869–870b, 869t
maximum flow problem 
destination node 876–877
Excel Solver 879–881, 880–881f, 880b
mathematical formulation 878–879, 878–879b, 878f
minimum spanning tree 837, 838f
network, definition 835, 836f
shortest path problem 
Excel Solver 875, 876b, 876–877f
mathematical formulation 873–875, 874–875b, 874f
supply capacity node 870–873
subgraph 837
supply nodes/sources 835
transhipment problem (TSP) 
Excel Solver 866–868, 866–868f, 866–867b
intermediate transhipment points 860–862
mathematical formulation 862–866, 862f, 864–865f, 864t, 864–866b
stages 860–862
transportation unit cost 862
transshipment nodes 835
tree structure 837, 837f
Nonbasic variables (NBV) 755, 755b
Nonhierarchical k-means agglomeration schedule 338–339
arbitrary allocation 341, 341t, 342f
Euclidian distance 346, 346t
explanatory variable 349–350
F significance level 348, 349f
F-test 340
logical sequence 339
mean 347, 347t
one-way analysis of variance (ANOVA) 348, 349t
procedure 339, 339f
reallocation 342–345t, 343f, 344
solution 345–346, 346f
SPSS  See IBM SPSS Statistics Software
Stata  See Stata Software
variation and F statistic 348t
Z-scores 340
Nonlinear programming (NLP) 733
Nonlinear regression models 443
binary and multinomial logistic models 497
Box-Cox transformation 497–498, 497b
exponential specification 495, 496f, 496b
linear specification 495, 496f, 496b
nonlinear behavior 495, 495f
Poisson and negative binomial regression models 497
quadratic specification 495, 496f, 496b
semilogarithmic specification 495, 496f, 496b
Nonmetric/qualitative variables 
dichotomous/binary variable (dummy) 16, 17t
nominal scale 10, 10t
arithmetic operations 10
Data View 11, 11f
descriptive statistics 10, 12
labels 11, 12t, 12f, 14f
Value Labels 11, 14f
variable selection 11, 13f
Variable View 10–11, 11f
ordinal scale 12–14, 15t, 15f
polychotomous 16
scales of accuracy 16, 16f
Nonparametric tests 
advantages 249
classification 250, 250t
disadvantages 249
K independent samples 
chi-square test 295–299, 296t, 296b, 296–299f
Kruskal-Wallis test 299–304, 300–302b, 301t, 301–304f
K paired samples 
Cochran’s Q test 286–290, 287–288b, 287t, 288–290f
Friedman’s test 290–295, 291–292t, 291–293b, 293–295f
one sample 
binomial test 250–254, 251–253b, 252t, 253–255f
chi-square test 255–257, 255–259f, 256b, 256t
sign test 257–262, 259–260b, 259t, 260–262f
two independent samples 
chi-square test 276–280, 277–278t, 277–278b, 277–280f
Mann-Whitney U test 281–286, 282–283t, 282–284b, 284–286f
two paired samples 
McNemar test 262–264, 263t, 263–264b, 265–266f
sign test 264–270, 267–268b, 267–268t, 268–271f
Wilcoxon test 270–276, 272–273t, 272–274b, 273–276f
Nonrandom sampling 169, 170f
advantages and disadvantages 169–170
convenience sampling 175, 175b
geometric propagation/snowball sampling 177, 177b
judgmental/purposive sampling 175, 175b
quota sampling 176–177, 176–177b, 176–177t
Northwest corner method 847, 848–849t, 848–850b, 854–856b
np chart 960–963, 963b, 964f

O

Oblique rotation methods 398
Ochiai similarity coefficient 323
Odds ratios 581, 581f, 1055
Oil-South Refinery 787–788, 787b, 788–789f
One-stage cluster sampling 173–174, 174b, 183
finite population, sample size 
mean estimation 184
proportion estimation 185
infinite population, sample size 
mean estimation 184
proportion estimation 184–185
One-way analysis of variance (one-way ANOVA) 937–938
Optimization models 
business modeling 736
classification 708, 708f
constraints 708
decision and parameter variables 707
decision concept 707
elements 707
linear programming (LP)  See Linear programming (LP)
objective function 708
real system behavior 707, 708f
Optimization Subroutine Library (OSL) 774
Ordinary Gauss-Hermite quadrature 1005
Ordinary least squares (OLS) method 191–192
autocorrelation 
Breusch-Godfrey test 493–494
causes 492, 492f
consequences 493
data time evolution 491
Durbin-Watson test 493, 493f
first-order autocorrelation 492
generalized least squares method 494
residuals problem 492, 492f
Box-Cox transformations 480–481
calculation spreadsheet 448, 448t
conditional mean 445
data analysis box 450, 451f
data insertion 450, 452f
dataset 445, 445t, 448, 448f
dependent variable 444–445
Excel Regression tool 450
expected value 445
explanatory variable 445
extrapolations 449–450
heteroskedasticity 
Breusch-Pagan/Cook-Weisberg test 489–490
chi-square distribution 490
consequences 489
discretionary income 489, 489f
Huber-White method 491
learning process 488
probability distribution 488
problem 488, 488f
residual vector 490
trial and error models 488, 488f
weighted least squares method 490
interpolations 449–450
linear regression estimation 450, 451f
linktest 480–481, 494–495
multicollinearity 
auxiliary regressions 487
causes of 481–482
Class A model 483, 483t, 484f
Class B model 484–485, 485f, 485t
Class C model 485–486, 486t, 486f
consequences 482–483
correlation matrix 487
dependent variable 481
matrix determinant 487
matrix form 481
orthogonal factors 487
parameter estimation 481
Tolerance 487
t statistics 487
VIF 487
normal distribution of residuals 480, 480f
presuppositions 479, 480b
regression equation coefficients 450, 453f
RESET test 480–481, 495
residuals conditions 446, 447f
residual sum of squares minimization 449, 450f
Shapiro-Wilk test/Shapiro-Francia test 480
simple linear regression model 445, 450, 450f
equation 448
outputs 450, 452f
Solver tool 448–449, 449f
travel time vs. distance traveled 445, 446f
Orthogonal rotation method 397
Overall model efficiency (OME) 560
Overdispersion 
negative binomial regression model 634
Poisson regression model 632–633, 632t, 633f
Stata Software 648, 648f, 658

P

Parametric tests 
ANOVA  See Analysis of variance (ANOVA)
population mean 
Student’s t-test  See Student’s t-test
Z test 219–220, 219–220b
univariate tests for normality 
Kolmogorov-Smirnov (K-S) test 201–203, 202–203t, 202–203b
Shapiro-Francia (S-F) tests 205–206, 205–206b, 206t
Shapiro-Wilk (S-W) test 203–205, 204t, 204–205b
SPSS Software  See IBM SPSS Statistics Software
Stata  See Stata Software
variance homogeneity tests 
Bartlett’s χ2 test 210–212, 211–212b, 211t
Cochran’s C test 212–213, 213b
Hartley’s Fmax test 213–214, 213–214b
Levene’s F-Test 214–218, 214–216b, 215–216t
null hypothesis 210
population variance 210
Pareto chart 21, 28–30, 29t, 29–30b, 30f
Partial correlation coefficients 387–388
Pascal distribution 147–148, 147f, 148b
P chart 959, 959f
defective fraction 959–960, 960–963f
Pearson’s contingency coefficient 107
Pearson’s correlation coefficient 315, 398, 399t, 413, 413f, 418–419, 420f, 427, 428f
bivariate descriptive statistics 119–121, 119–121b, 119–121f
Pearson’s first coefficient of skewness 62–63, 62–63b
Pearson’s linear correlation 384
correlation matrix 385
dataset model 385t
factor extraction 385, 388f
latent dimensions 386
linear adjustments 385, 387f
three-dimensional scatter plot 385, 386f
Pearson’s second coefficient of skewness 63, 63b
Percentile coefficient of kurtosis  See Coefficient of kurtosis
Percentiles 48–52
continuous data 50–52, 51–52b, 51t
grouped discrete data 50, 50b
ungrouped discrete and continuous data 48–50, 49–50b
Permutations 135, 135b
Phi coefficient 106, 106–108b, 107t, 109–110f
Pie charts 21, 27–28, 28b, 28t, 28f
Point estimation 189, 189b
maximum likelihood estimation 192
method of moments 190–191, 191b, 191t
ordinary least squares (OLS) 191–192
Poisson distribution 149–151, 150f, 150–151b
Poisson regression model 
confidence intervals 630–632, 631t, 632b
dependent variable 618
distribution 619, 619f
equidispersion of 620
explanatory variable 618
incidence rate ratio 618
maximum likelihood 621t
dependent variable mean and variance 621, 621t, 622f
Excel Solver tool 622, 624, 624f
log-linear model 625
non-negative and discrete values 620
overdispersion 621–622
parameters estimation 625, 626f
rate of incidence 622–623, 623t, 623f
results 624, 625t
mean 620
overdispersion 632–633, 632t, 633f
probability of occurrence 619, 619t
SPSS  See IBM SPSS Statistics Software
Stata  See Stata Software
statistical significance 626–630, 627–628f
variance 620
Polychotomous variable 16
Population 
definition 169
finite 169
infinite 169
moment of distribution 190
Portfolio selection problem 726–728b, 726–728t
Excel Solver 793–797, 793–797f, 794b, 796b
financial investments 724
investment portfolio risk minimization 725–728
investment portfolio’s expected return 724–725
Markowitz’s model 724
Position/location measures 
BACON algorithm 52
boxplot 53–54, 53f
central tendency 
arithmetic mean 38–42, 38–41t, 38–42b
median 42–45, 42–44t, 42–45b
mode 45–47, 45–47b, 45–46t
interquartile range (IQR) 52
outlier identification methods 52, 53b
quantiles 48–52
deciles 48
percentiles 48–52
quartiles 47–48
Principal components factor analysis 
Bartlett’s test of sphericity 387, 389–390
clusters 383, 390
coefficient of determination 395
communality 394
confirmatory factor analysis 383
confirmatory techniques 405
correlation coefficients 383
correlation matrix 391
Cronbach’s alpha’s magnitude 390
dataset 398, 398t
eigenvalues 391, 408, 408t
eigenvectors 391–392, 401–402
exploratory factor analysis 383
exploratory multivariate technique 383
factor loadings 394, 394t, 404, 404t, 406–407t
factor rotation 
Direct Oblimin methods 398
loading plot 395, 396f, 407f, 408
loadings 397, 407, 407t
oblique rotation methods 398
original factors 395, 396t, 396f
orthogonal rotation method 397
Promax methods 398
scores 397
factor scores 390–393, 403, 404t
first-order correlation coefficients 387–389, 399, 399t
higher-order correlation coefficients 387–389
Kaiser criterion 393
Kaiser-Meyer-Olkin (KMO) statistic 387, 389, 389t, 399
Karhunen-Loève transformation 384
latent root criterion 393
Likert scale 384
loading plot 405, 405f
mental factors 384
middling 400
multiple linear regression model 393
multivariate normal distribution 394
partial correlation coefficients 387–388
Pearson’s correlation coefficients 398, 399t
Pearson’s linear correlation 384
correlation matrix 385
dataset model 385t
factor extraction 385, 388f
latent dimensions 386
linear adjustments 385, 387f
three-dimensional scatter plot 385, 386f
second-order correlation coefficients 387–389, 399, 399t
significance level 400, 400f
SPSS  See IBM SPSS Statistics Software
Stata  See Stata Software
structural equation modeling 383
uncorrelated factors 383
variance table 401, 401t
weighted rank-sum criterion 408, 409t
zero-order correlation coefficients 387–388
Probability density functions (PDF) 920
negative binomial regression model 634
Probability theory 
Bayes’ theorem 132–133, 132–133b
combinatorial analysis 
arrangement 133–134, 133–134b
combinations 134, 134b
definition 133
permutations 135, 135b
complement 128, 128f, 130
conditional probability 131
multiplication rule 131–132, 131–132b, 132t
definition 129
empty set 129
events 127, 129b
independent 128, 130
mutually excluding/exclusive 128, 128f, 130
intersection 128, 128f
random experiment 127
sample space 127, 129
union 127, 128f
variation field 129
Probability variation field 129
Process, flowchart 935, 936f
Production and inventory problem 
costs and capacity 730t
decision variables 729
demand per product and period 730t
Fenix&Furniture, Excel Solver 798, 799–801f, 800b
general formulation 729
integer programming (IP) problem 731
inventory balance equations 731
maximum inventory capacity 732
maximum production capacity 731
model parameters 729
non-negativity conditions 729–732
non-negativity constraints 732
optimal solution 732t
Production mix problem 713–717, 714–717b, 715–716t
Promax methods 398
Proportional stratified sampling 173
Pythagorean distance formula 316, 317f

Q

Qualitative variables 
bivariate descriptive statistics 
chi-square statistic 102–110, 102–110b, 102–103t, 104–106f, 107t, 109–110f
joint frequency distribution tables  See Joint frequency distribution tables
Spearman’s coefficient 110–113, 110f, 111–113b, 111t, 112–113f
frequency distribution tables 22–23, 22–23b, 22–23t
univariate descriptive statistics 
bar charts 21, 26–27, 26t, 26–27b, 27f
Pareto chart 21, 28–30, 29t, 29–30b, 30f
pie charts 21, 27–28, 28b, 28t, 28f
Quantile regression models 48–52
deciles 48
dependent variables 533
leverage distances 532
median regression models 532
normality of residuals 533
percentiles 48–52
quartiles 47–48
Stata 
bacon algorithm 533
conditional distribution 537
dependent variable 533, 534f, 538, 538f
median regression model outputs 535, 535f
nonconditional median 535
OLS regression model 534
parameter estimation 536, 536–537f
Quantitative variables 
bivariate descriptive statistics 
covariance 118, 118b
Pearson’s correlation coefficient 119–121, 119–121b, 119–121f
scatter plot 114–118, 114–118f, 115–116b
continuous 16
discrete 16
interval scale 15
ratio scale 15
scales of accuracy 16, 16f
univariate descriptive statistics 
boxplots/box-and-whisker diagram 21, 37–38, 37f
histograms 21, 32–34, 32–33b, 32–33t, 33–34f
line graphs 21, 30–31, 30t, 30–31b, 31f
scatter plot 21, 31–32, 31–32b, 31t, 32f
stem-and-leaf plots 21, 34–37, 35–36t, 35–37b, 36–37f
Quartiles 47–48
continuous data 50–52, 51–52b, 51t
grouped discrete data 50, 50b
ungrouped discrete and continuous data 48–50, 49–50b
Quota sampling 176–177, 176–177b, 176–177t

R

Random coefficients models 988
Random effects parameters 988
Random experiment 127
Random intercepts and slopes model 1006–1011, 1007–1011f, 1037–1038, 1038f
Random intercepts model 993, 1004–1005, 1004f, 1006f, 1036, 1037f
Randomized block design (RBD) 937, 937f
Random sampling 169, 170f
advantages and disadvantages 169
one-stage cluster sampling 173–174, 174b
simple random sampling (SRS) 170–172, 171t, 171–172b
stratified sampling 173, 173b
systematic sampling 172, 172b
two-stage cluster sampling 174, 175b
Random slopes model 993
Random variables 
continuous random variable 139–141, 139f, 140–141b
chi-square distribution 159–160, 159–160f, 160b
exponential distribution 156–157, 156f, 157b
gamma distribution 157–158, 158f
normal distribution  See Gaussian distribution
Snedecor’s F distribution 162–164, 163b, 163f, 164t
Student’s t distribution 160–162, 161f, 162b
uniform distribution 151–152, 151t, 152f, 152b
discrete random variable 137–139, 138–139b
Bernoulli distribution 142–144, 143–144b, 143f
binomial distribution 144–145, 144f, 145b
discrete uniform distribution 141–142, 141f, 142t, 142b
geometric distribution 145–147, 146f, 146–147b
hypergeometric distribution 148–149, 148f, 149b
negative binomial distribution 147–148, 147f, 148b
Poisson distribution 149–151, 150f, 150–151b
random experiment 137
Range 54
R chart 947–952f, 948–949
Reduced cost 816–818, 817–818b
Reduced maximum likelihood 994
Reduced normal distribution 153
Regression models 
negative binomial regression model 617, 618f
Poisson model 617, 618f See also Poisson regression model
Regression specification error (RESET) test 495
Relative cumulative frequency 22
Relative frequency 22
Residual error 444
Residual sum of squares (RSS) 451, 468
minimization 449, 450f
two-way ANOVA 240
Restricted maximum likelihood (REML) 994, 1007–1008
Robit regression models 610f
Bernoulli distribution 609
definition 608
event occurrence 609–610, 610t
logistic distribution 609
sigmoid function 609
Stata 611–615, 611–614f
Rogers and Tanimoto similarity coefficient 323
Rule, definition 9
Russel and Rao similarity coefficient 323

S

Sample moment of distribution 190
Sample space 127, 129
Sampling 
definition 169
nonprobability sampling  See Nonrandom sampling
population 
definition 169
finite 169
infinite 169
probability sampling  See Random sampling
types 169
Scale, definition 9
Scatter plot 21, 31–32, 31–32b, 31t, 32f, 312, 312f
negative linear relationship 114, 115f
positive linear relationship 114, 114f
SPSS 116f
chart type 115, 116f
Simple Scatterplot dialog box 115, 117f
variables 115, 117f
on Stata 116, 118f
Second-order correlation coefficients 387–389, 399, 399t
Shadow price 812–816, 813–816b
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