In the course of one's research, the expediency of meeting contractual and other externally imposed deadlines too often seems to take priority over what may be more significant research findings in the longer run. Such is the case with this volume which, despite our best intentions, has been put aside time and again since 1971 in favor of what seemed to be more urgent matters. Despite this delay, to our knowledge the principal research results and documentation presented here have not been superseded by other publications. The background of this endeavor may be of some historical interest, especially to those who agree that research is not a straightforward, mechanistic process whose outcome or even direction is known in ad­ vance. In the process of this brief recounting, we would like to express our gratitude to those individuals and organizations who facilitated and supported our efforts. We were introduced to the Beale, Kendall and Mann algorithm, the source of all our efforts, quite by chance. Professor Britton Harris suggested to me in April 1967 that I might like to attend a CEIR half-day seminar on optimal regression being given by Professor M. G. Kendall in Washington. D. C. I agreed that the topic seemed interesting and went along. Had it not been for Harris' suggestion and financial support, this work almost certainly would have never begun.

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1.1 Orientation and Objective.- 1.2 Organization.- 2. Optimal Regression Analysis.- 2.1 Introduction.- 2.2 Description of the Algorithm.- 2.2.1 General Algorithm.- 2.2.2 Optimal Regression Algorithm.- 2.3 Strategies in Using the Program.- 2.3.1 Alternate Ways of Stopping the Program.- 2.3.2 Options for Using the Program.- 2.4 Related Multiple Regression Programs.- 2.5 Case Studies of Optimal vs. Stepwise Regression.- 2.6 Suggestions for a Strategy for Using the Program.- 2.7 Order and Detailed Description of Input Card Types.- 2.7.1 Title.- 2.7.2 Problem Definition.- 2.7.3 Equations Desired.- 2.7.4 Iteration Limits.- 2.7.5 Equations Previously Processed.- 2.7.6 Confidence Limits on F-ratios.- 2.7.7 Confidence Limits on t-tests.- 2.7.8 Lower Tolerance Limits on Durbin-Watson d-statistic.- 2.7.9 Upper Tolerance Limits on Durbin-Watson d-statistic.- 2.7.10 Variables to be Forced.- 2.7.11 Format of Data.- 2.7.12 Output Options.- 2.7.13 Labels for Variables.- 2.7.14 Subset of Original Variables.- 2.7.15 Data Deck.- 2.7.16 Unconditional Thresholds.- 2.7.17 Information from Previous Jobs.- 2.7.18 WARNING.- 2.8 Several Analyses on Different Sets of Data or the Same Data.- 2.9 Output of the Program.- 2.10 Machine Dependent Program Features and Suggestions for Modification.- 2.11 Description of Program by Subroutine.- 2.11.1 MAIN.- 2.11.2 SETUP.- 2.11.3 STAGE2.- 2.11.4 PRIMR.- 2.11.5 STAGE4.- 2.11.6 CHKVAR.- 2.11.7 STAGE8.- 2.11.8 FMAXØD.- 2.11.9 ØUTATl.- 2.11.10 ØUTATM.- 2.11.11 CØNDTH.- 2.11.12 PLACE(B,C).- 2.11.13 PIVØTR(ØRIG, STØRE, NG, INVRNØ, IDIM,IDØNE).- 2.11.14 RITØUT(ATRIX, INØUT, NEL).- 2.11.15 RESET.- 2.11.16 ØUTPUT.- 2.11.17 STG13A.- 2.11.18 STG4A.- 2.11.19 STG4AB.- 2.12 Definitions of the Square of the Multiple Correlation Coefficient.- 3. Interdependence Analysis.- 3.1 Introduction.- 3.2 Interdependence Analysis Algorithm.- 3.2.1 Pivot Operations.- 3.2.2 Description of the Algorithm.- 3.3 Example of Interdependence Analysis.- 3.4 Suggestions for a Strategy for Using the Program.- 3.5 Order and Detailed Description of Input Card Types.- 3.5.1 Title Card.- 3.5.2 Problem Definition.- 3.5.3 Values of N.- 3.5.4 Sets Previously Processed.- 3.5.5 Iteration Limits.- 3.5.6 Variables to be Forced.- 3.5.7 Format of Data.- 3.5.8 Output Options.- 3.5.9 Data Deck.- 3.5.10 Unconditional Thresholds.- 3.5.11 Information from Previous Jobs.- 3.5.12 WARNING.- 3.6 Output of the Program.- 3.7 Machine Dependent Program Features and Suggestions for Modification.- 3.8 Description of the Program by Subroutine.- 3.8.1 MAIN.- 3.8.2 SETUP.- 3.8.3 STAGE2.- 3.8.4 PRIMR.- 3.8.5 STAGE4.- 3.8.6 CHKVAR.- 3.8.7 STAGE8.- 3.8.8 FMAXØD.- 3.8.9 ØUTATl.- 3.8.10 ØUTATM.- 3.8.11 CØNDTH.- 3.8.12 PLACE(B,C).- 3.8.13 PIVØTR(ØRIG, STØRE, NG, INVRNØ, IDIM, IDØNE).- 3.8.14 RITØUT(ATRIX, INØUT, NEL).- 3.8.15 RESET.- 3.8.16 ØUTPUT.- 3.8.17 STG13A.- 3.8.18 STG4A.- 3.8.19 STG4AB.- 4. Optimal Network Analysis.- 4.1 Introduction.- 4.2 Optimal Network Algorithm.- 4.2.1 Minimum Path and Minimum Spanning Tree Algorithms.- 4.2.2 Description of the Algorithm.- 4.3 Examples of Optimal Network Analysis.- 4.4 Suggestions for a Strategy for Using the Program.- 4.5 Order and Detailed Description of Input Card Types.- 4.5.1 Title.- 4.5.2 Problem Definition.- 4.5.3 Budget Constraints.- 4.5.4 Iteration Limits.- 4.5.5 Networks Previously Processed.- 4.5.6 Links to be Forced.- 4.5.7 Output Options.- 4.5.8 Format of Links.- 4.5.9 Deck of Links.- 4.5.10 Unconditional Thresholds.- 4.5.11 Networks from Previous Jobs.- 4.5.12 WARNING.- 4.6 Output of the Program.- 4.7 Machine Dependent Features and Suggestions for Modification.- 4.8 Description of the Program by Subroutine.- 4.8.1 MAIN.- 4.8.2 SETUP.- 4.8.3 STAGE2.- 4.8.4 STAJ4A.- 4.8.5 Arrays and Variables with Same Definitions Throughout Remaining Subroutines.- 4.8.6 STG4AB.- 4.8.7 STAGE4.- 4.8.8 STAGE6(NØYES).- 4.8.9 STAGE8.- 4.8.10 CHKVAR.- 4.8.11 FMAXØD.- 4.8.12 STAJ16.- 4.8.13 STAJ17.- 4.8.14 STAJ18.- 4.8.15 STG13A.- 4.8.16 ØUTPUT.- 4.8.17 RESET.- 4:8.18 CØNECT(M1, M2).- 4.8.19 SPAN.- 4.8.20 MINDIS.- 4.8.21 LNKØUT(JP, KP, DP, PP, JPRINT).- 4.8.22 LINKIN(J, K, S, D, P, IPRINT).- 4.8.23 STAJ6B.