{"id":"https://openalex.org/W2552273832","doi":"https://doi.org/10.2307/2346330","title":"Use of Orthogonal Factors for Selection of Variables in a Regression Equation-An Illustration","display_name":"Use of Orthogonal Factors for Selection of Variables in a Regression Equation-An Illustration","publication_year":1970,"publication_date":"1970-01-01","ids":{"openalex":"https://openalex.org/W2552273832","doi":"https://doi.org/10.2307/2346330","mag":"2552273832"},"language":"en","primary_location":{"id":"doi:10.2307/2346330","doi":"https://doi.org/10.2307/2346330","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2346330","pdf_url":null,"source":{"id":"https://openalex.org/S2764642956","display_name":"Journal of the Royal Statistical Society Series C (Applied Statistics)","issn_l":"0035-9254","issn":["0035-9254","1467-9876"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Statistics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111802584","display_name":"Janet R. Daling","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1284772924","display_name":"Washington State Department of Health","ror":"https://ror.org/02x2akc96","country_code":"US","type":"funder","lineage":["https://openalex.org/I1284772924"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Janet R. Daling","raw_affiliation_strings":["Washington State Department of Health;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Washington State Department of Health;","institution_ids":["https://openalex.org/I1284772924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004458345","display_name":"Hirokuni Tamura","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. Tamura","raw_affiliation_strings":["University of Washington ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington ;","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2621,"currency":"GBP","value_usd":3456},"apc_paid":null,"fwci":1.4219,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.82159848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":"3","first_page":"260","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13141","display_name":"Statistical Methods and Applications","score":0.7738999724388123,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13141","display_name":"Statistical Methods and Applications","score":0.7738999724388123,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.18119999766349792,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.0284000001847744,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/feature-selection","display_name":"feature selection","score":0.968999981880188},{"id":"https://openalex.org/keywords/multiple-linear-regression","display_name":"multiple linear regression","score":0.8410000205039978},{"id":"https://openalex.org/keywords/orthogonal-factors","display_name":"orthogonal factors","score":0.7649999856948853},{"id":"https://openalex.org/keywords/principal-components","display_name":"principal components","score":0.7080000042915344},{"id":"https://openalex.org/keywords/factor-rotation","display_name":"factor rotation","score":0.47699999809265137},{"id":"https://openalex.org/keywords/correlation-matrix","display_name":"correlation matrix","score":0.6570000052452087},{"id":"https://openalex.org/keywords/prediction-equations","display_name":"prediction equations","score":0.6050000190734863},{"id":"https://openalex.org/keywords/multicollinearity","display_name":"multicollinearity","score":0.7120000123977661},{"id":"https://openalex.org/keywords/parsimony","display_name":"parsimony","score":0.734000027179718}],"concepts":[{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6607797145843506},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5956211686134338},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.5639145970344543},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5480950474739075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5135805606842041},{"id":"https://openalex.org/C71104824","wikidata":"https://www.wikidata.org/wiki/Q1476639","display_name":"Structural equation modeling","level":2,"score":0.48543864488601685},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.47242629528045654},{"id":"https://openalex.org/C90157343","wikidata":"https://www.wikidata.org/wiki/Q5188196","display_name":"Cross-sectional regression","level":4,"score":0.4426833391189575},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27033859491348267},{"id":"https://openalex.org/C120068334","wikidata":"https://www.wikidata.org/wiki/Q45343","display_name":"Polynomial regression","level":3,"score":0.165647953748703},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1507231891155243}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2346330","doi":"https://doi.org/10.2307/2346330","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2346330","pdf_url":null,"source":{"id":"https://openalex.org/S2764642956","display_name":"Journal of the Royal Statistical Society Series C (Applied Statistics)","issn_l":"0035-9254","issn":["0035-9254","1467-9876"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Statistics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310094","display_name":"University of Washington","ror":"https://ror.org/00cvxb145"},{"id":"https://openalex.org/F4320332505","display_name":"U.S. Public Health Service","ror":"https://ror.org/05xf94514"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1966382716","https://openalex.org/W1997320786","https://openalex.org/W2034562813","https://openalex.org/W2036987839","https://openalex.org/W2064403537"],"related_works":["https://openalex.org/W7220281745","https://openalex.org/W2340017302","https://openalex.org/W7063773137","https://openalex.org/W2035647069","https://openalex.org/W1593947159","https://openalex.org/W4232527824","https://openalex.org/W6992651427","https://openalex.org/W2363244778","https://openalex.org/W7097229398","https://openalex.org/W7023892997"],"abstract_inverted_index":{"SUMMARY":[0],"Selection":[1,319],"of":[2,26,33,63,91,106,123,131,183,191,215,235,237,257,261,274,293,316,320,325],"explanatory":[3,64,92,113,317,329],"variables":[4,93,114,173,238,303,322,330],"in":[5,14,83,94,103,146,174,199,239,252,259,331],"the":[6,34,40,44,53,73,77,84,104,112,121,128,132,143,160,175,184,200,213,216,223,233,255,275,284,298,307,332],"regression":[7,96,192,240,278],"equation":[8,176,186,217,251],"has":[9,98],"been":[10,99,140],"a":[11,16,27,59,100,219,249,272,312],"prime":[12,101],"problem":[13,102,162,234],"constructing":[15],"prediction":[17,250],"equation.":[18],"This":[19,227,242],"paper":[20,228],"describes":[21,229],"and":[22,152,164,188],"gives":[23],"an":[24,230],"illustration":[25],"selection":[28,88,137,236],"technique":[29,148,267],"which":[30],"makes":[31,115],"use":[32,214,273,292],"orthogonality":[35,294],"among":[36,111,264,295],"factors":[37,45],"extracted":[38],"from":[39],"correlation":[41],"matrix.":[42],"Using":[43],"not":[46,81,300],"as":[47,52,218,271,301,306],"new":[48,302],"variables,":[49],"but":[50,142,304],"merely":[51,305],"reference":[54,308],"frame,":[55],"we":[56,290],"can":[57,268],"identify":[58,311],"near":[60,181,313],"orthogonal":[61,314],"subset":[62,315],"variables.":[65,265,318],"It":[66],"is":[67,80,153],"indicated":[68],"that":[69,79],"this":[70],"approach":[71,231],"provides":[72],"model":[74],"builder":[75],"with":[76,208,248,254],"flexibility":[78],"available":[82],"conventional,":[85],"purely":[86],"mechanical,":[87],"methods.":[89],"SELECTION":[90],"multiple":[95],"analysis":[97,105],"unplanned":[107],"data.":[108,202],"The":[109,266],"interdependency":[110,263],"it":[116],"difficult":[117],"to":[118,127,155,170,196,232,245,286,310],"determine":[119],"empirically":[120],"contribution":[122],"each":[124,147],"independent":[125],"variable":[126],"observed":[129],"variation":[130],"dependent":[133],"variable.":[134],"Various":[135],"alternative":[136],"techniques":[138],"have":[139],"proposed,":[141],"criterion":[144],"employed":[145],"seems":[149],"quite":[150],"arbitrary":[151],"known":[154],"provide":[156],"different":[157],"solutions":[158],"for":[159],"same":[161],"(Draper":[163],"Smith,":[165],"1966,":[166],"p.":[167],"163).":[168],"Attempts":[169],"include":[171],"more":[172],"are":[177],"often":[178,205],"frustrated":[179],"by":[180,280,328],"singularity":[182],"normal":[185],"system,":[187],"make":[189,291],"estimates":[190],"coefficients":[193,207],"highly":[194],"sensitive":[195],"small":[197],"changes":[198],"original":[201],"Resulting":[203],"equations":[204],"contain":[206],"theoretically":[209],"incorrect":[210],"signs":[211],"restricting":[212],"functional":[220],"relationship":[221],"explaining":[222],"system":[224],"under":[225],"study.":[226],"analysis.":[241],"method":[243],"purports":[244],"come":[246],"up":[247],"accordance":[253],"principle":[256],"parsimony":[258],"terms":[260],"minimum":[262],"be":[269,287],"viewed":[270],"principal":[276],"components":[277,299],"proposed":[279],"Kendall":[281],"(1957).":[282],"In":[283],"procedure":[285],"described,":[288],"however,":[289],"components,":[296],"using":[297],"frame":[309],"such":[321],"minimizes":[323],"overlapping":[324],"information":[326],"supplied":[327],"regression.":[333]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-09-29T14:09:16.559479","created_date":"2016-11-30T00:00:00"}