{"id":"https://openalex.org/W1718959331","doi":null,"title":"Introduction to multivariate regression analysis.","display_name":"Introduction to multivariate regression analysis.","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W1718959331","mag":"1718959331","pmid":"https://pubmed.ncbi.nlm.nih.gov/21487487","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/3049417"},"language":"en","primary_location":{"id":"pmh:oai:europepmc.org:2085005","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3049417","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"Text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3049417","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067941544","display_name":"Evangelos C. Alexopoulos","orcid":"https://orcid.org/0000-0003-0449-918X","observed_orcids":["https://orcid.org/0000-0003-0449-918X"]},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"E C Alexopoulos","raw_affiliation_strings":["Department of Public Health, Medical School, University of Patras, Rio Patras, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Public Health, Medical School, University of Patras, Rio Patras, Greece","institution_ids":["https://openalex.org/I174878644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067941544"],"corresponding_institution_ids":["https://openalex.org/I174878644"],"apc_list":null,"apc_paid":null,"fwci":0.7736,"has_fulltext":false,"cited_by_count":365,"citation_normalized_percentile":{"value":0.75234253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"14","issue":"Suppl 1","first_page":"23","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14374","display_name":"Statistical Methods in Epidemiology","score":0.5220000147819519,"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/T14374","display_name":"Statistical Methods in Epidemiology","score":0.5220000147819519,"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/T13141","display_name":"Statistical Methods and Applications","score":0.21119999885559082,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.13989999890327454,"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/multivariate-regression","display_name":"multivariate regression","score":0.9229999780654907},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"statistical inference","score":0.6909999847412109},{"id":"https://openalex.org/keywords/confidence-intervals","display_name":"confidence intervals","score":0.6579999923706055},{"id":"https://openalex.org/keywords/p-values","display_name":"p-values","score":0.8299999833106995},{"id":"https://openalex.org/keywords/random-error","display_name":"random error","score":0.7170000076293945},{"id":"https://openalex.org/keywords/confounding","display_name":"confounding","score":0.824999988079071},{"id":"https://openalex.org/keywords/measurement-error","display_name":"measurement error","score":0.7889999747276306},{"id":"https://openalex.org/keywords/selection-bias","display_name":"selection bias","score":0.9490000009536743},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.671999990940094},{"id":"https://openalex.org/keywords/frequentist-inference","display_name":"frequentist inference","score":0.9169999957084656},{"id":"https://openalex.org/keywords/hypothesis-testing","display_name":"hypothesis testing","score":0.6980000138282776},{"id":"https://openalex.org/keywords/effect-estimation","display_name":"effect estimation","score":0.40799999237060547},{"id":"https://openalex.org/keywords/medical-statistics","display_name":"medical statistics","score":0.6669999957084656}],"concepts":[{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.8388903141021729},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6986328959465027},{"id":"https://openalex.org/C41426520","wikidata":"https://www.wikidata.org/wiki/Q1192065","display_name":"Point estimation","level":2,"score":0.5939412117004395},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.5164687633514404},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.49105334281921387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4853726625442505},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4635647237300873},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4567625820636749},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.4534268081188202},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.4332005977630615},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.4220142066478729},{"id":"https://openalex.org/C44036329","wikidata":"https://www.wikidata.org/wiki/Q253255","display_name":"p-value","level":3,"score":0.41381996870040894},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.33014947175979614},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31500664353370667},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15584927797317505}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:europepmc.org:2085005","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3049417","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:3049417","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3049417","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Hippokratia","raw_type":"Text"},{"id":"pmid:21487487","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21487487","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Hippokratia","raw_type":"Journal Article"},{"id":"mag:1718959331","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21487487","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"PubMed","raw_type":null}],"best_oa_location":{"id":"pmh:oai:europepmc.org:2085005","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3049417","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"Text"},"sustainable_development_goals":[{"score":0.504800021648407,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1583937157","https://openalex.org/W2034562813","https://openalex.org/W2064142190","https://openalex.org/W2106219136","https://openalex.org/W2118202495","https://openalex.org/W2163424852"],"related_works":["https://openalex.org/W1991476606","https://openalex.org/W3023568584","https://openalex.org/W2494575697","https://openalex.org/W2301055580","https://openalex.org/W7008845417","https://openalex.org/W2476525138","https://openalex.org/W156030924","https://openalex.org/W2582329768","https://openalex.org/W1587127669","https://openalex.org/W1899408690"],"abstract_inverted_index":{"Statistics":[0],"are":[1,12,62],"used":[2,13],"in":[3,55,144,150,238],"medicine":[4],"for":[5,105,110,124,154],"data":[6,53,203,213,224,232],"description":[7],"and":[8,78,214],"inference.":[9],"Inferential":[10],"statistics":[11],"to":[14,20,29,42,47,86,103,107,233],"answer":[15],"questions":[16],"about":[17],"the":[18,24,52,63,69,83,88,92,95,118,126,161,168,171,180,188,220,229],"data,":[19],"test":[21],"hypotheses":[22],"(formulating":[23],"alternative":[25],"or":[26,40,46,67,206,216],"null":[27],"hypotheses),":[28],"generate":[30],"a":[31,36,111,129,177],"measure":[32],"of":[33,38,65,68,71,113,122,146,173,192,202,210,219,240,245,251],"effect,":[34],"typically":[35],"ratio":[37],"rates":[39],"risks,":[41],"describe":[43],"associations":[44,66],"(correlations)":[45],"model":[48],"relationships":[49],"(regression)":[50],"within":[51],"and,":[54],"many":[56],"other":[57],"functions.":[58],"Usually":[59],"point":[60,84],"estimates":[61,85,198,237],"measures":[64,209,218],"magnitude":[70],"effects.":[72],"Confounding,":[73],"measurement":[74],"errors,":[75],"selection":[76],"bias":[77],"random":[79,96,155],"errors":[80],"make":[81],"unlikely":[82],"equal":[87],"true":[89,162,181],"ones.":[90],"In":[91],"estimation":[93,141],"process,":[94],"error":[97],"is":[98,106,135,165],"not":[99,184],"avoidable.":[100],"One":[101],"way":[102],"account":[104],"compute":[108],"p-values":[109,205],"range":[112,121],"possible":[114],"parameter":[115,182],"values":[116],"(including":[117],"null).":[119],"The":[120],"values,":[123],"which":[125],"p-value":[127],"exceeds":[128],"specified":[130],"alpha":[131],"level":[132],"(typically":[133],"0.05)":[134],"called":[136],"confidence":[137,193],"interval.":[138],"An":[139],"interval":[140],"procedure":[142],"will,":[143],"95%":[145],"repetitions":[147],"(identical":[148],"studies":[149],"all":[151],"respects":[152],"except":[153],"error),":[156],"produce":[157],"limits":[158,174],"that":[159,167,223],"contain":[160],"parameters.":[163],"It":[164],"argued":[166],"question":[169],"if":[170],"pair":[172],"produced":[175],"from":[176],"study":[178],"contains":[179],"could":[183],"be":[185],"answered":[186],"by":[187,199],"ordinary":[189],"(frequentist)":[190],"theory":[191],"intervals1.":[194],"Frequentist":[195],"approaches":[196],"derive":[197],"using":[200],"probabilities":[201],"(either":[204],"likelihoods)":[207],"as":[208,217],"compatibility":[211],"between":[212],"hypotheses,":[215],"relative":[221],"support":[222],"provide":[225],"hypotheses.":[226],"Another":[227],"approach,":[228],"Bayesian,":[230],"uses":[231],"improve":[234],"existing":[235],"(prior)":[236],"light":[239],"new":[241],"data.":[242],"Proper":[243],"use":[244],"any":[246],"approach":[247],"requires":[248],"careful":[249],"interpretation":[250],"statistics1,2.":[252]},"counts_by_year":[{"year":2025,"cited_by_count":32},{"year":2024,"cited_by_count":45},{"year":2023,"cited_by_count":44},{"year":2022,"cited_by_count":55},{"year":2021,"cited_by_count":58},{"year":2020,"cited_by_count":39},{"year":2019,"cited_by_count":21},{"year":2018,"cited_by_count":22},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3}],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2016-06-24T00:00:00"}