{"id":"https://openalex.org/W2404306181","doi":"https://doi.org/10.1002/9781119464761.ch2","title":"Simple linear regression and correlation","display_name":"Simple linear regression and correlation","publication_year":2020,"publication_date":"2020-10-21","ids":{"openalex":"https://openalex.org/W2404306181","doi":"https://doi.org/10.1002/9781119464761.ch2","mag":"2404306181","pmid":"https://pubmed.ncbi.nlm.nih.gov/7647489"},"language":"en","primary_location":{"id":"doi:10.1002/9781119464761.ch2","doi":"https://doi.org/10.1002/9781119464761.ch2","is_oa":false,"landing_page_url":"https://doi.org/10.1002/9781119464761.ch2","pdf_url":null,"source":{"id":"https://openalex.org/S4210188905","display_name":"Wiley series in probability and statistics","issn_l":"1940-6517","issn":["1940-6517","1940-6347"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Wiley Series in Probability and Statistics","raw_type":"other"},"volume":{"id":"https://openalex.org/W3094090898","display_name":"Predictive Analytics"},"type":"book-chapter","is_traditional":true,"indexed_in":["crossref","pubmed"],"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/A5079640568","display_name":"Ajit C. Tamhane","orcid":"https://orcid.org/0000-0003-2616-2959","observed_orcids":["https://orcid.org/0000-0003-2616-2959"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ajit C Tamhane","raw_affiliation_strings":["Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts, USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079640568"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":4.849,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.97094546,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"11","issue":"2","first_page":"7","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13141","display_name":"Statistical Methods and Applications","score":0.4641000032424927,"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":0.4641000032424927,"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":0.37940001487731934,"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/T14406","display_name":"Multidisciplinary Science and Engineering Research","score":0.12460000067949295,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/simple-linear-regression","display_name":"simple linear regression","score":0.9990000128746033},{"id":"https://openalex.org/keywords/correlation-analysis","display_name":"correlation analysis","score":0.9309999942779541},{"id":"https://openalex.org/keywords/least-squares-estimation","display_name":"least squares estimation","score":0.7710000276565552},{"id":"https://openalex.org/keywords/regression-assumptions","display_name":"regression assumptions","score":0.621999979019165},{"id":"https://openalex.org/keywords/normality","display_name":"normality","score":0.7329999804496765},{"id":"https://openalex.org/keywords/homogeneity-of-variances","display_name":"homoscedasticity","score":0.9980000257492065},{"id":"https://openalex.org/keywords/independence","display_name":"independence","score":0.8320000171661377},{"id":"https://openalex.org/keywords/linearity","display_name":"linearity","score":0.9380000233650208},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"joint probability distribution","score":0.5809999704360962},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"statistical inference","score":0.8420000076293945}],"concepts":[{"id":"https://openalex.org/C104409967","wikidata":"https://www.wikidata.org/wiki/Q1054836","display_name":"Homoscedasticity","level":3,"score":0.87650465965271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6892024278640747},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6572175025939941},{"id":"https://openalex.org/C162948026","wikidata":"https://www.wikidata.org/wiki/Q6553486","display_name":"Linear predictor function","level":5,"score":0.6535135507583618},{"id":"https://openalex.org/C32224588","wikidata":"https://www.wikidata.org/wiki/Q7250175","display_name":"Proper linear model","level":4,"score":0.6178087592124939},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.5724965929985046},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.5418511033058167},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5293596386909485},{"id":"https://openalex.org/C149769383","wikidata":"https://www.wikidata.org/wiki/Q7520804","display_name":"Simple linear regression","level":3,"score":0.5224843621253967},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5060564875602722},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.493113249540329},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.47103267908096313},{"id":"https://openalex.org/C120488996","wikidata":"https://www.wikidata.org/wiki/Q17016064","display_name":"Variance function","level":3,"score":0.4562687575817108},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4430431127548218},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.44162338972091675},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.4216439127922058},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.41135311126708984},{"id":"https://openalex.org/C120068334","wikidata":"https://www.wikidata.org/wiki/Q45343","display_name":"Polynomial regression","level":3,"score":0.2736431956291199},{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.24446657299995422},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.12385240197181702},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001699","descriptor_name":"Biometry","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1002/9781119464761.ch2","doi":"https://doi.org/10.1002/9781119464761.ch2","is_oa":false,"landing_page_url":"https://doi.org/10.1002/9781119464761.ch2","pdf_url":null,"source":{"id":"https://openalex.org/S4210188905","display_name":"Wiley series in probability and statistics","issn_l":"1940-6517","issn":["1940-6517","1940-6347"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Wiley Series in Probability and Statistics","raw_type":"other"},{"id":"pmid:7647489","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/7647489","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":"Nutrition (Burbank, Los Angeles County, Calif.)","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1502821627","https://openalex.org/W2491009529","https://openalex.org/W3176189213","https://openalex.org/W2490178218","https://openalex.org/W4230138241","https://openalex.org/W2477652162","https://openalex.org/W4313411349","https://openalex.org/W3122462903","https://openalex.org/W4313411334","https://openalex.org/W4242892722"],"abstract_inverted_index":{"One":[0],"of":[1,24,73],"the":[2,14,25,35,42,47,52,71,80,100,143],"simplest":[3,55],"and":[4,34,41,113,129],"yet":[5],"a":[6,31,38,65,75,89,126,139],"commonly":[7],"occurring":[8],"data":[9,63],"analytic":[10],"problem":[11,72],"is":[12,44,64],"exploring":[13],"relationship":[15,50],"between":[16,51],"two":[17,122],"numerical":[18,62],"variables.":[19],"In":[20],"many":[21],"applications,":[22],"one":[23,57],"variables":[26,124],"may":[27],"be":[28],"regarded":[29],"as":[30,37],"response":[32],"variable":[33,40],"other":[36],"predictor":[39],"goal":[43],"to":[45,60],"find":[46],"best":[48],"fitting":[49,74],"two.":[53],"The":[54,115],"equation":[56],"can":[58],"fit":[59],"bivariate":[61],"straight":[66,76],"line.":[67],"This":[68],"chapter":[69,116],"considers":[70],"line":[77],"by":[78,120,137],"using":[79],"least":[81],"squares":[82],"method.":[83],"It":[84],"discusses":[85,130],"statistical":[86,131],"inferences":[87],"for":[88,142],"simple":[90,101],"linear":[91,102],"regression":[92,103],"model.":[93,104],"There":[94],"are":[95,106],"four":[96],"assumptions":[97],"implicit":[98],"in":[99],"They":[105],"normality,":[107],"constant":[108],"variance":[109],"(called":[110],"homoscedasticity),":[111],"independence,":[112],"linearity.":[114],"describes":[117],"correlation":[118,135],"analysis":[119],"assuming":[121,138],"random":[123],"with":[125],"joint":[127,144],"distribution":[128],"inference":[132],"on":[133],"population":[134],"coefficient":[136],"probability":[140],"model":[141],"distribution.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}