{"id":396338,"date":"2019-01-17T09:56:11","date_gmt":"2019-01-17T17:56:11","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=396338"},"modified":"2019-01-17T09:56:11","modified_gmt":"2019-01-17T17:56:11","slug":"note-linear-regression-functions","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/note-linear-regression-functions\/","title":{"rendered":"A Note On Linear Regression Functions"},"content":{"rendered":"<div class=\"hlFld-Abstract test\">\n<div class=\"abstractSection abstractInFull\">\n<p>It is shown that if\u00a0<i>X<\/i>\u00a0and\u00a0<i>Y<\/i>\u00a0are jointly distributed random variables such that the regression function of\u00a0<i>Y<\/i>\u00a0on\u00a0<i>X<\/i>is linear and is the inverse of that of\u00a0<i>X<\/i>\u00a0on\u00a0<i>Y<\/i>\u00a0then the joint distribution of\u00a0<i>X<\/i>\u00a0and\u00a0<i>Y<\/i>\u00a0is degenerate, if second moments exist.<\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>It is shown that if\u00a0X\u00a0and\u00a0Y\u00a0are jointly distributed random variables such that the regression function of\u00a0Y\u00a0on\u00a0Xis linear and is the inverse of that of\u00a0X\u00a0on\u00a0Y\u00a0then the joint distribution of\u00a0X\u00a0and\u00a0Y\u00a0is degenerate, if second moments exist.<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13546],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-396338","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"1992-06-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"665-666","msr_chapter":"","msr_isbn":"","msr_journal":"Communications 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