{"id":5571,"date":"2023-02-26T20:22:08","date_gmt":"2023-02-26T20:22:08","guid":{"rendered":"https:\/\/www.goodacademic.com\/blog\/questions\/dummy-variable-prob\/"},"modified":"2023-02-26T20:22:08","modified_gmt":"2023-02-26T20:22:08","slug":"dummy-variable-prob","status":"publish","type":"questions","link":"https:\/\/www.goodacademic.com\/blog\/questions\/dummy-variable-prob\/","title":{"rendered":"Dummy variable prob"},"content":{"rendered":"<div class=\"col-sm-12 messageContent\">\n <b>Learning Goal: <\/b>I&#8217;m working on a statistics question and need the explanation and answer to help me learn.<\/p>\n<p>Consider the two variable regression problem with a dummy variable in the design matrix: <span class=\"katex\"><span class=\"katex-html\"><span class=\"base\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><em>y<\/em><span class=\"accent-body\"><span class=\"overlay\"><br \/>\n           <svg preserveaspectratio=\"\" viewbox=\"\">\n            <path><\/path>\n           <\/svg><\/span><\/span><\/span><\/span><span class=\"vlist-r\"><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><em>\u00ce\u00b2<\/em><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-r\"><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><em>\u00ce\u00b2<\/em><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-r\"><\/span><\/span><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><em>x<\/em><span class=\"accent-body\"><span class=\"overlay\"><br \/>\n           <svg preserveaspectratio=\"\" viewbox=\"\">\n            <path><\/path>\n           <\/svg><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><em>\u00ce\u00b3<\/em><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><em>d<\/em><span class=\"accent-body\"><span class=\"overlay\"><br \/>\n           <svg preserveaspectratio=\"\" viewbox=\"\">\n            <path><\/path>\n           <\/svg><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><em>\u00cf\u00b5<\/em><span class=\"accent-body\"><span class=\"overlay\"><br \/>\n           <svg preserveaspectratio=\"\" viewbox=\"\">\n            <path><\/path>\n           <\/svg><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span> where <span class=\"katex\"><span class=\"katex-html\"><span class=\"base\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><em>d<\/em><span class=\"accent-body\"><span class=\"overlay\"><br \/>\n           <svg preserveaspectratio=\"\" viewbox=\"\">\n            <path><\/path>\n           <\/svg><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> is a dummy-variable that is coded 1 if the observation satisfies a certain condition, and is 0 otherwise. Consider replacing the 0 and 1 values in <span class=\"katex\"><span class=\"katex-html\"><span class=\"base\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><em>d<\/em><span class=\"accent-body\"><span class=\"overlay\"><br \/>\n           <svg preserveaspectratio=\"\" viewbox=\"\">\n            <path><\/path>\n           <\/svg><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> with <span class=\"katex\"><span class=\"katex-html\"><span class=\"base\"><span class=\"mord\">\u00e2\u02c6\u2019<\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span> and <span class=\"katex\"><span class=\"katex-html\"><span class=\"base\"><span class=\"mord\">0.5<\/span><\/span><\/span><\/span>, respectively. What is the resulting regression equation? In particular, how does the dummy variable parameter in the recoded model relate to <span class=\"katex\"><span class=\"katex-html\"><span class=\"base\"><em>\u00ce\u00b3<\/em><\/span><\/span><\/span> ? Describe how to interpret the parameters of the recoded model. Is there a reason to prefer one coding over the other?<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Learning Goal: I&#8217;m working on a statistics question and need the explanation and answer to help me learn. Consider the two variable regression problem with a dummy variable in the design matrix: y =\u00ce\u00b20+\u00ce\u00b21x +\u00ce\u00b3d +\u00cf\u00b5 , where d is a dummy-variable that is coded 1 if the observation satisfies a certain condition, and is [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":[],"disciplines":[658],"paper_types":[],"tagged":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/5571"}],"collection":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/comments?post=5571"}],"version-history":[{"count":0,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/5571\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/media?parent=5571"}],"wp:term":[{"taxonomy":"disciplines","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/disciplines?post=5571"},{"taxonomy":"paper_types","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/paper_types?post=5571"},{"taxonomy":"tagged","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/tagged?post=5571"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}