{"id":11933,"date":"2021-03-03T13:04:14","date_gmt":"2021-03-03T13:04:14","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=11933"},"modified":"2026-01-22T08:16:56","modified_gmt":"2026-01-22T08:16:56","slug":"dummy-variables-regression-analysis","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/","title":{"rendered":"Dummy Variables in Regression Analysis"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"How many dummy variables are needed when modeling quarterly seasonality with one reference quarter?\",\n    \"text\": \"Ninel Khan, a technical trader, is analyzing the seasonality of the price of the GBP\/USD. Khan believes that the price is significantly different in the first quarter relative to the other three quarters. She uses the first quarter as the reference point in the regression. The number of dummy variables that Khan will need in her regression equation is most likely:\\n\\nA. 2.\\nB. 3.\\nC. 4.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"B. 3. When modeling n categories in a regression, n \u2212 1 dummy variables are required to avoid multicollinearity. With four quarters and the first quarter as the reference category, three dummy variables are needed.\"\n    }\n  }\n}\n<\/script><\/p>\n<h3 id=\"mce_22\" class=\"editor-rich-text__tinymce mce-content-body\" data-is-placeholder-visible=\"false\"><iframe loading=\"lazy\"\n  width=\"611\"\n  height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/8E2AbtAb0a8\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  referrerpolicy=\"strict-origin-when-cross-origin\"\n  allowfullscreen><br \/>\n<\/iframe><\/h3>\n<p>Dummy variables are binary variables used to quantify the effect of qualitative independent variables. A dummy variable is assigned a value of 1 if a particular condition is met and a value of 0 otherwise. The number of dummy variables for n different classes must equal n-1<strong>.<\/strong><\/p>\n<p>The intercept term measures the average value of the dependent variable of the omitted class, and the estimated coefficient on each dummy variable measures the average incremental effect of that dummy variable on the dependent variable.<\/p>\n<h3>Example: Incorporating Dummy Variables in a Multiple Regression Model<\/h3>\n<p>Adil Suleman, CFA, wishes to identify possible drivers of a company\u2019s percentage return on capital (ROC). Suleman identifies performance measures including margin (%), sales and debt ratio, and demographic measures such as the region and the economic sector as possible drivers of ROC.<\/p>\n<p>The dummy variable \u201cregion\u201d is coded 1 when the company is located in the Northern region and 0 in the Southern region. On the other hand, the dummy variable \u201ceconomic sector\u201d is coded 1 when a company belongs to the banking sector and 0 when it belongs to the technology sector.<\/p>\n<p>Suleman regresses ROC against sales, debt ratio, profit margin, region, and sector to obtain the following regression output.<\/p>\n<p>$$\\small{\\begin{array}{lr}\\hline{}\\textbf{Regression Statistics}\\\\ \\hline\\text{Multiple R} &amp; 0.8851\\\\ \\text{R Square} &amp; 0.7833\\\\ \\text{Adjusted R Square} &amp; 0.7263\\\\ \\text{Standard Error} &amp; 0.9561\\\\ \\text{Observations} &amp; 25\\\\ \\hline\\end{array}}$$<\/p>\n<p>$$ \\textbf{ANOVA} $$<\/p>\n<p>$$\\small{\\begin{array}{lccccc}\\hline{}&amp; \\textbf{Df} &amp; \\textbf{SS} &amp; \\textbf{MS} &amp; \\textbf{F} &amp; \\textbf{Significance F}\\\\ \\hline\\text{Regression} &amp; 5 &amp; 62.7924 &amp; 12.5585 &amp; 13.7389 &amp; 0.0000\\\\ \\text{Residual} &amp; 19 &amp; 17.3676 &amp; 0.9141 &amp; &amp;{}\\\\ \\text{Total} &amp; 24 &amp; 80.1600 &amp; &amp; &amp;{}\\\\ \\hline\\end{array}}$$<\/p>\n<p>$$\\small{\\begin{array}{lccccc}\\hline{}&amp; \\textbf{Coefficients} &amp; \\textbf{Standard Error} &amp; \\textbf{t Stat} &amp; \\textbf{P-value}\\\\ \\hline\\text{Intercept} &amp; 10.1241 &amp; 0.8503 &amp; 11.9069 &amp; 0.0000\\\\ \\text{Sales} &amp; 0.0010 &amp; 0.0004 &amp; 2.4003 &amp; 0.0268\\\\ \\text{Debt ratio} &amp; 0.0166 &amp; 0.0138 &amp; 1.2017 &amp; 0.2443\\\\ \\text{Profit Margin} &amp; 0.1807 &amp; 0.0552 &amp; 3.2713 &amp; 0.0040\\\\ \\text{Region} &amp; 2.1755 &amp; 0.6061 &amp; 3.5896 &amp; 0.0020\\\\ \\text{Sector} &amp; -0.8703 &amp; 0.4202 &amp; -2.0709 &amp; 0.0522\\\\ \\hline\\end{array}}$$<\/p>\n<h2>Interpreting the Results<\/h2>\n<p>From the above results, the multiple regression equation can be expressed as:<\/p>\n<p>$$\\text{ROC}=10.1241+0.001SAL+0.0166DR+0.1807PM+2.1755REG-0.8703SEC$$<\/p>\n<h3>Adjusted R<sup>2<\/sup><\/h3>\n<p>72.63% of the variation in the return on capital is explained by three quantitative regressors (sales, debt ratio, and profit margin) and two qualitative regressors (region and sector).<\/p>\n<h4>Test Significance of Overall Model<\/h4>\n<p>\\(H_{0}:b_{1}=b_{2}=b_{3}=b_{4}=b_{5}=0\\) versus at \\(H_{a}:\\) At least one \\(b_{j}\u22600\\)<\/p>\n<p>From the ANOVA table, column \u201cSignificance F,\u201d notice that the p-value is less than 5%.<\/p>\n<p>Thus, reject \\(H_{0}\\) in favor of \\(H_{a}\\).\u00a0Conclude that the model is statistically significant.<\/p>\n<h4>Test Significance of Dummy Variables<\/h4>\n<p>The coefficient of the region in this regression model is positive and statistically significant at the 0.05 level as the p-value is less than 0.05. We can therefore conclude that the northern region is significantly different from the southern region at the 5% significance level.<\/p>\n<p>On the contrary, the banking sector is not significantly different from the technology sector as the p-value is greater than 0.05. Additionally, the sign of this coefficient is negative.<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>Ninel Khan, a technical trader, is analyzing the seasonality of the price of the GBP\/USD. Khan believes that the price is significantly different in the first quarter relative to the other three quarters. She uses the first quarter as the reference point in the regression. The number of dummy variables that Khan will need in her regression equation is <em>most likely:<\/em><\/p>\n<p>\u00a0 \u00a0 \u00a0A. 2.<\/p>\n<p>\u00a0 \u00a0 \u00a0B. 3.<\/p>\n<p>\u00a0 \u00a0 \u00a0C. 4.<\/p>\n<h3>Solution<\/h3>\n<p><strong>The correct answer is B.<\/strong><\/p>\n<p>If we need to differentiate among <em>n<\/em> categories, the regression should include <em>n \u2212 1<\/em> dummy variables. In this case, we have four quarters. Thus, three dummy variables are needed.<\/p>\n<\/blockquote>\n<p>Reading 2: Multiple Regression<\/p>\n<p><em>LOS 2 (j) Formulate and interpret a multiple regression, including qualitative independent variables.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dummy variables are binary variables used to quantify the effect of qualitative independent variables. A dummy variable is assigned a value of 1 if a particular condition is met and a value of 0 otherwise. The number of dummy variables&#8230;<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[102,229],"tags":[216,247,230],"class_list":["post-11933","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-quantitative-method","tag-cfa-level-2","tag-dummy-variables-in-regression-analysis","tag-quantitative-method","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Dummy Variables in Regression Analysis - CFA, FRM, and Actuarial Exams Study Notes<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Dummy Variables in Regression Analysis - CFA, FRM, and Actuarial Exams Study Notes\" \/>\n<meta property=\"og:description\" content=\"Dummy variables are binary variables used to quantify the effect of qualitative independent variables. A dummy variable is assigned a value of 1 if a particular condition is met and a value of 0 otherwise. The number of dummy variables...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/\" \/>\n<meta property=\"og:site_name\" content=\"CFA, FRM, and Actuarial Exams Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2021-03-03T13:04:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-01-22T08:16:56+00:00\" \/>\n<meta name=\"author\" content=\"Irene R\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Irene R\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/\"},\"author\":{\"name\":\"Irene R\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5\"},\"headline\":\"Dummy Variables in Regression Analysis\",\"datePublished\":\"2021-03-03T13:04:14+00:00\",\"dateModified\":\"2026-01-22T08:16:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/\"},\"wordCount\":636,\"keywords\":[\"CFA-level-2\",\"Dummy Variables in Regression Analysis\",\"Quantitative Method\"],\"articleSection\":[\"CFA Level II Study Notes\",\"Quantitative Method\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/\",\"url\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/\",\"name\":\"Dummy Variables in Regression Analysis - CFA, FRM, and Actuarial Exams Study Notes\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/#website\"},\"datePublished\":\"2021-03-03T13:04:14+00:00\",\"dateModified\":\"2026-01-22T08:16:56+00:00\",\"author\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5\"},\"breadcrumb\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/analystprep.com\/study-notes\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Dummy Variables in Regression Analysis\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/#website\",\"url\":\"https:\/\/analystprep.com\/study-notes\/\",\"name\":\"CFA, FRM, and Actuarial Exams Study Notes\",\"description\":\"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/analystprep.com\/study-notes\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5\",\"name\":\"Irene R\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g\",\"caption\":\"Irene R\"},\"url\":\"https:\/\/analystprep.com\/study-notes\/author\/irene\/\"}]}<\/script>\n<meta property=\"og:video\" content=\"https:\/\/www.youtube.com\/embed\/8E2AbtAb0a8\" \/>\n<meta property=\"og:video:type\" content=\"text\/html\" \/>\n<meta property=\"og:video:duration\" content=\"3343\" \/>\n<meta property=\"og:video:width\" content=\"480\" \/>\n<meta property=\"og:video:height\" content=\"270\" \/>\n<meta property=\"ya:ovs:adult\" content=\"false\" \/>\n<meta property=\"ya:ovs:upload_date\" content=\"2021-03-03T13:04:14+00:00\" \/>\n<meta property=\"ya:ovs:allow_embed\" content=\"true\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Dummy Variables in Regression Analysis - CFA, FRM, and Actuarial Exams Study Notes","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/","og_locale":"en_US","og_type":"article","og_title":"Dummy Variables in Regression Analysis - CFA, FRM, and Actuarial Exams Study Notes","og_description":"Dummy variables are binary variables used to quantify the effect of qualitative independent variables. A dummy variable is assigned a value of 1 if a particular condition is met and a value of 0 otherwise. The number of dummy variables...","og_url":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/","og_site_name":"CFA, FRM, and Actuarial Exams Study Notes","article_published_time":"2021-03-03T13:04:14+00:00","article_modified_time":"2026-01-22T08:16:56+00:00","author":"Irene R","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Irene R","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/"},"author":{"name":"Irene R","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5"},"headline":"Dummy Variables in Regression Analysis","datePublished":"2021-03-03T13:04:14+00:00","dateModified":"2026-01-22T08:16:56+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/"},"wordCount":636,"keywords":["CFA-level-2","Dummy Variables in Regression Analysis","Quantitative Method"],"articleSection":["CFA Level II Study Notes","Quantitative Method"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/","url":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/","name":"Dummy Variables in Regression Analysis - CFA, FRM, and Actuarial Exams Study Notes","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/#website"},"datePublished":"2021-03-03T13:04:14+00:00","dateModified":"2026-01-22T08:16:56+00:00","author":{"@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5"},"breadcrumb":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dummy-variables-regression-analysis\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/study-notes\/"},{"@type":"ListItem","position":2,"name":"Dummy Variables in Regression Analysis"}]},{"@type":"WebSite","@id":"https:\/\/analystprep.com\/study-notes\/#website","url":"https:\/\/analystprep.com\/study-notes\/","name":"CFA, FRM, and Actuarial Exams Study Notes","description":"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/analystprep.com\/study-notes\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5","name":"Irene R","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g","caption":"Irene R"},"url":"https:\/\/analystprep.com\/study-notes\/author\/irene\/"}]},"og_video":"https:\/\/www.youtube.com\/embed\/8E2AbtAb0a8","og_video_type":"text\/html","og_video_duration":"3343","og_video_width":"480","og_video_height":"270","ya_ovs_adult":"false","ya_ovs_upload_date":"2021-03-03T13:04:14+00:00","ya_ovs_allow_embed":"true"},"_links":{"self":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/11933","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/comments?post=11933"}],"version-history":[{"count":18,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/11933\/revisions"}],"predecessor-version":[{"id":42163,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/11933\/revisions\/42163"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/media?parent=11933"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/categories?post=11933"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/tags?post=11933"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}