{"id":11979,"date":"2021-03-03T19:16:47","date_gmt":"2021-03-03T19:16:47","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=11979"},"modified":"2026-01-06T19:56:44","modified_gmt":"2026-01-06T19:56:44","slug":"multicollinearity","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/multicollinearity\/","title":{"rendered":"Multicollinearity"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Regression problem leading to Type II errors\",\n    \"text\": \"The regression problem that will most likely increase the chances of making Type II errors is:\\n\\nA. Multicollinearity.\\n\\nB. Conditional heteroskedasticity.\\n\\nC. Positive serial correlation.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A. Multicollinearity.\\n\\nMulticollinearity occurs when independent variables in a regression model are highly correlated, leading to inflated standard errors for the slope coefficients. This results in an increased likelihood of Type II errors, where the null hypothesis is not rejected when it is false (incorrectly concluding that a variable is not significant).\\n\\nB is incorrect because conditional heteroskedasticity inflates t-statistics, increasing Type I errors.\\n\\nC is incorrect because positive serial correlation leads to underestimated standard errors, inflating t-statistics and increasing Type I errors.\"\n    }\n  }\n}\n<\/script><br \/>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"@id\": \"https:\/\/analystprep.com\/study-notes\/images\/cfa-level-2-multicollinearity\",\n  \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-2-multicollinearity.png\",\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-2-multicollinearity.png\",\n  \"caption\": \"Multicollinearity\",\n  \"width\": 1373,\n  \"height\": 1041,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\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\" src=\"\/\/www.youtube.com\/embed\/8E2AbtAb0a8?autoplay=0&amp;loop=0&amp;rel=0\" width=\"611\" height=\"344\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/h3>\n<p>Multicollinearity occurs when two or more independent variables are significantly correlated to each other.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12876\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-2-multicollinearity.png\" sizes=\"auto, (max-width: 1373px) 100vw, 1373px\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-2-multicollinearity.png 1373w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-2-multicollinearity-300x227.png 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-2-multicollinearity-1024x776.png 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-2-multicollinearity-768x582.png 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/03\/cfa-level-2-multicollinearity-400x303.png 400w\" alt=\"\" width=\"1373\" height=\"1041\" \/>It results from the violation of the multiple regression assumptions that there is no apparent linear relationship between two or more of the independent variables. Multicollinearity is common with financial data.<\/p>\n<h2>Effects of Multicollinearity<\/h2>\n<p>Multicollinearity does not alter the consistency of the regression estimates. However, it renders them imprecise and unreliable. Multicollinearity makes it nearly impossible to determine how the independent variables influence the dependent variable individually. This inflates the standard errors for the regression coefficients, increasing the possibility of Type II errors.<\/p>\n<h2>Detecting Multicollinearity<\/h2>\n<p>A high value of R<sup>2<\/sup> and a significant F-statistic that contradicts the t-test signals multicollinearity. The insignificant t-statistic implies that the standard errors are overestimated. In addition, a high correlation between independent variables indicates multicollinearity. It is important to note that a low correlation between independent variables does not imply the absence of multicollinearity.<\/p>\n<h2>Correcting Multicollinearity<\/h2>\n<p>The most common way to attenuate the problem of multicollinearity is to exclude some of the regression variables, provided that we do not omit relevant variables. However, it is hard to identify the variables that need to be eliminated. This is why stepwise regression is employed to systematically eliminate variables from the regression until multicollinearity is minimized.<\/p>\n<p>Finally, we can summarize the problems in linear regression and their solutions as per the following table:<\/p>\n<p>$$\\small{\\begin{array}{l|l|l}\\textbf{Problem} &amp; \\textbf{Effect} &amp; \\textbf{Solution}\\\\ \\hline\\text{Heteroskedasticity} &amp; \\text{Incorrect standard errors} &amp; \\text{Use robust standard errors}\\\\ \\hline\\text{Serial correlation} &amp; \\text{Incorrect standard errors} &amp; \\text{Use robust standard errors}\\\\ \\hline\\text{Multicollinearity} &amp; \\text{High R-squared and low t-statistics} &amp; \\text{Eliminate one or more independent variables}\\\\ \\hline{}&amp; {}&amp; \\text{Stepwise regression}\\\\ \\end{array}}$$<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>The regression problem that will <em>most likely<\/em> increase the chances of making Type II errors is:<\/p>\n<p>\u00a0 \u00a0A. Multicollinearity.<\/p>\n<p>\u00a0 \u00a0B. Conditional heteroskedasticity.<\/p>\n<p>\u00a0 \u00a0C. Positive serial correlation.<\/p>\n<h3>Solution<\/h3>\n<p><strong>The correct answer is A.<\/strong><\/p>\n<p>Multicollinearity makes the standard errors of the slope coefficients to be artificially inflated. This increases the likelihood of incorrectly concluding that a variable is not statistically significant (Type II error).<\/p>\n<p><strong>B is incorrect. <\/strong>Conditional heteroskedasticity underestimates standard errors while the coefficient estimates remain unaffected. This inflates the t-statistics leading to the frequent rejection of the null hypothesis of no statistical significance. (Type I error).<\/p>\n<p><strong>C is incorrect.<\/strong>\u00a0Positive serial correlation makes the ordinary least squares standard errors for the regression coefficients to underestimate the true standard errors. This inflates the estimated t-statistics, making them appear to be more significant than they really are. This increases Type I error.<\/p>\n<\/blockquote>\n<p>Reading 2: Multiple Regression<\/p>\n<p><em>LOS 2 (l) Describe multicollinearity and explain its causes and effects in regression analysis.<\/em><\/p>\n<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Multiple Regression (2022 Level II CFA\u00ae Exam \u2013 Reading 2)\",\n  \"description\": \"This full-length video by AnalystPrep covers all Learning Outcome Statements (LOS) for Reading 2 \u2013 Multiple Regression, a key topic in the CFA Level II Quantitative Methods syllabus. 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It results from the violation of the multiple regression assumptions that there is no apparent linear relationship between two or more of the independent variables. Multicollinearity&#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":[216,249,230],"class_list":["post-11979","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-quantitative-method","tag-cfa-level-2","tag-multicollinearity","tag-quantitative-method","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Multicollinearity - 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\/multicollinearity\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Multicollinearity - CFA, FRM, and Actuarial Exams Study Notes\" \/>\n<meta property=\"og:description\" content=\"Multicollinearity occurs when two or more independent variables are significantly correlated to each other. 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