{"id":11833,"date":"2021-03-02T07:04:32","date_gmt":"2021-03-02T07:04:32","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=11833"},"modified":"2026-01-08T15:13:53","modified_gmt":"2026-01-08T15:13:53","slug":"assumptions-multiple-regression-model","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/assumptions-multiple-regression-model\/","title":{"rendered":"Assumptions of Multiple Regression Model"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following is least likely an assumption of the multiple linear regression model?\",\n    \"text\": \"Which of the following is least likely an assumption of the multiple linear regression model? A. The independent variables are not random. B. The error term is correlated across all observations. C. The expected value of the error term, conditional on the independent variables, is equal to zero.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is B. The error term is uncorrelated across all observations. Multiple linear regression assumes that the error terms are not correlated. Correlation of the error term violates one of the classical linear regression assumptions.\"\n    }\n  }\n}\n<\/script><\/p>\n<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/8E2AbtAb0a8?si=EjCo0WNwrsYSe3jU\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p>Multiple regression models are built on the following assumptions.<\/p>\n<ul>\n<li>The relationship between the dependent variable, \\(Y\\), and the independent variables, \\(X_{1}, X_{2},&#8230;, X_{k}\\) is linear.<\/li>\n<li>The independent variables\u00a0\\((X_{1}, X_{2},&#8230;, X_{k})\\) are not random.<\/li>\n<li>There exists no definite linear relationship between two or more of the independent variables. A high correlation between two or more independent variables is known as multicollinearity.<\/li>\n<div style=\"margin: 0 0 20px 0;\">\n  <a\n    href=\"https:\/\/analystprep.com\/free-trial\/\"\n    style=\"\n      display: inline-block;\n      border: 2px solid #1e63ff;\n      color: #1e63ff;\n      background: #ffffff;\n      padding: 10px 14px;\n      border-radius: 10px;\n      font-weight: 500;\n      line-height: 1.35;\n      text-decoration: none;\n    \"\n    target=\"_blank\"\n    rel=\"noopener noreferrer\"\n  ><br \/>\n    Want to practice multiple regression assumptions and violations with CFA\u00ae-style questions? Try AnalystPrep\u2019s free trial now.<br \/>\n  <\/a>\n<\/div>\n<li>The expected value of the error term, conditional on the independent variables, is equal to 0.<\/li>\n<\/ul>\n<p>$$E(\\epsilon|X_{1}, X_{2},&#8230;, X_{k})=0$$<\/p>\n<ul>\n<li>The variance of the error term is equal for all observations.<\/li>\n<\/ul>\n<p>$$E(\\epsilon_{i}^{2})=\\sigma_{\\epsilon}^{2}, i=1,2,&#8230;,n$$<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(This is known as the homoskedasticity assumption.)<\/p>\n<ul>\n<li>The error term is uncorrelated across all observations.<\/li>\n<\/ul>\n<p>$$E(\\epsilon_{i}\\epsilon_{j})=0 {}\u2200 i\u2260j$$<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>Which of the following is <em>least likely<\/em> an assumption of the multiple linear regression model?<\/p>\n<p>\u00a0 \u00a0 A. The independent variables are not random.<\/p>\n<p>\u00a0 \u00a0 B. The error term is correlated across all observations.<\/p>\n<p>\u00a0 \u00a0 C. The expected value of the error term, conditional on the independent variables, is equal to zero.<\/p>\n<h3>Solution<\/h3>\n<p><strong>The correct answer is B.<\/strong><\/p>\n<p>The error term i<strong>s uncorrelated <\/strong>across all observations.<\/p>\n<p>$$E(\\epsilon_{i}\\epsilon_{j})=0\u00a0\u2200i\u2260j$$<\/p>\n<p>Other assumptions of the classical normal multiple linear regression model include:<\/p>\n<p>\u00a0 \u00a0 i. The independent variables are not random. Additionally, there is no exact linear relationship between two or more of the independent variables.<\/p>\n<p>\u00a0 \u00a0ii. The error term is normally distributed.<\/p>\n<p>\u00a0 iii. The expected value of the error term, conditional on the independent variables, is equal to 0.<\/p>\n<p>\u00a0 iv. The variance of the error term is the same for all observations.<\/p>\n<p>\u00a0 v. A linear relation exists between the dependent variable and the independent variables.<\/p>\n<\/blockquote>\n<p>Reading 2: Multiple Regression<\/p>\n<p><em>LOS 2 (f) Explain the assumptions of a multiple regression model.<\/em><\/p>\n<div style=\"text-align: center; margin: 32px 0;\">\n  <a\n    href=\"https:\/\/analystprep.com\/free-trial\/\"\n    style=\"\n      display: inline-block;\n      background-color: #1e63ff;\n      color: #ffffff;\n      padding: 12px 26px;\n      border-radius: 12px;\n      font-weight: 600;\n      font-size: 16px;\n      text-decoration: none;\n    \"\n    target=\"_blank\"\n    rel=\"noopener noreferrer\"\n  ><br \/>\n    Start Free Trial \u2192<br \/>\n  <\/a><\/p>\n<div style=\"margin-top: 10px; font-size: 14px; color: #374151;\">\n    Practice regression assumptions, common violations, and model diagnostics with full solutions (CFA Level II Quant).\n  <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiple regression models are built on the following assumptions. The relationship between the dependent variable, \\(Y\\), and the independent variables, \\(X_{1}, X_{2},&#8230;, X_{k}\\) is linear. The independent variables\u00a0\\((X_{1}, X_{2},&#8230;, X_{k})\\) are not random. There exists no definite linear relationship between&#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":[243,216,230],"class_list":["post-11833","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-quantitative-method","tag-assumptions-of-multiple-regression-model","tag-cfa-level-2","tag-quantitative-method","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Assumptions of Multiple Regression | CFA Level II<\/title>\n<meta name=\"description\" content=\"Reviews key multiple regression assumptions, including error term properties, independence, homoskedasticity, and model specification issues.\" \/>\n<meta name=\"robots\" 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