{"id":45687,"date":"2023-08-16T11:18:55","date_gmt":"2023-08-16T11:18:55","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=45687"},"modified":"2026-02-02T06:48:19","modified_gmt":"2026-02-02T06:48:19","slug":"assumptions-underlying-linear-regression-2","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/","title":{"rendered":"Assumptions Underlying Linear Regression"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Simple Linear Regression \u2013 Part I (2025 CFA\u00ae Level I Exam \u2013 Quantitative Methods \u2013 Learning Module 10)\",\n  \"description\": \"CFA\u00ae Level I Quantitative Methods video lesson from AnalystPrep covering Simple Linear Regression \u2013 Part I. This session explains the structure of a simple linear regression model, the least squares estimation of regression coefficients, and how to interpret slope and intercept estimates. It also covers the key assumptions of linear regression, residual analysis, measures of fit, and hypothesis testing for regression coefficients, with exam-focused intuition and examples.\",\n  \"uploadDate\": \"2023-09-21\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/46f00c-jDkA\/hqdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=46f00c-jDkA\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/46f00c-jDkA\",\n  \"duration\": \"PT38M27S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Which statement most likely violates the assumptions of a single-variable regression model?\",\n    \"text\": \"A regression model with one independent variable requires several assumptions for valid conclusions. Which of the following statements most likely violates those assumptions?\\n\\nA. The independent variable is random.\\nB. The error term is distributed normally.\\nC. There exists a linear relationship between the dependent variable and the independent variable.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The independent variable is random.\\n\\nIn classical linear regression, the independent variable is assumed to be non-random. This assumption ensures unbiased and consistent estimation of the regression coefficients. Normality of the error term and a linear relationship between the dependent and independent variables are standard assumptions that support valid hypothesis testing and model specification.\",\n      \"dateCreated\": \"2026-01-02\"\n    }\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/images\/linear-regression-assumptions-lm10-img4\",\n  \"contentUrl\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-1024x828.jpg\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-1024x828.jpg\",\n  \"caption\": \"Assumptions Underlying Linear Regression\",\n  \"width\": 1024,\n  \"height\": 828,\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  \"isPartOf\": {\n    \"@type\": \"WebPage\",\n    \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\"\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/images\/linear-regression-assumptions-lm10-img5\",\n  \"contentUrl\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG5-1024x864.jpg\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG5-1024x864.jpg\",\n  \"caption\": \"Assumptions Underlying Linear Regression\",\n  \"width\": 1024,\n  \"height\": 864,\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  \"isPartOf\": {\n    \"@type\": \"WebPage\",\n    \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\"\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/images\/linear-regression-assumptions-lm10-img6\",\n  \"contentUrl\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG6-768x637.jpg\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG6-768x637.jpg\",\n  \"caption\": \"Assumptions Underlying Linear Regression\",\n  \"width\": 768,\n  \"height\": 637,\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  \"isPartOf\": {\n    \"@type\": \"WebPage\",\n    \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\"\n  }\n}\n<\/script>\n\n\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/46f00c-jDkA\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Assume that we have samples of size \\(n\\) for dependent variable \\(Y\\) and independent variable \\(X\\). We wish to estimate the simple regression of \\(Y\\) and \\(X\\). The classic normal linear regression model assumptions are as follows:<\/p>\n<ol type=\"I\">\n<li style=\"list-style-type: none;\">\n<ol type=\"I\">\n<li style=\"list-style-type: none;\">\n<ol type=\"I\">\n<li><strong>Linearity<\/strong>: A linear relationship implies that the change in \\(Y\\) due to a one-unit change in \\(X\\) is constant, regardless of the value \\(X\\) takes. If the relationship between the two is not linear, the regression model will not accurately capture the trend, resulting in inaccurate predictions. The model will be biased and underestimate or overestimate \\(Y\\) at various points. For example, the model \\(Y=b_0+b_1e^{b_1x}\\) is nonlinear in \\(b_1\\). For this reason, we should not attempt to fit a linear model between \\(X\\) and \\(Y\\). It also follows that the independent variable, \\(X\\), must be non-stochastic (must not be random). A random independent variable rules out a linear relationship between the dependent and independent variables. In addition, linearity means the residuals should not exhibit an observable pattern when plotted against the independent variable. Instead, they should be completely random. In the example below, we&#8217;re looking at a scenario where the residuals appear to show a pattern when plotted against the independent variable, \\(X\\). This effectively indicates a nonlinear relation.\n<p><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"828\" class=\"aligncenter size-large wp-image-45671\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-1024x828.jpg\" alt=\"\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-1024x828.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-300x243.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-768x621.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-400x323.jpg 400w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4.jpg 1430w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<\/li>\n<li><strong>Normality Assumption<\/strong>: This assumption implies that the error terms (residuals) must follow a normal distribution. It&#8217;s important to note that this doesn&#8217;t mean the dependent and independent variables must be normally distributed. However, checking the distribution of the dependent and independent variables is crucial to identify any outliers. A histogram of the residuals can be used to detect if the error term is normally distributed. A symmetric bell-shaped histogram indicates that the normality assumption is likely to be true.<\/li>\n<li><strong>Homoskedasticity<\/strong>: Homoskedasticity implies that the variance of the error terms is <strong>constant<\/strong> across all observations. Mathematically, this is expressed as:$$ E\\left(\\epsilon_i^2\\right)=\\sigma_\\epsilon^2,\\ \\ i=1,2,\\ldots,n $$If the variance of residuals varies across observations, then we refer to this as heteroskedasticity (not homoscedasticity). We plot the least square residuals against the independent variable to test for heteroscedasticity. If there is an evident pattern in the plot, that is a manifestation of heteroskedasticity.\n<p><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"864\" class=\"aligncenter size-large wp-image-45672\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG5-1024x864.jpg\" alt=\"\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG5-1024x864.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG5-300x253.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG5-768x648.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG5-400x337.jpg 400w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG5.jpg 1430w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>In case residuals and the predicted values increase simultaneously, then such a situation is known as <strong>heteroscedasticity<\/strong> (or heteroskedasticity).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"849\" class=\"aligncenter size-large wp-image-45673\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG6-1024x849.jpg\" alt=\"\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG6-1024x849.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG6-300x249.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG6-768x637.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG6-400x332.jpg 400w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG6.jpg 1430w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<\/li>\n<li><strong>Independence Assumption<\/strong>: The independence assumption implies that the observations \\(X_i\\) and \\(Y_i\\) are independent of each other. Failure to satisfy this assumption implies the variables are not independent, and thus, residuals will be correlated. To ascertain this assumption, we visually and statistically analyze the residuals to check whether residual shows exhibit a pattern.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<blockquote>\n<h2>Question<\/h2>\n<p>A regression model with one independent variable requires several assumptions for valid conclusions. Which of the following statements <em>most likely<\/em> violates those assumptions?<\/p>\n<ol type=\"A\">\n<li>The independent variable is random.<\/li>\n<li>The error term is distributed normally.<\/li>\n<li>There exists a linear relationship between the dependent variable and the independent variable.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p><strong>The correct answer is A<\/strong>.<\/p>\n<p>Linear regression assumes that the independent variable, X, is NOT random. This ensures that the model produces the correct estimates of the regression coefficients.<\/p>\n<p><strong>B is incorrect<\/strong>. The assumption that the error term is distributed normally allows us to easily test a particular hypothesis about a linear regression model.<\/p>\n<p><strong>C is incorrect<\/strong>. Essentially, the assumption that the dependent and independent variables have a linear relationship is the key to a valid linear regression. If the parameters of the dependent and independent variables are not linear, then the estimation of that relation can yield invalid results.<\/p>\n<\/blockquote>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Assume that we have samples of size \\(n\\) for dependent variable \\(Y\\) and independent variable \\(X\\). We wish to estimate the simple regression of \\(Y\\) and \\(X\\). The classic normal linear regression model assumptions are as follows: Linearity: A linear&#8230;<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-45687","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","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>Assumptions of Linear Regression | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Understand key assumptions of linear regression, including linearity, normality, homoskedasticity, and independence, for accurate model predictions.\" \/>\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\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Assumptions of Linear Regression | CFA Level 1\" \/>\n<meta property=\"og:description\" content=\"Understand key assumptions of linear regression, including linearity, normality, homoskedasticity, and independence, for accurate model predictions.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\" \/>\n<meta property=\"og:site_name\" content=\"AnalystPrep | CFA\u00ae Exam Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-16T11:18:55+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-02-02T06:48:19+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1430\" \/>\n\t<meta property=\"og:image:height\" content=\"1156\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Kajal\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Kajal\" \/>\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\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\"},\"author\":{\"name\":\"Kajal\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/3cde53d128c8d0cfdd46d8732e8c3048\"},\"headline\":\"Assumptions Underlying Linear Regression\",\"datePublished\":\"2023-08-16T11:18:55+00:00\",\"dateModified\":\"2026-02-02T06:48:19+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\"},\"wordCount\":596,\"image\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-1024x828.jpg\",\"articleSection\":[\"Quantitative Methods\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\",\"name\":\"Assumptions of Linear Regression | CFA Level 1\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-1024x828.jpg\",\"datePublished\":\"2023-08-16T11:18:55+00:00\",\"dateModified\":\"2026-02-02T06:48:19+00:00\",\"author\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/3cde53d128c8d0cfdd46d8732e8c3048\"},\"description\":\"Understand key assumptions of linear regression, including linearity, normality, homoskedasticity, and independence, for accurate model predictions.\",\"breadcrumb\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#primaryimage\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4.jpg\",\"contentUrl\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4.jpg\",\"width\":1430,\"height\":1156},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Assumptions Underlying Linear Regression\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#website\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/\",\"name\":\"AnalystPrep | CFA\u00ae Exam Study Notes\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/3cde53d128c8d0cfdd46d8732e8c3048\",\"name\":\"Kajal\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/12\/tarryn-150x150.png\",\"contentUrl\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/12\/tarryn-150x150.png\",\"caption\":\"Kajal\"},\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/author\/kajal\/\"}]}<\/script>\n<meta property=\"og:video\" content=\"https:\/\/www.youtube.com\/embed\/46f00c-jDkA\" \/>\n<meta property=\"og:video:type\" content=\"text\/html\" \/>\n<meta property=\"og:video:duration\" content=\"2308\" \/>\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=\"2023-08-16T11:18:55+00:00\" \/>\n<meta property=\"ya:ovs:allow_embed\" content=\"true\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Assumptions of Linear Regression | CFA Level 1","description":"Understand key assumptions of linear regression, including linearity, normality, homoskedasticity, and independence, for accurate model predictions.","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\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/","og_locale":"en_US","og_type":"article","og_title":"Assumptions of Linear Regression | CFA Level 1","og_description":"Understand key assumptions of linear regression, including linearity, normality, homoskedasticity, and independence, for accurate model predictions.","og_url":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/","og_site_name":"AnalystPrep | CFA\u00ae Exam Study Notes","article_published_time":"2023-08-16T11:18:55+00:00","article_modified_time":"2026-02-02T06:48:19+00:00","og_image":[{"width":1430,"height":1156,"url":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4.jpg","type":"image\/jpeg"}],"author":"Kajal","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Kajal","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/"},"author":{"name":"Kajal","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/3cde53d128c8d0cfdd46d8732e8c3048"},"headline":"Assumptions Underlying Linear Regression","datePublished":"2023-08-16T11:18:55+00:00","dateModified":"2026-02-02T06:48:19+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/"},"wordCount":596,"image":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#primaryimage"},"thumbnailUrl":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-1024x828.jpg","articleSection":["Quantitative Methods"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/","name":"Assumptions of Linear Regression | CFA Level 1","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#website"},"primaryImageOfPage":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#primaryimage"},"image":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#primaryimage"},"thumbnailUrl":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4-1024x828.jpg","datePublished":"2023-08-16T11:18:55+00:00","dateModified":"2026-02-02T06:48:19+00:00","author":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/3cde53d128c8d0cfdd46d8732e8c3048"},"description":"Understand key assumptions of linear regression, including linearity, normality, homoskedasticity, and independence, for accurate model predictions.","breadcrumb":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#primaryimage","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4.jpg","contentUrl":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/08\/LM10_IMG4.jpg","width":1430,"height":1156},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/assumptions-underlying-linear-regression-2\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/cfa-level-1-exam\/"},{"@type":"ListItem","position":2,"name":"Assumptions Underlying Linear Regression"}]},{"@type":"WebSite","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#website","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/","name":"AnalystPrep | CFA\u00ae Exam Study Notes","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/analystprep.com\/cfa-level-1-exam\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/3cde53d128c8d0cfdd46d8732e8c3048","name":"Kajal","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/image\/","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/12\/tarryn-150x150.png","contentUrl":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/12\/tarryn-150x150.png","caption":"Kajal"},"url":"https:\/\/analystprep.com\/cfa-level-1-exam\/author\/kajal\/"}]},"og_video":"https:\/\/www.youtube.com\/embed\/46f00c-jDkA","og_video_type":"text\/html","og_video_duration":"2308","og_video_width":"480","og_video_height":"270","ya_ovs_adult":"false","ya_ovs_upload_date":"2023-08-16T11:18:55+00:00","ya_ovs_allow_embed":"true"},"_links":{"self":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/45687","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/comments?post=45687"}],"version-history":[{"count":39,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/45687\/revisions"}],"predecessor-version":[{"id":58569,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/45687\/revisions\/58569"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/media?parent=45687"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/categories?post=45687"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/tags?post=45687"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}