{"id":36681,"date":"2021-10-29T02:39:02","date_gmt":"2021-10-29T02:39:02","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=36681"},"modified":"2026-03-27T15:15:02","modified_gmt":"2026-03-27T15:15:02","slug":"dependent-and-independent-variables","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/dependent-and-independent-variables\/","title":{"rendered":"Dependent and Independent Variables"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Introduction to Linear Regression (2025 Level I CFA\u00ae Exam \u2013 Quantitative Methods \u2013 Module 7)\",\n  \"description\": \"This video introduces linear regression, covering model components, least squares estimation, regression assumptions, coefficient interpretation, ANOVA use, hypothesis testing for coefficients, prediction calculations, and functional forms of regressions. Key metrics like the F-statistic, coefficient of determination, and standard error of estimate are explained in the context of simple linear regression.\",\n  \"uploadDate\": \"2021-11-04T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/10\/page-135.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/6ouI_27iDVM\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/6ouI_27iDVM\",\n  \"duration\": \"PT56M38S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/10\/page-135.jpg\",\n  \"caption\": \"Image Showing Linear Regression\",\n  \"width\": 1463,\n  \"height\": 1151,\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>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/img_2.jpg\",\n  \"caption\": \"Image Showing Inflation Rate Vs. Unemployment From 2011-2020\",\n  \"width\": 1590,\n  \"height\": 949,\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>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"The independent variable in a regression model is most likely the:\",\n      \"answerCount\": 3,\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"The correct answer is B. predicting variable. An independent variable explains the variation of the dependent variable. It is also called the explanatory variable, exogenous variable, or the predicting variable. A and C are incorrect because a dependent variable is the variable predicted by the independent variable and is also known as the predicted variable, explained variable, or endogenous variable.\"\n      }\n    }\n  ]\n}\n<\/script>\n\n\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/6ouI_27iDVM\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Linear regression forecasts the value of a dependent variable given the value of an independent variable. It assumes that there is a linear relationship between dependent and independent variables.<\/p>\n<p>A dependent variable is predicted by an independent variable and is also known as the explained variable or endogenous variable. \u00a0An independent variable, on the other hand, explains the variation in the dependent variable. It is also known as the exogenous variable, explanatory variable, or predicting variable.<\/p>\n<p>The following is a simple linear regression equation:<\/p>\n<p>$$Y=\\beta_0 +\\beta_1X_1+\\epsilon$$<\/p>\n<p>Where:<\/p>\n<p>\\(Y\\) = dependent variable.<\/p>\n<p>\\(\\beta_0\\) = intercept.<\/p>\n<p>\\(\\beta_1\\) = slope coefficient.<\/p>\n<p>\\(X\\) = independent variable.<\/p>\n<p>\\(\\epsilon\\) = error term (Noise).<\/p>\n<p>\\(\\beta_0\\) and \\(\\beta_1\\) are known as\u00a0<strong>regression coefficients<\/strong>.<\/p>\n<p>The <strong>error term<\/strong> refers to the part of the dependent variable that cannot be explained by the independent variable.<\/p>\n<p>Below is an illustration of a simple linear regression model.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-6973 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/10\/page-135.jpg\" alt=\"Image Showing Linear Regression\" width=\"1463\" height=\"1151\" \/><\/p>\n<h3>Example: Dependent and Independent Variables<\/h3>\n<p>Arth Shah is using regression analysis to forecast inflation given unemployment data from 2011 to 2020.<\/p>\n<p>The following table shows the relevant data from 2011 to 2020.<\/p>\n<p>$$\\small{\\begin{array}{c|c|c}\\textbf{Year} &amp; \\textbf{Unemployment Rate} &amp; \\textbf{Inflation rate}\\\\ \\hline 2011 &amp; 6.1\\% &amp; 1.7\\%\\\\ \\hline 2012 &amp; 7.4\\% &amp; 1.2\\%\\\\ \\hline 2013 &amp; 6.2\\% &amp; 1.3\\%\\\\ \\hline 2014 &amp; 6.2\\% &amp; 1.3\\%\\\\ \\hline 2015 &amp; 5.7\\% &amp; 1.4\\%\\\\ \\hline 2016 &amp; 5.0\\% &amp; 1.8\\%\\\\ \\hline 2017 &amp; 4.2\\% &amp; 3.3\\%\\\\ \\hline 2018 &amp; 4.2\\% &amp; 3.1\\%\\\\ \\hline 2019 &amp; 4.0\\% &amp; 4.7\\%\\\\ \\hline 2020 &amp; 3.9\\% &amp; 3.6\\%\\\\ \\end{array}}$$<\/p>\n<p>A scatter plot of the inflation rates against unemployment rates from 2011 to 2020 is shown in the following figure.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-14836 size-full\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/img_2.jpg\" alt=\"Image Showing Inflation Rate Vs. Unemployment From 2011-2020\" width=\"1590\" height=\"949\" \/>What variable is the dependent variable?<\/p>\n<h4>Solution<\/h4>\n<p>Inflation is the <strong>dependent variable<\/strong>: It is the variable predicted using the unemployment rates.<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>The independent variable in a regression model is <em>most likely<\/em> the:<\/p>\n<p>\u00a0 \u00a0 A. predicted variable.<\/p>\n<p>\u00a0 \u00a0 B. predicting variable.<\/p>\n<p>\u00a0 \u00a0 C. endogenous variable.<\/p>\n<h3>Solution<\/h3>\n<p>The correct answer is <strong>B<\/strong>.<\/p>\n<p>An independent variable explains the variation of the dependent variable. It is also called the explanatory variable, exogeneous variable, or the <strong>predicting variable<\/strong>.<\/p>\n<p><strong>A <\/strong>and<strong> C <\/strong>are incorrect. A dependent variable is a variable predicted by the independent variable. It is also known as the <strong>predicted variable<\/strong>, explained variable, or the <strong>endogenous variable<\/strong>.<\/p>\n<\/blockquote>","protected":false},"excerpt":{"rendered":"<p>Linear regression forecasts the value of a dependent variable given the value of an independent variable. It assumes that there is a linear relationship between dependent and independent variables. A dependent variable is predicted by an independent variable and is&#8230;<\/p>\n","protected":false},"author":15,"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-36681","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 v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Dependent vs Independent Variables Explained | CFA Level 1<\/title>\n<meta name=\"description\" content=\"A dependent variable depends on an independent variable. 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