{"id":11473,"date":"2021-02-24T11:18:11","date_gmt":"2021-02-24T11:18:11","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=11473"},"modified":"2026-03-11T14:16:40","modified_gmt":"2026-03-11T14:16:40","slug":"dependent-independent-variables","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/quantitative-method\/dependent-independent-variables\/","title":{"rendered":"Dependent and Independent Variables"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"In a regression model, which term best describes the independent variable?\",\n    \"text\": \"The independent variable in a regression model is most likely the:\\n\\nA. Predicted variable.\\nB. Predicting variable.\\nC. Endogenous variable.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is B. The independent variable explains variation in the dependent variable and is also known as the explanatory variable, exogenous variable, or predicting variable. In contrast, the dependent variable is the predicted or endogenous variable.\"\n    }\n  }\n}\n<\/script><br \/>\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\/cfa-level-2-linear-regression.jpg\",\n  \"caption\": \"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><\/p>\n<p><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\": \"Inflation Rate vs Unemployment from 2011 to 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><\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/r3Hs3NHW-GE\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Linear regression attempts to forecast 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 <strong>Simple Linear Regression <\/strong>relates a dependent and one independent variable by estimating a linear relationship.<\/p>\n<p>A dependent variable is a variable predicted by the independent variable. It is also known as the explained variable or endogenous variable. On the other hand, the independent variable 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>$$Y=b_0+b_1X_1+\\epsilon$$<\/p>\n<p>Where:<\/p>\n<p>\\(Y\\) = Dependent variable<\/p>\n<p>\\(b_0\\) = Intercept<\/p>\n<p>\\(b_1\\) = Slope coefficient<\/p>\n<p>\\(X\\) = independent variable<\/p>\n<p>\\(\\epsilon\\) = Error term (Noise)<\/p>\n<p>\\(b_0\\) and \\(b_1\\) are known as <strong>regression coefficients.<\/strong><\/p>\n<p>The error term is the part of the dependent variable that the independent variable cannot explain.<\/p>\n<p>The figure below illustrates a simple linear regression model:<\/p>\n<h3><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-12738 size-full\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/cfa-level-2-linear-regression.jpg\" alt=\"\" width=\"1463\" height=\"1151\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/cfa-level-2-linear-regression.jpg 1463w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/cfa-level-2-linear-regression-300x236.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/cfa-level-2-linear-regression-1024x806.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/cfa-level-2-linear-regression-768x604.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/cfa-level-2-linear-regression-400x315.jpg 400w\" sizes=\"auto, (max-width: 1463px) 100vw, 1463px\" \/><\/h3>\n<h3>Example: Dependent and Independent Variables<\/h3>\n<p>Artur\u00a0 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 size-full wp-image-14836\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/img_2.jpg\" alt=\"\" width=\"1590\" height=\"949\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/img_2.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/img_2-300x179.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/img_2-1024x611.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/img_2-768x458.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/img_2-1536x917.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/02\/img_2-400x239.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>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<h4>Solution<\/h4>\n<p><strong>The correct answer is B.<\/strong><\/p>\n<p>An independent variable explains the variation of the dependent variable. It is also called the explanatory variable, exogeneous variable, <strong>predicting variable<\/strong>.<\/p>\n<p><strong>A and C are incorrect. <\/strong>A dependent variable is a variable predicted by the independent variable. It is also known as the <strong>predicted variable<\/strong>, explained variable, <strong>endogenous variable<\/strong>.<\/p>\n<\/blockquote>\n<p>Reading 0: Introduction to Linear Regression<\/p>\n<p><em>LOS 0 (a) Describe a simple linear regression model and the roles of the dependent and independent variables in the model<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Linear regression attempts to forecast 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 Simple Linear Regression relates a dependent and one&#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":[216,231,230],"class_list":["post-11473","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-quantitative-method","tag-cfa-level-2","tag-dependent-and-independent-variables","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>Dependent and Independent Variables<\/title>\n<meta name=\"description\" content=\"Learn the difference between dependent and independent variables in regression analysis and how they are used in statistical models.\" \/>\n<meta name=\"robots\" content=\"index, follow, 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