{"id":94420,"date":"2021-07-14T10:27:00","date_gmt":"2021-07-14T14:27:00","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=94420"},"modified":"2022-11-21T09:47:44","modified_gmt":"2022-11-21T14:47:44","slug":"grokking-linear-regression-analysis-in-finance-part-ii","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/grokking-linear-regression-analysis-in-finance-part-ii\/","title":{"rendered":"Grokking Linear Regression Analysis in Finance &#8211; Part II"},"content":{"rendered":"\n<p><em>See <a href=\"\/campus\/ibkr-quant-news\/grokking-linear-regression-analysis-in-finance\/\">Part I<\/a> for an overview of the linear models and the concept of &#8220;regression&#8221;.<\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"aidnomenclatureanomenclature\">Nomenclature<\/h2>\n\n\n\n<p>When we read and learn about regression (and econometrics), every term or concept goes by a variety of names. <\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#cfeadf\">Visit QuantInsti website to view the complete Nomenclature table Vivek Krishnamoorthy has created: <a href=\"https:\/\/blog.quantinsti.com\/linear-regression\/#nomenclature\">https:\/\/blog.quantinsti.com\/linear-regression\/#nomenclature<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"typesoflinearregression\">Types of linear regression<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"1simplelinearregression\">1. Simple linear regression<\/h3>\n\n\n\n<p>Imagine that we hold the Coca-Cola (<em>NYSE : KO<\/em>) stock and are interested in its returns. Conventionally, we denote our variable of interest with the letter&nbsp;YY. We usually have multiple observations (taken to be&nbsp;nn) of it. So, the&nbsp;YY&nbsp;that we previously mentioned is an n-dimensional vector containing values&nbsp;YiYi.<\/p>\n\n\n\n<p>Here and throughout this post, I use the scalar versions of the equations. You can refer to&nbsp;<a href=\"https:\/\/blog.quantinsti.com\/linear-regression\/#nomenclature\">this section<\/a>&nbsp;to view the matrix forms. You can also read a more detailed treatment of the analytical expressions and derivations in standard econometric textbooks like&nbsp;<a href=\"https:\/\/blog.quantinsti.com\/linear-regression\/#baltagi\">Baltagi (2011)<\/a>,&nbsp;<a href=\"https:\/\/blog.quantinsti.com\/linear-regression\/#woolridge\">Woolridge (2015)<\/a>&nbsp;and&nbsp;<a href=\"https:\/\/blog.quantinsti.com\/linear-regression\/#greene\">Greene (2018)<\/a>.<\/p>\n\n\n\n<p>We want to examine the relationship between our stock\u2019s returns(<strong>Y<\/strong>) and the market returns(denoted as <strong>X<\/strong>). We believe the market returns i.e. the SPDR S&amp;P 500 ETF (<em>NYSEARCA : SPY<\/em>) should tell us something about <em>KO<\/em>&#8216;s returns. For each observation <em>i<\/em>,<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"734\" height=\"107\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2021\/07\/image-25.png\" alt=\"\" class=\"wp-image-94965 lazyload\" data-srcset=\"https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2021\/07\/image-25.png 734w, https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2021\/07\/image-25-700x102.png 700w, https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2021\/07\/image-25-300x44.png 300w\" data-sizes=\"(max-width: 734px) 100vw, 734px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 734px; aspect-ratio: 734\/107;\" \/><\/figure>\n\n\n\n<p>Equation <a href=\"https:\/\/blog.quantinsti.com\/linear-regression\/#mjx-eqn-eq1\">1<\/a> is just a dolled-up version of <em>y<\/em>=<em>mx<\/em>+<em>c<\/em> that we&#8217;d seen earlier with an additional <em>\u03f5i<\/em> term. In it <em>\u03b2<\/em>0 and <em>\u03b2<\/em>1 are commonly referred to as the intercept and the slope respectively.<\/p>\n\n\n\n<p>This is the simple linear regression model.<\/p>\n\n\n\n<p>We call it simple, since there is only one explanatory variable here; and we call it linear, since the equation is that of a straight line. It&#8217;s easy for us to visualize it in our mind\u2019s eye since they are like the <em>X<\/em>&#8211; and <em>Y<\/em> -coordinates on a Cartesian plane.<\/p>\n\n\n\n<p>A linear regression is <em>linear in its regression coefficients<\/em>.<\/p>\n\n\n\n<p>A natural extension to this model is the multiple linear regression model.<\/p>\n\n\n\n<p><em>Stay tuned for the next installment in which Vivek will discuss multiple linear regression.<\/em><\/p>\n\n\n\n<p><em>Visit QuantInsti for additional insight on this topic:&nbsp;<a href=\"https:\/\/blog.quantinsti.com\/linear-regression\/\">https:\/\/blog.quantinsti.com\/linear-regression\/<\/a>.<\/em><\/p>\n\n\n\n<p><em>Disclaimer: All investments and trading in the stock market involve risk. Any decisions to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.<\/em><\/p>\n\n\n\n<p><em>Any trading symbols displayed are for illustrative purposes only and are not intended to portray recommendations.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vivek Krishnamoorthy reviews regression in the context of econometrics and showcases a simple linear regression model.<\/p>\n","protected":false},"author":646,"featured_media":20117,"comment_status":"closed","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[339,338,350,341,344],"tags":[4922,4404,10009,10008,10010],"contributors-categories":[13654],"class_list":{"0":"post-94420","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-science","8":"category-ibkr-quant-news","9":"category-quant-asia-pacific","10":"category-quant-development","11":"category-quant-regions","12":"tag-econometrics","13":"tag-linear-regression","14":"tag-multiple-linear-regression-model","15":"tag-regression-coefficient","16":"tag-simple-linear-regression-model","17":"contributors-categories-quantinsti"},"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium 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