{"id":1403,"date":"2018-12-19T02:32:34","date_gmt":"2018-12-19T08:02:34","guid":{"rendered":"https:\/\/www.questionbang.com\/blog\/?p=1403"},"modified":"2020-01-08T03:55:31","modified_gmt":"2020-01-08T09:25:31","slug":"predicting-jee-cut-off","status":"publish","type":"post","link":"https:\/\/www.questionbang.com\/blog\/2018\/12\/19\/predicting-jee-cut-off\/","title":{"rendered":"Predicting JEE cut-off"},"content":{"rendered":"<p>&nbsp;<\/p>\n<p>The cut-off is a popular word during the admission season, especially in India. For us at Questionbang, the cut-off is something often asked by mock-set-plus users &#8211; Has my score is good enough to qualify Joint Entrance Examination (JEE)? Hence, we decided to predict the cut-off for the next season and have it in\u00a0<a href=\"https:\/\/www.questionbang.com\/site\/doc\/social\/result-analysis\">result analysis<\/a>.<\/p>\n<p><code><\/code><\/p>\n<h3><strong>Background<\/strong><\/h3>\n<p>Most of us have used basic regression analysis during our class 12th maths, e.g, time series and forecasting. In reality, the outcomes of such predictions are going to be dependent on various factors. The use of simple regression may not be sufficient in such cases.<\/p>\n<p>Let us consider our requirement &#8211; predicting cut-off marks for JEE. The table below shows cut-off scores for the\u00a0<span id=\"GingerWidget-correction-2\" class=\"correction alternate\">last 6 years<\/span>.<\/p>\n<figure id=\"attachment_1407\" aria-describedby=\"caption-attachment-1407\" style=\"width: 263px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/10\/Table-1.png\"><img class=\"wp-image-1407\" src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/10\/Table-1.png\" alt=\"JEE cut-off data\" width=\"263\" height=\"300\" srcset=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/10\/Table-1.png 306w, https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/10\/Table-1-263x300.png 263w\" sizes=\"(max-width: 263px) 100vw, 263px\" \/><\/a><figcaption id=\"caption-attachment-1407\" class=\"wp-caption-text\">Table 1. Cut-off scores for the last 6 years.<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p style=\"text-align: left\">Let us try a simple curve fitting approach (Figure 1); this is giving a prediction of 69 for the year 2019. However, we cannot relate these points to any reasoning. As we can see, the\u00a0cut-off\u00a0(Y) was 113 for the year 2013 and became 74 in 2018 (Table 1). Surely many factors influence the cut-off.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_1415\" aria-describedby=\"caption-attachment-1415\" style=\"width: 450px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/10\/Figure-1-1.png\"><img class=\"wp-image-1415\" src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/10\/Figure-1-1.png\" alt=\"scatter plot diagram for JEE cut-off\" width=\"450\" height=\"272\" srcset=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/10\/Figure-1-1.png 755w, https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/10\/Figure-1-1-300x182.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/a><figcaption id=\"caption-attachment-1415\" class=\"wp-caption-text\">Figure 1. Scatter plot diagram for table 1.<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: right\"><a style=\"color: transparent;background-color: transparent;text-decoration: none\" href=\"http:\/\/www.questionbang.com\/ws\/\" target=\"_blank\" rel=\"noopener\"><span style=\"background-color: #ff4f4f;padding: 12px 20px;font-size: 15px;color: white;margin-bottom: 10px;font-weight: 900\"> \u00a0PRACTICE \u00a0JEE \u00a0ONLINE\u00a0 TESTS \u00a0 \u00a0<strong>&gt;&gt;<\/strong><\/span><\/a><\/h3>\n<h3><\/h3>\n<p>&nbsp;<\/p>\n<h3><strong>Assumptions<\/strong><\/h3>\n<p>Let us assume those cut-offs (Table 1) are a measure of competition and hence, are a function of the following variables:<\/p>\n<ul>\n<li>Number of seats available (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01a7b7b5dca66cb33a1207e1f39c1140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/>),<\/li>\n<li>Difficulty level (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f1cd6be340b4fce14489cf5b565a169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/>),<\/li>\n<li>Number of applicants (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f68f8a27fff8dae071cf74e8fa42e735_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/>).<\/li>\n<\/ul>\n<p>How these individual variables influence the outcome is something to be predicted.<\/p>\n<p>&nbsp;<\/p>\n<h3><strong>Choosing a regression method<\/strong><\/h3>\n<p>What is the regression analysis?<\/p>\n<p>In\u00a0statistical modeling,\u00a0<b>regression analysis<\/b>\u00a0is a set of statistical processes for\u00a0estimating\u00a0the relationships among variables. It includes many techniques for modeling and analyzing several variables when the focus is on the relationship between a\u00a0dependent variable\u00a0and one or more\u00a0independent variables [<a href=\"https:\/\/en.wikipedia.org\/wiki\/Regression_analysis\">wiki<\/a>].<\/p>\n<p>There are many different types of regression techniques. They are mainly of two categories &#8211;\u00a0 linear regression and non-linear regression.<\/p>\n<p>In our case, the cut-off score (predictor) is dependent on three independent variables (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01a7b7b5dca66cb33a1207e1f39c1140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/>, <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f1cd6be340b4fce14489cf5b565a169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/>, <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f68f8a27fff8dae071cf74e8fa42e735_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/>) as discussed before. Hence, this is going to be a multiple linear regression scenario.<\/p>\n<p>The table below (Table 2) is an extension of Table 1 (Cut-off scores for the last 6 years) to include the number of seats available, difficulty level and the number of applicants.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_1999\" aria-describedby=\"caption-attachment-1999\" style=\"width: 850px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/12\/new-table.png\"><img class=\"wp-image-1999 size-full\" src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/12\/new-table.png\" alt=\"JEE cut-off observations\" width=\"850\" height=\"377\" srcset=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/12\/new-table.png 850w, https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/12\/new-table-300x133.png 300w, https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/12\/new-table-768x341.png 768w\" sizes=\"(max-width: 850px) 100vw, 850px\" \/><\/a><figcaption id=\"caption-attachment-1999\" class=\"wp-caption-text\">Table 2. Extended table to include other variables.<br \/>The difficulty level is a categorical variable having level 1 (high) or 0 (moderate).<\/figcaption><\/figure>\n<h4><strong>About data<\/strong><\/h4>\n<p>The data &#8211; cut-off scores, seat availability, number of applicants and difficulty level have been gathered from online news portals. The JEE format changed a few times during the past 20+ years. It has a two-phase (Mains &amp; Advanced) format\u00a0since 2013.\u00a0 We will use data from 2013\u00a0 to\u00a0 2018.<\/p>\n<h3><\/h3>\n<h3 style=\"text-align: right\"><a style=\"color: transparent;background-color: transparent;text-decoration: none\" href=\"http:\/\/www.questionbang.com\/ws\/\" target=\"_blank\" rel=\"noopener\"><span style=\"background-color: #ff4f4f;padding: 12px 20px;font-size: 15px;color: white;margin-bottom: 10px;font-weight: 900\">\u00a0PRACTICE\u00a0 JEE\u00a0 MOCK\u00a0 TESTS\u00a0 \u00a0<strong>&gt;&gt;<\/strong><\/span><\/a><\/h3>\n<p>&nbsp;<\/p>\n<h3><strong>Revisiting the basics\u00a0of\u00a0least square regression method &#8211; a single independent variable condition<\/strong><\/h3>\n<p>&nbsp;<\/p>\n<h4><\/h4>\n<p>Assume a single independent variable condition and set of values as below (Table 3). Let us call these observations.<\/p>\n<table class=\" aligncenter\" style=\"height: 203px;margin-bottom: 10px\" width=\"252\">\n<tbody>\n<tr style=\"text-align: center;background-color: #e9ecef;color: #4d5057\">\n<td style=\"background-color: #e9ecef;color: #4d5057\" width=\"312\"><strong><b><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bb3c186e5c65fcd066bb23dec8f4e48a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"\/><\/b><\/strong><\/td>\n<td width=\"312\"><strong><b><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c8700e0258243116de0d4f288e2e3b44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"\/><\/b><\/strong><\/td>\n<\/tr>\n<tr style=\"border: none;text-align: center\">\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d48db79635c1ec05bd332325e278f268_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01a7b7b5dca66cb33a1207e1f39c1140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/><\/td>\n<\/tr>\n<tr style=\"border: none;text-align: center\">\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-445c2fb0b8c763c14a5736dc7f43a558_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f1cd6be340b4fce14489cf5b565a169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/><\/td>\n<\/tr>\n<tr style=\"border: none;text-align: center\">\n<td width=\"312\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/strong><\/td>\n<td width=\"312\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/strong><\/td>\n<\/tr>\n<tr style=\"text-align: center\">\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-14d044f0df2ad0803a44e0f2109915bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-2c83758b12d1eb192c053e5f0ac1a434_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"\/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center\">Table 3. Observations.<br \/>\n<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c8700e0258243116de0d4f288e2e3b44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"\/> &#8211; Independent variable,<br \/>\n<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bb3c186e5c65fcd066bb23dec8f4e48a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"\/> &#8211; Actual dependent variable.<\/p>\n<p>Following is an equation for simple linear regression:<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;border: none\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 17px;\"><span class=\"ql-right-eqno\"> (1) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-404b633c2a104c5a0cd50dc1c7f62d86_l3.png\" height=\"17\" width=\"86\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125; &#121;&#61;&#32;&#97;&#43;&#32;&#98;&#32;&#120;&#46; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\r\n<\/pre>\n<p>Let us compute predictions <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-74081481dc2db1d438329ee701db56a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"34\" style=\"vertical-align: -6px;\"\/> , using the the above values (Table 3):<\/p>\n<p style=\"text-align: center\">\u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b521c9e5c68c97e2dd19fafafae2dcda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#49;&#61;&#32;&#97;&#43;&#32;&#98;&#32;&#123;&#120;&#95;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"116\" style=\"vertical-align: -6px;\"\/><\/p>\n<p style=\"text-align: center\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-0b039a3f86372e3d1ba6439ce46a09d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#50;&#61;&#32;&#97;&#43;&#32;&#98;&#32;&#123;&#120;&#95;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -6px;\"\/><\/p>\n<p style=\"text-align: center\"><strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<span style=\"color: #000000\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 <span style=\"color: #000000\">\u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/strong><strong>\u00a0 \u00a0\u00a0<\/strong><\/p>\n<p style=\"text-align: center\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-9f1c21a5a83df1efb292593acc1dc856_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#110;&#61;&#32;&#97;&#43;&#32;&#98;&#32;&#123;&#120;&#95;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"119\" style=\"vertical-align: -6px;\"\/>.<\/p>\n<p style=\"text-align: left\">In generic form,\u00a0 the equation for predicted value will become:<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;border: none\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 18px;\"><span class=\"ql-right-eqno\"> (2) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f3ed4c604c9a5a5bd1f80360a72968ce_l3.png\" height=\"18\" width=\"99\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125; &#121;&#95;&#112;&#61;&#32;&#97;&#43;&#32;&#98;&#32;&#123;&#120;&#95;&#105;&#125;&#46; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\r\n<\/pre>\n<table class=\" aligncenter\" style=\"height: 203px;margin-bottom: 10px\" width=\"421\">\n<tbody>\n<tr style=\"background-color: #e9ecef;color: #4d5057;text-align: center\">\n<td width=\"312\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bb3c186e5c65fcd066bb23dec8f4e48a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"\/><\/strong><\/td>\n<td width=\"319\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c8700e0258243116de0d4f288e2e3b44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"\/><\/strong><\/td>\n<td width=\"319\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b79e7f68feebbbda96d302c220b9ddf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -6px;\"\/><\/strong><\/td>\n<\/tr>\n<tr style=\"border: none;text-align: center\">\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d48db79635c1ec05bd332325e278f268_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01a7b7b5dca66cb33a1207e1f39c1140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-75f5716218712b359994dee1cc83a7ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"35\" style=\"vertical-align: -6px;\"\/><\/td>\n<\/tr>\n<tr style=\"border: none;text-align: center\">\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-445c2fb0b8c763c14a5736dc7f43a558_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f1cd6be340b4fce14489cf5b565a169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-de0c17f8e2e7db96aed8fcdf4ed00e15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"36\" style=\"vertical-align: -6px;\"\/><\/td>\n<\/tr>\n<tr style=\"border: none;text-align: center\">\n<td width=\"312\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/strong><\/td>\n<td width=\"319\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/strong><\/td>\n<td width=\"319\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/strong><\/td>\n<\/tr>\n<tr style=\"text-align: center\">\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-14d044f0df2ad0803a44e0f2109915bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-2c83758b12d1eb192c053e5f0ac1a434_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-74e100fc7f766738d2ff284501807240_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -6px;\"\/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center\">Table 4. Observations and predictions.<br \/>\n<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b79e7f68feebbbda96d302c220b9ddf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -6px;\"\/> &#8211; Predicted\u00a0value.<\/p>\n<p>&nbsp;<\/p>\n<p>Let us verify the accuracy of our prediction (Table 5),<\/p>\n<table class=\" aligncenter\" style=\"height: 201px;margin-bottom: 10px\" width=\"589\">\n<tbody>\n<tr style=\"text-align: center;background-color: #e9ecef;color: #4d5057\">\n<td width=\"312\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bb3c186e5c65fcd066bb23dec8f4e48a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"\/><\/strong><\/td>\n<td width=\"329\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c8700e0258243116de0d4f288e2e3b44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"\/><\/strong><\/td>\n<td width=\"312\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b79e7f68feebbbda96d302c220b9ddf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -6px;\"\/><\/strong><\/td>\n<td width=\"312\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d33c164f455b97af0a78c1c0eaac4383_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"\/><\/strong><\/td>\n<\/tr>\n<tr style=\"border: none;text-align: center\">\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d48db79635c1ec05bd332325e278f268_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01a7b7b5dca66cb33a1207e1f39c1140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-75f5716218712b359994dee1cc83a7ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"35\" style=\"vertical-align: -6px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-47a7acb6950d00f0948b31307bbb91e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#49;&#32;&#45;&#32;&#32;&#32;&#40;&#121;&#95;&#112;&#41;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"74\" style=\"vertical-align: -6px;\"\/><\/td>\n<\/tr>\n<tr style=\"border: none;text-align: center\">\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-445c2fb0b8c763c14a5736dc7f43a558_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f1cd6be340b4fce14489cf5b565a169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-de0c17f8e2e7db96aed8fcdf4ed00e15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"36\" style=\"vertical-align: -6px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-334f24e827ccd5b24568ef24e006cd91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#50;&#32;&#45;&#32;&#40;&#121;&#95;&#112;&#41;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -6px;\"\/><\/td>\n<\/tr>\n<tr style=\"border: none;text-align: center\">\n<td width=\"312\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/strong><\/td>\n<td width=\"319\"><strong><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/strong><\/td>\n<td width=\"319\"><strong>\u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/strong><\/td>\n<td width=\"319\"><strong>\u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b06190063675f61fa1d5e09ffdaecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/strong><\/td>\n<\/tr>\n<tr style=\"text-align: center\">\n<td width=\"312\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-14d044f0df2ad0803a44e0f2109915bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-2c83758b12d1eb192c053e5f0ac1a434_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-74e100fc7f766738d2ff284501807240_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#95;&#112;&#41;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -6px;\"\/><\/td>\n<td width=\"319\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ba5b02fd5bc9d4537ffd1cebc695fac8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#110;&#32;&#45;&#32;&#40;&#121;&#95;&#112;&#41;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"78\" style=\"vertical-align: -6px;\"\/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"padding-left: 30px;text-align: center\">Table 5. Observations, predictions and errors.<br \/>\n<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d33c164f455b97af0a78c1c0eaac4383_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"\/> =\u00a0error term.<\/p>\n<p>&nbsp;<\/p>\n<p>As you can see, we subtracted the predictions (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b79e7f68feebbbda96d302c220b9ddf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -6px;\"\/>) from the actual observations (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bb3c186e5c65fcd066bb23dec8f4e48a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"\/>) to compute errors (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d33c164f455b97af0a78c1c0eaac4383_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"\/>). The next objective would be to refit the line so that the error (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d33c164f455b97af0a78c1c0eaac4383_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"\/>) is minimized.<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;border: none\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 13px;\"><span class=\"ql-right-eqno\"> (3) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-8b0ae0bc89c65d7a4a268c7d772bcc1c_l3.png\" height=\"13\" width=\"93\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125; &#101;&#95;&#105;&#61;&#121;&#95;&#105;&#32;&#45;&#32;&#121;&#95;&#112;&#44; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/pre>\n<p>From (2) and (3),<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;border: none\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 53px;\"><span class=\"ql-right-eqno\"> (4) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-036bed325b10398ef8a0f525ae1b4481_l3.png\" height=\"53\" width=\"213\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125; &#92;&#115;&#117;&#109;&#95;&#123;&#105;&#61;&#49;&#125;&#94;&#123;&#78;&#125;&#123;&#101;&#95;&#105;&#94;&#50;&#125;&#32;&#61;&#32;&#92;&#115;&#117;&#109;&#95;&#123;&#105;&#61;&#49;&#125;&#94;&#123;&#78;&#125;&#123;&#121;&#95;&#105;&#32;&#45;&#32;&#40;&#97;&#43;&#98;&#120;&#95;&#105;&#41;&#125;&#94;&#50;&#32;&#125;&#46; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\r\n<\/pre>\n<p>Eq (4) is a squared error function; we need to find coefficients <strong>a<\/strong> &amp; <strong>b<\/strong> to achieve minimum (zero) error. Take the\u00a0<span id=\"GingerWidget-correction-1\" class=\"correction alternate\">partial derivative<\/span>\u00a0of eq (4) with respect to\u00a0\u00a0<strong>a<\/strong> and <strong>b<\/strong>:<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;border: none\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 60px;\"><span class=\"ql-right-eqno\"> (5) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-18f2cca4bc8d4b5b6a29ef62139fd49d_l3.png\" height=\"60\" width=\"93\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125; &#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#97;&#114;&#116;&#105;&#97;&#108;&#32;&#92;&#115;&#117;&#109;&#32;&#92;&#108;&#105;&#109;&#105;&#116;&#115;&#95;&#123;&#105;&#61;&#49;&#125;&#94;&#123;&#110;&#125;&#123;&#101;&#95;&#105;&#94;&#50;&#125;&#125;&#123;&#92;&#112;&#97;&#114;&#116;&#105;&#97;&#108;&#32;&#97;&#125;&#61;&#48;&#44; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/pre>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;border: none\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 60px;\"><span class=\"ql-right-eqno\"> (6) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-2debf37b33da348c3c51e0177d06b7f0_l3.png\" height=\"60\" width=\"93\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#32; &#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#97;&#114;&#116;&#105;&#97;&#108;&#32;&#92;&#115;&#117;&#109;&#32;&#92;&#108;&#105;&#109;&#105;&#116;&#115;&#95;&#123;&#105;&#61;&#49;&#125;&#94;&#123;&#110;&#125;&#123;&#101;&#95;&#105;&#94;&#50;&#125;&#125;&#123;&#92;&#112;&#97;&#114;&#116;&#105;&#97;&#108;&#32;&#98;&#125;&#61;&#48;&#46; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/pre>\n<p>From (5) and (6),<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;border: none\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 25px;\"><span class=\"ql-right-eqno\"> (7) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-8fe82c7ae0a544b959425780d2ad1e04_l3.png\" height=\"25\" width=\"181\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125; &#92;&#115;&#117;&#109;&#123;&#121;&#95;&#105;&#125;&#32;&#61;&#32;&#92;&#115;&#117;&#109;&#123;&#97;&#125;&#43;&#98;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#105;&#125;&#32;&#32; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\r\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 25px;\"><span class=\"ql-right-eqno\"> (8) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-57d6b3ddeb7eb7dc95cb7a63dec3907d_l3.png\" height=\"25\" width=\"221\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125; &#92;&#115;&#117;&#109;&#123;&#121;&#95;&#105;&#120;&#95;&#105;&#125;&#32;&#61;&#32;&#97;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#105;&#125;&#43;&#98;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#105;&#94;&#50;&#125;&#46;&#32; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\r\n\r\n<\/pre>\n<h3 style=\"text-align: right\"><a style=\"color: transparent;background-color: transparent;text-decoration: none\" href=\"http:\/\/www.questionbang.com\/ws\/\" target=\"_blank\" rel=\"noopener\"><span style=\"background-color: #ff4f4f;padding: 12px 20px;font-size: 15px;color: white;margin-bottom: 10px;font-weight: 900\">PRACTICE\u00a0 FREE\u00a0 JEE\u00a0 MOCK\u00a0 TESTS\u00a0 ONLINE \u00a0\u00a0<strong>&gt;&gt;<\/strong><\/span><\/a><\/h3>\n<h3><\/h3>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<h3><strong>Computing JEE Cut-off &#8211; three independent variable condition\u00a0<\/strong><\/h3>\n<h4><\/h4>\n<p>&nbsp;<\/p>\n<p>In our case, we have three independent variables &#8211; <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01a7b7b5dca66cb33a1207e1f39c1140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/>, <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f1cd6be340b4fce14489cf5b565a169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/>, <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f68f8a27fff8dae071cf74e8fa42e735_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/> and coefficients &#8211; <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>, <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>, <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-4e8716946f6a868f015e0d62f28bc540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\"\/>. The regression equation becomes,<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;padding-top: 25px\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 18px;\"><span class=\"ql-right-eqno\"> (9) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-e755f374c2b8af6d460f62331bc3870f_l3.png\" height=\"18\" width=\"197\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125; &#38;&#123;&#121;&#95;&#112;&#125;&#61;&#97;&#32;&#43;&#32;&#98;&#120;&#95;&#49;&#43;&#99;&#120;&#95;&#50;&#43;&#100;&#120;&#95;&#51;&#46; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/pre>\n<p>&nbsp;<\/p>\n<p>Intercept\u00a0<i>a<\/i>\u00a0is:<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;padding-top: 25px;border: none;font-size: 16px;padding-left: 0px;padding-right: 0\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b01717bc7499983b192f292e460b29dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#108;&#105;&#103;&#110;&#101;&#100;&#125; &#97;&#61;&#121;&#95;&#105;&#32;&#45;&#32;&#98;&#32;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#32;&#120;&#125;&#95;&#49;&#125;&#32;&#45;&#32;&#99;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#32;&#120;&#95;&#50;&#125;&#32;&#45;&#32;&#100;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#32;&#120;&#95;&#51;&#125;&#32;&#92;&#108;&#97;&#98;&#101;&#108;&#123;&#101;&#113;&#49;&#125;&#44;&#32; &#92;&#101;&#110;&#100;&#123;&#97;&#108;&#105;&#103;&#110;&#101;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"194\" style=\"vertical-align: 0px;\"\/>                                                     (10)<\/pre>\n<p>where;<br \/>\n<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b8183fd7868377cfb555c426ec23dc56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#120;&#125;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: -4px;\"\/>,\u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-a1c95e326f883b81e77999948dd18d4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#120;&#125;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -3px;\"\/> and\u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7ec403705b2bed6bad77b07e13ba7443_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#120;&#125;&#95;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -3px;\"\/> are means of respective variable values.<\/p>\n<p>And\u00a0the normal equations are,<\/p>\n<p style=\"text-align: left;padding-left: 180px\"><a name=\"id2401277183\"><\/a><\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 21px;\"><span class=\"ql-right-eqno\"> (11) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-e571be97cc44810050eaff8e8c7fd2e2_l3.png\" height=\"21\" width=\"315\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#36;&#92;&#115;&#117;&#109;&#123;&#121;&#95;&#105;&#120;&#95;&#49;&#125;&#36;&#32;&#61;&#32;&#36;&#98;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#94;&#50;&#125;&#43;&#99;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#32;&#43;&#100;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#36;&#44;&#32;&#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p style=\"text-align: left;padding-left: 180px\"><a name=\"id3705553461\"><\/a><\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 20px;\"><span class=\"ql-right-eqno\"> (12) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-e7632743de063ec3b62b3350787f6b3c_l3.png\" height=\"20\" width=\"315\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#36;&#92;&#115;&#117;&#109;&#123;&#121;&#95;&#105;&#120;&#95;&#50;&#125;&#36;&#32;&#61;&#32;&#36;&#98;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#43;&#99;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#94;&#50;&#125;&#32;&#43;&#100;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#32;&#36;&#44;&#32;&#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p style=\"text-align: left;padding-left: 180px\"><a name=\"id2113063550\"><\/a><\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 20px;\"><span class=\"ql-right-eqno\"> (13) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-3dd8ff46fb0b6bcd1258354ede57447e_l3.png\" height=\"20\" width=\"315\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#36;&#92;&#115;&#117;&#109;&#123;&#121;&#95;&#105;&#120;&#95;&#51;&#125;&#36;&#32;&#61;&#32;&#36;&#98;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#43;&#99;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#32;&#43;&#100;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#32;&#36;&#46;&#32;&#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>&nbsp;<\/p>\n<p><span id=\"GingerWidget-correction-0\" class=\"correction alternate\">Writing<\/span>\u00a0the above equations in matrix form and solving using <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cramer%27s_rule\">Cramer\u2019s rule<\/a>:<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;padding-top: 25px;border: none\"><\/pre>\n<p style=\"text-align: left\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-e3fe4529e3de5110b03bce53f6142264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#117;&#109;&#123;&#121;&#95;&#105;&#120;&#95;&#49;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#94;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#40;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#41;&#093;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#32;&#32;&#41;&#093;&#32;&#43;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#125;&#94;&#50;&#32;&#32;&#41;&#093;&#32;&#125;&#123;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#94;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#94;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#40;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#94;&#50;&#41;&#093;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#32;&#32;&#41;&#093;&#32;&#43;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#125;&#94;&#50;&#32;&#32;&#41;&#093;&#125;&#44;&#32;&#32;&#32;&#32;&#32;&#32;&#40;&#49;&#52;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"766\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: left\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1c4698234decbcf72b27b4717a2c10cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#94;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#40;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#51;&#125;&#41;&#093;&#45;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#49;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#32;&#32;&#41;&#093;&#32;&#43;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#51;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#50;&#125;&#41;&#093;&#32;&#125;&#123;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#94;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#94;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#40;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#94;&#50;&#41;&#093;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#32;&#32;&#41;&#093;&#32;&#43;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#125;&#94;&#50;&#32;&#32;&#41;&#093;&#125;&#44;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#40;&#49;&#53;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"766\" style=\"vertical-align: -12px;\"\/><\/p>\n<p style=\"text-align: left\"><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-3dc351f71772f47994dee1a70691ac6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#94;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#94;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#51;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#32;&#32;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#50;&#125;&#093;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#51;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#50;&#125;&#32;&#32;&#41;&#093;&#32;&#43;&#32;&#92;&#115;&#117;&#109;&#123;&#121;&#120;&#95;&#49;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#94;&#50;&#125;&#41;&#093;&#32;&#125;&#123;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#94;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#94;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#40;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#94;&#50;&#41;&#093;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#51;&#94;&#50;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#32;&#32;&#41;&#093;&#32;&#43;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#091;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#50;&#125;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#120;&#95;&#51;&#125;&#45;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#49;&#120;&#95;&#51;&#125;&#32;&#92;&#115;&#117;&#109;&#123;&#120;&#95;&#50;&#125;&#94;&#50;&#32;&#32;&#41;&#093;&#125;&#46;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#40;&#49;&#54;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"781\" style=\"vertical-align: -12px;\"\/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: right\"><a style=\"color: transparent;background-color: transparent;text-decoration: none\" href=\"http:\/\/www.questionbang.com\/ws\/\" target=\"_blank\" rel=\"noopener\"><span style=\"background-color: #ff4f4f;padding: 12px 20px;font-size: 15px;color: white;margin-bottom: 10px;font-weight: 900\">PRACTICE\u00a0 FREE\u00a0 JEE\u00a0 TEST\u00a0 SERIES\u00a0 \u00a0\u00a0<strong>&gt;&gt;<\/strong><\/span><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>Let us calculate the coefficients\u00a0<strong>a<\/strong>, <strong>b<\/strong>, <strong>c<\/strong> and <strong>d<\/strong> using Microsoft Excel.<br \/>\n(Courtesy: <a href=\"https:\/\/onlinecourses.science.psu.edu\/stat501\/node\/380\/\">https:\/\/onlinecourses.science.psu.edu\/stat501\/node\/380\/<\/a>)<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_1895\" aria-describedby=\"caption-attachment-1895\" style=\"width: 346px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/12\/excel-table-2.png\"><img class=\"wp-image-1895 size-full\" src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/12\/excel-table-2.png\" alt=\"JEE cut-off computation\" width=\"346\" height=\"187\" srcset=\"https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/12\/excel-table-2.png 346w, https:\/\/www.questionbang.com\/blog\/wp-content\/uploads\/2018\/12\/excel-table-2-300x162.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/a><figcaption id=\"caption-attachment-1895\" class=\"wp-caption-text\">Figure 2: Excel showing observations.<\/figcaption><\/figure>\n<p>Using data analysis toolkit in MS Excel:<\/p>\n<p style=\"text-align: left\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0a = 26.0402,<\/p>\n<p style=\"text-align: left\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0b = -0.00225,<\/p>\n<p style=\"text-align: left\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0c = -6.4645,<\/p>\n<p style=\"text-align: left\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0d = 0.000119.<\/p>\n<p>After substituting the above coefficients, eq (9) becomes,<\/p>\n<pre class=\"lang-tex prettyprint prettyprinted\" style=\"background-color: white;padding-top: 25px\"><a name=\"id50938569\"><\/a><p class=\"ql-center-displayed-equation\" style=\"line-height: 18px;\"><span class=\"ql-right-eqno\"> (17) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b2c8fc59f2d9b78cd75704dc4f02d216_l3.png\" height=\"18\" width=\"395\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125; &#123;&#121;&#95;&#112;&#125;&#61;&#32;&#50;&#54;&#46;&#48;&#52;&#48;&#50;&#32;&#45;&#32;&#48;&#46;&#48;&#48;&#50;&#50;&#53;&#32;&#120;&#95;&#49;&#32;&#32;&#45;&#32;&#54;&#46;&#52;&#54;&#52;&#53;&#32;&#120;&#95;&#50;&#32;&#43;&#32;&#48;&#46;&#48;&#48;&#48;&#49;&#49;&#57;&#32;&#120;&#95;&#51;&#46; &#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/pre>\n<p>&nbsp;<\/p>\n<p>We can use the above eq (17) to compute the JEE cut-off.<\/p>\n<p>&nbsp;<\/p>\n<p>We will assume the following values for the year 2019:<\/p>\n<p style=\"text-align: left\">Number of seats (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01a7b7b5dca66cb33a1207e1f39c1140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/>) = 36500,<\/p>\n<p style=\"text-align: left\">Difficulty level\u00a0(<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f1cd6be340b4fce14489cf5b565a169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/>) = 1 or 0,<\/p>\n<p style=\"text-align: left\">Number of applicants\u00a0(<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f68f8a27fff8dae071cf74e8fa42e735_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/>) = 11 lakh.<\/p>\n<p>&nbsp;<\/p>\n<p>A)\u00a0 \u00a0 Using eq (10),\u00a0 high difficulty\u00a0 (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-5e3d83fdf57749786be77ccb257331e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;&#32;&#61;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: -3px;\"\/>)<\/p>\n<table class=\" aligncenter \" style=\"height: 122px\" width=\"632\">\n<tbody>\n<tr style=\"border-color: white\">\n<td style=\"width: 632px\"><\/td>\n<\/tr>\n<tr style=\"border-color: white\">\n<td style=\"width: 632px\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-0d980eb1fe33c671da00d483ccdd1538_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#95;&#112;&#125;&#61;&#32;&#50;&#54;&#46;&#48;&#52;&#48;&#50;&#43;&#32;&#40;&#32;&#45;&#48;&#46;&#48;&#48;&#50;&#50;&#53;&#32;&#41;&#32;&#51;&#54;&#53;&#48;&#48;&#32;&#43;&#32;&#40;&#32;&#45;&#54;&#46;&#52;&#54;&#52;&#53;&#32;&#41;&#32;&#49;&#32;&#43;&#32;&#40;&#32;&#48;&#46;&#48;&#48;&#48;&#49;&#49;&#57;&#32;&#41;&#32;&#49;&#49;&#48;&#48;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"523\" style=\"vertical-align: -6px;\"\/><\/td>\n<\/tr>\n<tr style=\"border-color: white\">\n<td style=\"width: 632px\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-00506e2aacec77f0cf747b6dd4ec9dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#61;&#32;&#54;&#56;&#46;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"59\" style=\"vertical-align: 0px;\"\/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 632px\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>B)\u00a0 \u00a0 Using eq (10),\u00a0 moderate difficulty\u00a0 (<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ff9e57808bb1636a3756e1aa539001ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;&#32;&#61;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: -3px;\"\/>)<\/p>\n<table class=\" aligncenter \" style=\"height: 122px\" width=\"632\">\n<tbody>\n<tr style=\"border-color: white\">\n<td style=\"width: 632px\"><\/td>\n<\/tr>\n<tr style=\"border-color: white\">\n<td style=\"width: 632px\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-e5c5c3e30ac51285700f6184d605e460_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#95;&#112;&#125;&#61;&#32;&#50;&#54;&#46;&#48;&#52;&#48;&#50;&#43;&#32;&#40;&#32;&#45;&#48;&#46;&#48;&#48;&#50;&#50;&#53;&#32;&#41;&#32;&#51;&#54;&#53;&#48;&#48;&#32;&#43;&#32;&#40;&#32;&#45;&#54;&#46;&#52;&#54;&#52;&#53;&#32;&#41;&#32;&#48;&#32;&#43;&#32;&#40;&#32;&#48;&#46;&#48;&#48;&#48;&#49;&#49;&#57;&#32;&#41;&#32;&#49;&#49;&#48;&#48;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"523\" style=\"vertical-align: -6px;\"\/><\/td>\n<\/tr>\n<tr style=\"border-color: white\">\n<td style=\"width: 632px\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-688fc9c082cc1adaf7a2598fe87fc0d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#32;&#61;&#32;&#55;&#52;&#46;&#57;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: -1px;\"\/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 632px\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<table class=\" aligncenter \" style=\"border: 1px solid #e74c3c;height: 84px;width: 626px\">\n<tbody>\n<tr style=\"border-color: white\">\n<td style=\"width: 632px;text-align: left\"><\/td>\n<\/tr>\n<tr style=\"border-color: white;border-bottom: border: 1px solid #e74c3c\">\n<td style=\"width: 632px\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Cut-off score range:\u00a0 \u00a0<img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-3e3b92253edc96beb52811ed30fc440d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\"\/>\u00a0 &#8211;\u00a0 <img src=\"https:\/\/www.questionbang.com\/blog\/wp-content\/ql-cache\/quicklatex.com-da7843edb510e285d79daaeecac66b11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\"\/>.<\/td>\n<\/tr>\n<tr style=\"border-bottom: 1px solid #e74c3c\">\n<td style=\"width: 632px\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h3><strong>Conclusion<\/strong><\/h3>\n<p>The above prediction may not be accurate as it is based on a very limited set of data. It is to be noted that,\u00a0this prediction is not relevant for the year 2019 (onwards), as the cut-off is going to be in percentile not in the score.<\/p>\n<p>Questionbang users can find these values in the\u00a0<a href=\"https:\/\/www.questionbang.com\/ws\/\">mock-set-plus<\/a> <a href=\"https:\/\/www.questionbang.com\/site\/doc\/social\/result-analysis\">result analysis<\/a> section.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: right\"><a style=\"color: transparent;background-color: transparent;text-decoration: none\" href=\"http:\/\/www.questionbang.com\/ws\/\" target=\"_blank\" rel=\"noopener\"><span style=\"background-color: #ff4f4f;padding: 12px 20px;font-size: 15px;color: white;margin-bottom: 10px;font-weight: 900\">\u00a0PRACTICE\u00a0 JEE\u00a0 TESTS\u00a0 ONLINE \u00a0\u00a0<strong>&gt;&gt;<\/strong><\/span><\/a><\/p>\n<h3><\/h3>\n<p>&nbsp;<\/p>\n<p>We value your <a href=\"https:\/\/www.questionbang.com\/site\/contact\">feedback<\/a> and welcome any comments to help us serve you better.<\/p>\n<p>&nbsp;<\/p>\n<h3>References:<\/h3>\n<ul>\n<li><a href=\"https:\/\/www.questionbang.com\/site\/result-analysis\">https:\/\/www.questionbang.com\/site\/result-analysis<\/a><\/li>\n<li><a href=\"https:\/\/www.questionbang.com\/site\/mock-set-plus\/jee\">https:\/\/www.questionbang.com\/site\/mock-set-plus\/jee<\/a><\/li>\n<li><a href=\"https:\/\/www.questionbang.com\/\">https:\/\/www.questionbang.com\/<\/a><\/li>\n<li><a href=\"https:\/\/www.questionbang.com\/ws\/\">https:\/\/www.questionbang.com\/ws\/<\/a><\/li>\n<li><a href=\"https:\/\/onlinecourses.science.psu.edu\/stat501\/node\/380\/\">https:\/\/onlinecourses.science.psu.edu\/stat501\/node\/380\/<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Cramer%27s_rule\">https:\/\/en.wikipedia.org\/wiki\/Cramer%27s_rule<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Regression_analysis\">https:\/\/en.wikipedia.org\/wiki\/Regression_analysis<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Microsoft_Excel\">https:\/\/en.wikipedia.org\/wiki\/Microsoft_Excel<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; The cut-off is a popular word during the admission season, especially in India. For us at Questionbang, the cut-off is something often asked by mock-set-plus users &#8211; Has my score is good enough to qualify Joint Entrance Examination (JEE)? Hence, we decided to predict the&hellip;<\/p>\n","protected":false},"author":4,"featured_media":2454,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[13,42,16],"tags":[117,61,62],"coauthors":[23],"_links":{"self":[{"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/posts\/1403"}],"collection":[{"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/comments?post=1403"}],"version-history":[{"count":0,"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/posts\/1403\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/media\/2454"}],"wp:attachment":[{"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/media?parent=1403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/categories?post=1403"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/tags?post=1403"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.questionbang.com\/blog\/wp-json\/wp\/v2\/coauthors?post=1403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}