{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Fitting a Line using Least Squares #SoME2' data-url='/boclips/videos/638cea7f3da28e036c8b909e' data-video-url='/boclips/videos/638cea7f3da28e036c8b909e' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nFitting a Line using Least Squares #SoME2\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30360345\" href=\"/search?publisher_ids%5B%5D=30360345\"\u003eVirtually Passed\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003e The Least Squares method is widely used to fit curves to data. This is called Least Squares regression. This video shows how to solve the ordinary least squares minimization problem for 1 unknown and 2 unknowns. In practice though, it...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003e The Least Squares method is widely used to fit curves to data. This is called Least Squares regression. This video shows how to solve the ordinary least squares minimization problem for 1 unknown and 2 unknowns. In practice though, it can be used to fit many different types of nonlinear functions too! As long as the minimization can be expressed like this:\u003cbr/\u003e min || [A]X - b ||\u003cbr/\u003e \u003cbr/\u003e Then the solution is\u003cbr/\u003e X = inv([A]^T[A])[A]^T b\u003cbr/\u003e \u003cbr/\u003e Chapters:\u003cbr/\u003e 0:00 Intro\u003cbr/\u003e 0:40 Problem Definition\u003cbr/\u003e 1:32 Def 1: Vertical Distance: min || r || (1 norm)\u003cbr/\u003e 2:15 Def 2: Perpendicular distance \u003cbr/\u003e 2:38 Def 3: Least Squares min || r || (2 norm)\u003cbr/\u003e 3:28 Calculate Error\u003cbr/\u003e 5:06 Convex Parabola (1D)\u003cbr/\u003e 6:06 Proof (1D)\u003cbr/\u003e 8:51 2D Intro\u003cbr/\u003e 9:27 Calculate Error in Matrix form\u003cbr/\u003e 11:52 Convex Parabaloid (2D)\u003cbr/\u003e 12:45 Proof (2D)\u003cbr/\u003e 15:58 MATLAB code \u0026 summary\u003cbr/\u003e 16:47 Outro\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='action-container flex justify-between'\u003e\n\u003cbutton aria-expanded='false' aria-label='Read more description' 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