{"id":1675,"date":"2014-08-11T04:22:37","date_gmt":"2014-08-11T11:22:37","guid":{"rendered":""},"modified":"2020-07-31T10:57:22","modified_gmt":"2020-07-31T17:57:22","slug":"1675","status":"publish","type":"post","link":"https:\/\/www.vernier.com\/til\/1675","title":{"rendered":"How do Curve Fits work in the LabQuest App?"},"content":{"rendered":"<p>LabQuest App curve fit coefficients are computed in one of two ways.<\/p>\n<p>*** Linear form ***<br \/>\nLinear: y = mx +b<\/p>\n<p>LabQuest App uses the same approach as Logger <i>Pro<\/i>. See:<br \/>\n<a href=\"\/til\/1869\/\">How do you calculate linear fits in Logger <i>Pro<\/i>?<\/a><br \/>\n<\/p>\n<p>*** Non-linear forms ***<br \/>\nProportional: y = Ax<br \/>\nQuadratic: y = Ax^2+Bx+C<br \/>\nPower: y = Ax^B<br \/>\nNatural Exponent: y = Aexp(-Cx)+B<br \/>\nGaussian: y = A*e^(-(x-B)^2\/(2*C^2))+D<br \/>\nSine: y = A*sin(B*x+C)+D<br \/>\nCosine: y = A*cos(B*x+C)+D<br \/>\nCosine Squared: y = A*(cos(B*x+C))^2+D<br \/>\nNatural Logarithm: y = A*ln(B*x)<\/p>\n<p>The coefficients of the non-linear forms are computed using the iterative, best-fit values approach of the Levenburg-Marquadt method. See <a href=\"http:\/\/en.wikipedia.org\/wiki\/Levenberg\u2013Marquardt_algorithm\">http:\/\/en.wikipedia.org\/wiki\/Levenberg\u2013Marquardt_algorithm<\/a><\/p>\n<p>The root mean square error (RMSE) and uncertainties for each coefficient are also computed.<\/p>","protected":false},"excerpt":{"rendered":"<p>LabQuest App curve fit coefficients are computed in one of two ways. *** Linear form *** Linear: y = mx +b LabQuest App uses the&#8230;<\/p>\n","protected":false},"author":31,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[],"tags":[2503,2502,2505,2497,2504,2397,2496,2191,2498,163,2500,2499,2501],"class_list":["post-1675","post","type-post","status-publish","format-standard","hentry","tag-analysis","tag-cosine","tag-cosine-squared","tag-curve-fitting","tag-gaussian","tag-labquest","tag-labquest-app","tag-linear","tag-natural-exponent","tag-power","tag-proportional","tag-quadratic","tag-sine"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/posts\/1675","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/users\/31"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/comments?post=1675"}],"version-history":[{"count":0,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/posts\/1675\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/media?parent=1675"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/categories?post=1675"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/tags?post=1675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}