Most of our curve fitting (except for very simple fits, like linear) is done using a non-linear n-dimensional search following methods described in books like Data Reduction and Error Analysis For the Physical Sciences<\/i>, by Bevington and Robinson.<\/p>\n
The uncertainties on the coefficients are the standard deviations of the coefficients as the fitting process takes place. If the goodness of fit depends strongly on a particular fit coefficient, the uncertainty will be low. If the parameter doesn’t change the fit of the line to the points very much, the uncertainty will be large.<\/p>\n
Other information on fitting: The mathematical discussion regarding the uncertainties of fitted parameters in Bevington, or that found in the “Parameter Errors and Correlation” section at https:\/\/en.wikipedia.org\/wiki\/Linear_least_squares_(mathematics)#Weighted_linear_least_squares<\/a>, is how<\/em> the calculations are done.<\/p>\n Next, what do the uncertainties mean<\/em>?<\/p>\n The uncertainties of the fitted parameters are a measure of how strongly the parameter depends on the data. Let’s use the intercept as an example. If the value of the intercept is changed a lot by a little change in the data, then the intercept will have a bigger uncertainty. This is the same as said above, but stated in terms of data points.<\/p>\n Below is a Logger Pro<\/i> file showing two linear fits of almost the same data; the data sets are just horizontally offset by 100 units. The slopes (and the slope uncertainty) are the same. Changing one of the points a little bit won’t have a big effect on the slope, but in the case of the points out past 100 on the x axis, changing a point will change the intercept by a lot because of that distance from the x=0 line (that is, the y axis). You can see that Logger Pro<\/i> calculates the uncertainty of the y-intercept in the two fits very differently. The data out past 100 have a very fuzzy (large uncertainty) y-intercept value because a little change in the data will change the intercept a lot.<\/p>\n Another way of saying that is that the y-intercept is not well determined by Data Set 1.<\/p>","protected":false},"excerpt":{"rendered":" Most of our curve fitting (except for very simple fits, like linear) is done using a non-linear n-dimensional search following methods described in books like…<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[],"tags":[5486,5484,5483,5487,5488,5485],"class_list":["post-3247","post","type-post","status-publish","format-standard","hentry","tag-coefficients","tag-curve-fits","tag-fits","tag-quadradic","tag-standard-deviation","tag-uncertainties"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/posts\/3247","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\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/comments?post=3247"}],"version-history":[{"count":0,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/posts\/3247\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/media?parent=3247"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/categories?post=3247"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/tags?post=3247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nHow do you calculate linear fits in Logger Pro<\/i>?<\/a>
\nWhy don't Logger Pro<\/i> (or Graphical Analysis) curve fits always work? Why do curve fits sometimes change on opening a file?<\/a><\/p>\n
\nhttp:\/\/www2.vernier.com\/til\/3247\/intercept_uncertainty_example.cmbl<\/a><\/p>\n