creating_formula_images
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Table of Contents
Creating formula images
Motivation
Many concepts in neuroscience can be condensed into a (series of) mathematical equation(s). A prominent example is the ordinary least-squares multiple regression case, which uses the outcome of the matrix inversion of the covariance matrix of the design:
The data (y) is being explained by the product of the regression weights (beta/s) and the design matrix (X), plus the residual error term (epsilon):
After solving the normal equation that suffices the condition that the sum of squares of errors (SSE) is minimized, the result is:
Of course, this is just an example! :)
Requirements
- the actual (set of) formula(s) to be plotted
- access to a web browser (which you obviously have…)
- understanding of how to re-write the formula in the required markup
Instructions
- if you haven't done so (and the formula isn't already in written form), take a moment and write down the formula on a piece of paper, which will help you in creating the required markup language
- go to the PhpMathPublisher web page on this server
- enter the size of the output (the formula images above were made with a size setting of 14)
- translate the formula into markup language
- create the formula image and, if necessary, re-fine the markup language
- once you're satisfied, save the image onto your local computer (e.g. CTRL-click into the image and select “Save image”)
W.r.t. the formulas on this page, here is the code that was used to generate the images above:
- OLS data equation:
y = X beta ~ + ~ varepsilon
- OLS solution:
hat{beta} = (X^T X)^ {-1} X^T y
creating_formula_images.1274910727.txt.gz · Last modified: 2010/05/26 21:52 by jochen