{"id":3747,"date":"2022-02-27T16:55:00","date_gmt":"2022-02-27T19:55:00","guid":{"rendered":"https:\/\/www.blogs.unicamp.br\/zero\/?p=3747"},"modified":"2022-05-23T17:59:29","modified_gmt":"2022-05-23T20:59:29","slug":"what-does-multiple-linear-regression-teach-us-about-losing-weight","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/zero\/3747\/","title":{"rendered":"What does Multiple Linear Regression teach us about losing weight?"},"content":{"rendered":"\n

This is a Math post, not a Nutrition post!<\/em><\/p>\n\n\n\n

We suggest that before any change in your routine to lose\/gain weight, look for a specialist.<\/em><\/p>\n\n\n\n

A few years ago I needed to learn about Multiple Linear Regression to help a master’s student in Engineering. It was an interesting and reasonably effective learning experience to address the problem he was researching (Sewage Treatment Plants). However, there is more to this method than the calculations and values \u200b\u200bthat allow us to estimate linear models for the behavior of unknown functions from their observable data. I say there is an application of great interest to most of us who are concerned about getting overweight.<\/p>\n\n\n\n

For starters, let’s see exactly what Multiple Linear Regression does (in a very succinct and generic way).<\/p>\n\n\n\n

We have a record of measurements of various events\/equipment\/actions\u2026 and we suppose that there is a mathematical function that is linear and that explains from this set of \u201cvariables\u201d that we measure, the output of the system. So, for each variable that we recorded, we were able to stipulate how much it actually influences the output of the system (Calm down, maybe the conversation is a little complicated so far, but if you’ve made it this far, congratulations! from now).<\/p>\n\n\n\n

We will give our system a name, it will be called \u201cweight gain\u201d. Our intention, for example, may be that this output is close to zero (ie, we keep our weight as is).<\/p>\n\n\n\n

So, we started to list a series of 26 actions within our routine that we believe influence the \u201cweight gain\u201d system (I will creatively call them the 26 letters of the alphabet).<\/p>\n\n\n\n

a, b, c, d, e, \u2026, x, y, z.<\/strong><\/p>\n\n\n\n

If this action-dependent system can be roughly expressed as a linear model, then, for each action, there must be an influence factor represented by a real number \u03b1i, where i is a natural number between 1 and 26, like this:<\/p>\n\n\n\n

\u03b1\u2081a + \u03b1\u2082b + \u03b1\u2083c + \u03b1\u2084d + \u03b1\u2085e + \u2026 + \u03b1\u2082\u2084x + \u03b1\u2082\u2085y + \u03b1\u2082\u2086z + ERROR = weight gain<\/p>\n\n\n\n

This \u201cERROR\u201d represents the very imprecision of the model. So, if the ERROR is 0, it means that we have actually found a linear model that explains our system. Although in the simplest exercises this occurs, in practice (or in the most fun exercises) the ERROR will always be different from 0, no matter how precise the model is and how much the system adapts to it. In case the ERROR is very large, this is an indication that the model in question is not good, and perhaps other variables should be included.<\/p>\n\n\n\n

If we have the measurements of these 26 variables at hand (for example, variable a, \u201chow many times a month do we eat chocolate\u201d, variable b, \u201chow many minutes a week do we practice moderate physical activity\u201d, \u2026) and we know how the \u201cweight gain\u201d varies \u201d, we were able to determine (if there is a linear model) what the values \u200b\u200bof \u03b1\u2081, \u03b1\u2082, \u03b1\u2083, \u03b1\u2084, \u03b1\u2085, \u2026 ,\u03b1\u2082\u2084, \u03b1\u2082\u2085, \u03b1\u2082\u2086 would be. So:<\/p>\n\n\n\n