Multiple regression supreme discipline of correlation-causality calculations Data Fitting by Sophia
Channel: transistor
Date: 2021-08-16

#MultipleRegression or multivariable calculus (the supreme discipline among correlation-causality calculations) | Data Fitting Science by Sophia Transistor.
This is my contribution for the #3Blue1Brown "The Summer of Math Exposition Competition" #SoME1 Multiple Regression
Presentation of mathematics in public and development of new approaches to mathematics in non relevant real life applications.
The importance of mathematical models and methods in electrical engineering. Power electronics and semiconductor physics combined with data acquisition methods and data poking.
With multiple regression, any non-linear or linear solver function can be fitted to coefficients with the aid of a well known calibration data set.
The model found in this way can now be used to functionally and quickly calculate the "value of interest".
A bipolar transistor made of silicon carbide (a so-called SiC-BJT) serves as a concrete application-oriented example. For the physical background and mechanism of action, there is a connection with logarithmus naturalis between:
virtual junction temperature Tvj, on-state base-emitter voltage Vbe, on, collector current Ic, on-state-collector-emitter voltage Vce, on and base current Ib.
With the help of the temperature-sensitive electrical parameters, which are easy to measure, a measuring board is set up (TIS board), where all values ​​can be sampled simultaneously in real time by means of an ADC.
This makes it possible to numerically determine the virtual junction temperature of the bipolar transistor chip in real time and in on-state normal operation.
If we can measure the temperature, we can also use it to calculate the curve of the transient thermal impedance Zth. This describes the behavior of the power component along a cooling path.
A reference curve can be compared with curves from aged components and the shape and course of the curve can even be used to determine the location of the fault.
The starting model for the multiple regression contains 4 independent variables and with the help of the found solver function and the expected variance in the measured values, it can be determined which parameters have the greatest possible influence.
The actual calculation can be carried out with the help of a computer using math software such as: Matlab, GNU Octave or SciLab.
So what makes people engage with math?
Basically, this post was created because someone wanted to tell a great non-relevant story ;-)

Table of contents with timestamps:
00:00 Intro to spark joy
00:08 Not all correlations are created equal
00:22 Data Fitting Problem Multiple Regression
01:22 What is a math function?
02:36 Massive Maths-Teacher
04:37 Discovery and adventure journalism
05:28 Physical background and mechanism of action
06:41 Transistor Solver Function
07:44 How bipolar transistors work
09:37 The "value of interest"
10:33 Temperature measurement: infrared camera, thermocouple
12:29 ADC measurement (analog-to-digital converter)
18:40 Measurement results evaluation
21:33 Calculation: Matlab, SciLab, GNU Octave
24:14 Off-Moderation with wise closing words

References and sources:
Videos:
3Blue1Brown:
20210716: Why aren't you making math videos? (So, a 3b1b podcast)
20170502: What is special about Euler's number e? | Essence of Calculus, Chapter 5
20180824: Q&A with Grant Sanderson (3blue1brown)
DorFuchs:
20130301: Linear Functions (Math Song)
20130509: My IQ and the normal distribution
MaiLab:
20180628: Beyoncé makes you stupid | Correlation vs. causality
20181101: The worst arguments on the internet
Gillian Perkins: 20210413: what I JUST LEARNED about how to get views on YouTube (this is big !!)
TEDx Talks: 20200313: What Makes People Engage With Math | Grant Sanderson | TEDxBerkeley
LearnChemE: 20121130: Model Fitting and Regression in MATLAB
Advertisement: Berlitz Language for life | We are sinking! | What are you thinking about?
Sophia Transistor: 20191126: Battery Condition Diagnostics & Testing | by Sophia Transistor
20120826: Apollo 11 launch with altitude and velocity data

Pictures:
Bathtub distribution: By Bathtub_curve.jpg: Wyattsderivative work: McSush (talk) - Bathtub_curve.jpg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=7458336
Animation of an alternative transistor model, based on an illustration from the KOSMOS Radiomann electronics kit, around 1963 (source: booklet with the function of a transistor.

Websites:
Mathematics competition of the DMV:
https://www.mathematik.de/presse/2880-dmv-lobt-dieses-jahr-wieder-zwei-medienpreise-aus
The Summer of Math Exposition Competition:
https://www.3blue1brown.com/blog/some1
https://mathworld.wolfram.com/HeartCurve.html
http://www.mathematische-basteleien.de/herz.htm

Music:
YouTube audio media library: Bach, Beethoven, Mozart
Wdr Bigband Very Personal: What Now and Funklaus

Multiple Regression

Video researched and edited by Sophia Transistor
Support me / Donate:
https://ko-fi.com/sophiatransistor
https://linktr.ee/sophiatransistor