Tag: Regression

COVID19 Regression Model and Other Thoughts

March 28, 2020
I am not an epidemiologist but do regression modeling for a living. I have done regression modeling to predict student grades just after the first test, and now we will be using adaptive learning metrics to improve our identification schemes even earlier in the semester. It is not to spell boom or doom to a student but only to intervene early with personalized recommendations.
Looking at whatever data I can use and have time to scrape, four things are reasonably clear at this time to me about COVID19.
1) First, the rate of infection is exponential but it does not stay like that forever.  The logistic function of the infection rate is analogous to how the mass of a moving rocket decreases as it burns up its fuel. F=ma, but m is not a constant.
2) Second, President Trump is finally thinking about quarantining NY, NJ, CT area. A little late but it will definitely decrease the power of the exponent.
3) Third, we have to get more testing done but one which is totally random. We could have found the effect of the spring breakers coming to FL and of the college kids being sent home to parents who are having kids late in life. Please do not send your grandkids to grandpa/grandma’s retirement home. They may be the children of the corn.
4) Fourth, Florida and Louisiana need to get their head straightened out and use tougher rules to keep people inside and a method to keep outsiders out. They are the next hot zone.

How do I do polynomial regression in MATLAB?

Many students ask me how do I do this or that in MATLAB.  So I thought why not have a small series of my next few blogs do that.  In this blog, I show you how to do polynomial regression.

  • The MATLAB program link is here.
  • The HTML version of the MATLAB program is here.
  • DO NOT COPY AND PASTE THE PROGRAM BELOW BECAUSE THE SINGLE QUOTES MAY NOT TRANSLATE TO THE CORRECT SINGLE QUOTES IN MATLAB EDITOR OR IT MAY NOT PASTE HARD RETURNS.  DOWNLOAD THE MATLAB PROGRAM DIRECTLY INSTEAD
%% HOW DO I DO THAT IN MATLAB SERIES?
% In this series, I am answering questions that students have asked
% me about MATLAB.  Most of the questions relate to a mathematical
% procedure.

%% TOPIC
% How do I do polynomial regression?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://nm.mathforcollege.com/blog/regression_polynomial.m;
% Last Revised : August 3, 2009;
% Abstract: This program shows you how to do polynomial regression?
%           .
clc
clear all
clf

%% INTRODUCTION

disp('ABSTRACT')
disp('   This program shows you how to do polynomial regression')
disp(' ')
disp('AUTHOR')
disp('   Autar K Kaw of http://autarkaw.wordpress.com')
disp(' ')
disp('MFILE SOURCE')
disp('   http://nm.mathforcollege.com/blog/regression_polynomial.m')
disp(' ')
disp('LAST REVISED')
disp('   August 3, 2009')
disp(' ')

%% INPUTS
% y vs x data to regress
% x data
x=[-340 -280 -200 -120 -40 40 80];
% ydata
y=[2.45  3.33 4.30 5.09 5.72 6.24 6.47];
% Where do you want to find the values at
xin=[-300 -100 20  125];
%% DISPLAYING INPUTS
disp('  ')
disp('INPUTS')
disp('________________________')
disp('     x         y  ')
disp('________________________')
dataval=[x;y]';
disp(dataval)
disp('________________________')
disp('   ')
disp('The x values where you want to predict the y values')
dataval=[xin]';
disp(dataval)
disp('________________________')
disp('  ')

%% THE CODE
% Using polyfit to conduct polynomial regression to a polynomial of order 1
pp=polyfit(x,y,1);
% Predicting values at given x values
yin=polyval(pp,xin);
% This is only for plotting the regression model
% Find the number of data points
n=length(x);
xplot=x(1):(x(n)-x(1))/10000:x(n);
yplot=polyval(pp,xplot);
%% DISPLAYING OUTPUTS
disp('  ')
disp('OUTPUTS')
disp('________________________')
disp('   xasked   ypredicted  ')
disp('________________________')
dataval=[xin;yin]';
disp(dataval)
disp('________________________')

xlabel('x');
ylabel('y');
title('y vs x ');
plot(x,y,'o','MarkerSize',5,'MarkerEdgeColor','b','MarkerFaceColor','b')
hold on
plot(xin,yin,'o','MarkerSize',5,'MarkerEdgeColor','r','MarkerFaceColor','r')
hold on
plot(xplot,yplot,'LineWidth',2)
legend('Points given','Points found','Regression Curve','Location','East')
hold off
disp('  ')

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://nm.mathforcollege.com/videos and http://www.youtube.com/numericalmethodsguy

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