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    Matlab normal equations without polyfit

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    Does anyone know how to do this without using Matlab functions such as polyfit and etc? The regression and error analysis needs to be performed by solving the normal equations. I also attached an example of how it is supposed to be modeled.

    %Tossing a lead weight: example of linear regression error from BME221 lecture

    %matrix of modeling functions: first column of ones, second column = t,
    %third column = -0.5*t^2 (data is modeled by h = h0 +V0*t +0.5g*t^2).
    %We shall denote our model by the vector equation A*x=b
    %height measurements in meters
    h=[0.3 14.8 20.7 15.9 2]'
    % our modeling parameters, (h0,V0,g)
    %variance in data
    %variance in first modeling parameter, for demonstration only.
    %other variances and covariances can be extracted from the symmetric SIGMAxsq.
    %SIGMAbsq: matrix of covariance of the observations b.
    %If the observations are independent then SIGMAbsq will be diagonal only.
    %We further assume that all observations have the same variance.
    %(a common assumption)
    %matrix of covariance of the regression parameters
    %Suppose we wish to determine the model value at 100 points ranging from 0 to 4.
    %Thus, we now have the vector equation: bm = Am*x
    %Finally, we have the matrix of covariance of bm.
    %In general, only the diagonal elements of SIGMAbmsq are of interest.
    hold on
    hold off
    legend('data','best-fit model','69% confidence (1sigma) interval')
    xlabel('t (sec)')
    ylabel('h (m)')

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    Solution Preview

    The example you gave did indeed help.

    The attached file follows the example you gave.

    function Michaelis3()

    % Data for Rxn rate with progesterone - case 1: with progesterone
    dog1 = [ 5 10 20 25 30 40 50 60 ] ; % dog is C in the formula
    rxn1 = [ 3.25 2.4 5.1 6 7.2 7.7 9.1 9.05 ] ; % Rxn is R in the formula

    % The variables in which we do linear regression:
    % x = 1/C and y = 1/R
    x1 = 1./dog1' ;
    y1 = 1./rxn1' ;

    % model: y1 = (Km/Rmax)*x1 + (1/Rmax)
    % matrix of modeling functions:
    A1 = [ ones(1,length(x1)) ; x1' ]' ;
    K1 = inv(A1'*A1)*A1'
    % Modeling parameters: ModPars = [ (1/Rmax), (Km/Rmax) ]
    ModPars1 = K1 * y1

    % Now we know what Km and Rmax are in the fit:
    Rmax1 = 1/ModPars1(1)
    Km1 = ModPars1(2)/ModPars1(1)
    % This answers the 1st question
    % but we also have to look for confidence intervals

    % Data Variance: subtract 2 as here we have 2 modeling parameters
    % and so used 2 degrees of freedom in the ...

    Solution Summary

    The expert uses Matlab normal equations without using the polyfit function.