Get the minimum residual and the minimum distance in terms of the x axis using solver functions?

Question

Ronan 2015-12-2

0
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https://ww2.mathworks.cn/matlabcentral/answers/258539-get-the-minimum-residual-and-the-minimum-distance-in-terms-of-the-x-axis-using-solver-functions

I have a set of linear data and I used regression to best fit the data. I m trying to identify the data point that has the smallest distance in terms of the x axis and the smallest residual. So it appears that I need a solver function for finding the optimal value of two variables. So, looking at some of the solver functions, they require the fun of the polynomial you are using. So if I define this function based on the polynomials of the best fit line, how do I get the optimal residual at one data point. I was trying to use fminsearch but it seems that this is for multivariables of a single function. So maybe there is a way i can define a function that describes both the best fit line as well as the residuals. Like a 3D plot? Alternatively the lagrange multiplier seems to use 2 functions, so maybe I can do something like that. Any suggestions, attached is the code.

    yVals = zeros(1,10);
    yVals(1,1) = 2;
    yVals(1,2) = 5;
    yVals(1,3) = 6;
    yVals(1,4) = 9;
    yVals(1,5) = 14;
    yVals(1,6) = 18;
    yVals(1,7) = 25;
    yVals(1,8) = 21;
    yVals(1,9) = 23;
    yVals(1,10) = 27;
    xVals = 1:10;
    xVals = xVals';
    yVals = yVals/max(yVals); 
    yVals = yVals'
    scatter(xVals, yVals);
    hold on;
    [logitCoef,dev, stats] = glmfit(xVals,yVals,'binomial','logit');
    logitFit = glmval(logitCoef,xVals,'logit');
    figure(1);
    plot(xVals,logitFit,'g-','MarkerSize', 2 );xlabel('Distance'); ylabel('Value');
    legend('logit');
    A = stats.resid;
    M = mean(A);
    S = std(A);
    MAX = max(A);
    MIN = min(A);
    [residuals residualIndex] = sort(stats.resid);
    figure(2);
    PDF = normpdf(residuals, M, S);
    plot(residuals, PDF);xlabel('Residuals'); ylabel('Density');