Correlation regression lines between two parameters

Question

Amjad Iqbal 2021-11-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1581704-correlation-regression-lines-between-two-parameters

评论： Adam Danz 2021-11-9

采纳的回答： yanqi liu

Hello dear Researchers,

I have a query need your expertise to resolve.

I want to add correlation regression for two paramters for comparison purpose.

I have attached sub-plots which are scatter plots among two orientations.

Now purpose is to add correlation regression line i.e., one plot I added from a reference.

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Answer 1

yanqi liu 2021-11-9

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1581704-correlation-regression-lines-between-two-parameters#answer_826909

编辑：yanqi liu 2021-11-9

在 MATLAB Online 中打开

sir, may be upload some data, use lsqcurvefit、polyfit and so on to compute the coef

please check the follow code to get some information

for more information,you can read the book 《计算机视觉与深度学习实战》，Thank you！

clc; clear all; close all;

xdata = linspace(0,3);

ydata = 1.3*xdata + 0.05*randn(size(xdata));

lb = [];

ub = [];

fun = @(x,xdata)x(1)*xdata+x(2);

x0 = [0,0];

x = lsqcurvefit(fun,x0,xdata,ydata,lb,ub)

Local minimum found. Optimization completed because the size of the gradient is less than the value of the optimality tolerance.

x = 1×2

1.3048 -0.0023

plot(xdata,ydata,'ko',xdata,fun(x,xdata),'r-','LineWidth',2)

legend('Data','Fitted exponential')

title('Data and Fitted Curve')

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Amjad Iqbal 2021-11-9

I understand the fact linear fit. It seems in a good agreement by using both methods recommended by you and yanqi liu. Many many thanks once agian all, also @Image Analyst for your expertised suggestions. It really helps me. Final result is now up to the mark.

Adam Danz 2021-11-9

在 MATLAB Online 中打开

Yes, lsqcurvefit will provide the same results as polyfit or fitlm but the latter two are designed for linear models and do not require making initial guesses to the parameter values. I'm not trying to convince anyone to change their approach (or their selected answer). I'm arguing that lsqcurvefit is not the best tool for linear regression.

polyfit is much more efficient than lsqcurvefit (95x faster):

x = rand(1,100);
y = 4.8*x+2.1 +rand(1,100);
n = 5000;
tic
for i = 1:n
    opts = struct('Display','off');
    fun = @(x,xdata)x(1)*xdata+x(2);
    p = lsqcurvefit(fun, [0,0],x,y,[],[],opts);
end
T1 = toc % time in seconds
T1 = 13.2634
p
p = 1×2
    4.9170    2.4408
tic
for i = 1:n
    p2 = polyfit(x,y,1);
end
T2 = toc % time in seconds
T2 = 0.1386
p2 % same results
p2 = 1×2
    4.9170    2.4408
% Difference in time
T1/T2
ans = 95.7249

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Answer 2

Adam Danz 2021-11-8

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1581704-correlation-regression-lines-between-two-parameters#answer_826624

编辑：Adam Danz 2021-11-8

Common methods of adding a simple linear regression line

1. Use lsline which will add a regression line for each set of data in the plot.

2. Use polyfit (degree 1) & refline to compute the regression coefficients and plot the line.

3. Use fitlm & refline to compute the regression coefficients and plot the line.

Examples of #1 & #2

https://www.mathworks.com/matlabcentral/answers/421072-add-trend-line-to-a-scatter-plot#answer_338738

Example of #3

https://www.mathworks.com/matlabcentral/answers/277495-how-to-fit-linear-regression-models-to-a-scatter-graph#answer_492643

If you want to compute correlation, see corr or corrcoeff.

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Image Analyst 2021-11-9

在 MATLAB Online 中打开

Just to build on Adam's #3, this is how you'd do it:

% First get your model for fitted y values.
% Determine and say how well we did with our predictions, numerically, using several metrics like RMSE and MAE.
% Fit a linear model between predicted and true so we can get the R squared.
mdl = fitlm(actualy, fittedy)
rSquared = mdl.Rsquared.Ordinary;
rmse = mdl.RMSE;
mdlMSE = mdl.MSE;
residuals = abs(y - x);
% Find the mean and median absolute deviations of the elements in X.
meandev = mad(residuals,0,'all');
mediandev = mad(residuals,1,'all');
aveResidual = mean(residuals, 'omitnan');
maxResidual = max(residuals);
fprintf('The RMSE value is %.5f.\n', rmse);
fprintf('The  R^2 value is %.5f.\n', rSquared);
fprintf('The  MSE value is %.5f.\n', mdlMSE);
fprintf('The fitted y is different from the actual y by an average of %.2f units.\n', aveResidual);
fprintf('The fitted y is different from the actual y by an average of %.2f units.\n', meandev);
fprintf('The fitted y is different from the actual y by a median of %.2f units.\n', mediandev);
fprintf('The max residual from the average human grade is %.2f PSU.\n', maxResidual);

Amjad Iqbal 2021-11-9

Thanks a lot dear Adam Danz and Image Analyst

That's seems a proper way to add several numerical comparisons. It helps a lot.

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