MATLAB: Obtaining the variance-covariance matrix

MATLABmatricesmatrix

i wanted to ask if by doing the result will be equal to E as in the equation shown

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That appears to me to be the covariance matrix of the parameters of the linear regression, so in a word, No. The cov function will not do what you want in that situation.

If you have the Statistics and Machine Learning Toolbox, use the LinearModel (specifically: fitlm) to return the CoefficientCovariance matrix for you. It will also do all the necessary calculations to estimate the confidence intervals on the parameters, so there is no need for you to code them separately.

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MATLAB: Estimate confidence intervals after regress!

The ‘BINT’ matrix contains the parameter confidence intervals.

If you want both parameter and prediction confidence intervals, use fitlm:

x = (1:10)';                                        % Create Data

y = 1.5 + 2.3*x + 1.5*randn(size(x));               % Create Data
mdl = fitlm(x, y);                                  % Fit Data
B = mdl.Coefficients.Estimate;                      % Coefficients
CI = coefCI(mdl);                                   % Coefficient Confidence Intervals
[Ypred,YCI] = predict(mdl, x);                      % Fitted Regression Line & Confidence Intervals
figure(1)
plot(x, y, 'pg')
hold on
plot(x, Ypred,'-r',    x, YCI, '--r')
hold off
grid

MATLAB: 95% confidence intervalsof regression line!

I like regress, even with its limitations. However, it would probably be best for you to re-run your regression with the fitlm (link) function, then use the predict (link) function to calculate the confidence intervals. The ‘Xnew’ in the documentation are your existing independent variable values.

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Related Solutions

MATLAB: Estimate confidence intervals after regress!

MATLAB: 95% confidence intervalsof regression line!

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