How do I validate multiple linear regression with validation data?

I used the following code:

if true
  % code
%b=regress(y,X) %returns a p-by-1 vector b of coefficient estimates for a multilinear regression of the responses in y on the predictors in X. X is an n-by-p matrix of p predictors at each of n observations. y is an n-by-1 vector of observed responses.
x1 = TrainingBootstrap;
x2 = TrainingDimension;
x3 = TrainingTNSPEC;
y = TrainingMatrix(:,4);

X = [ones(size(x1)) x1 x2 x3 x1.*x2 x1.*x3 x2.*x3 x1.*x2.*x3]; b = regress(y,X) % Removes NaN data end

I got the following answer: b =

   1.0e+03 *

    1.1847
   -0.0000
   -0.0000
   -0.0000
    0.0000
   -0.0000
    0.0000
   -0.0000

How do I test goodness of fit of that line to validation data?

Answer 1

[Mudambi Srivatsa]

One way to verify the goodness of fit is by plotting the fit using validation data. Refer to the following link for plotting the "regress" fit:

https://www.mathworks.com/help/stats/regress.html#btzaffj

In this case, you might have to manually compute the goodness of fit statistics like R-square, adjusted R square, RMSE and so on using the generated model. However, if you would like MATLAB to auto-generate goodness of fit statistics, consider using 'fitlm' to fit the model to your data.

Refer to the following links for more information:

 https://www.mathworks.com/help/stats/fitlm.html
 https://www.mathworks.com/help/stats/linear-regression-workflow.html