How fitrlinear determines Lambda when 10fold cross-validation is on?

Here is my code and my questions are at the end of the code.

%% Predict Values Using Ridge Regression

% Predict miles per gallon (MPG) values using ridge regression.

%

% Load the |carbig| data set.

clearvars;

load carbig

X = [Acceleration Weight Displacement Horsepower];

y = MPG;

% remove NaN entries in y

idxNaN=find(isnan(y));

X(idxNaN,:)=[];

y(idxNaN)=[];

% remove NaN entries in remaining X

[r, c] = find(isnan(X));

idxNaN=unique(c);

X(idxNaN,:)=[];

y(idxNaN)=[];

%%

% Split the data into training and test sets.

n = length(y);

rng('default') % For reproducibility

c = cvpartition(n,'HoldOut',0.3);

idxTrain = training(c,1);

idxTest = ~idxTrain;

%%

%Predict miles per gallon (MPG) values using ridge regression

mdl2=fitrlinear(X(idxTrain,:),y(idxTrain),'Learner','leastsquares','Regularization','ridge','CrossVal','on','KFold',10)

% examine one CV model

mdl2.Trained{2}

% If I change the number in {}, I get slightly different Lambda. How is it

% determined? If it's determined by the cross-validation, then test error

% can't be derived from yhat.

% I assume that I cannot use predict function on the test data based on my

% understanding.

% yhat2=predict(mdl2,X(idxTest,:));

% what is the best way to train a model using the entire training data

% (i.e., idxTrain) based on the cross-validation models?

[Ive J]

"If I change the number in {}, I get slightly different Lambda. How is it determined?"

I suggest reading the doc, especially the "Find Good Lasso Penalty Using Cross-Validation" example. Your mdl2 contains 10 models from 10-fold CV, each was run on different chunk (non-overlapping) of data, so of course, they're different.

[Peter He]

Now I got it. Thanks!