AddLinearModel and CompactLinearModel class objects along with introduction of fitlm and stepwiselm

[Pasta-coder]

This PR introduces a major overhaul and implementation LinearModel and CompactLinearModel class objects along with introduction of fitlm . it also introduces stepwiselm but it's unusable .

textinfos , demos , BISTs are added but are not sufficient (as per statistics package convention)

related to #266 . (if not mergeable then it can definitely be used as a reference pr)

few successful manual tests are (while the entire testsuite against which i am testing can be found in the file final_test.md) -

rng(0);
n = 100;
x1 = randn(n, 1);
x2 = randn(n, 1);
x3 = randn(n, 1);
catVar = randi([1, 3], n, 1);  % 3 levels
y = 2 + 1.5*x1 - 0.7*x2 + 0.3*(catVar==2) + 0.6*(catVar==3) + 0.5*randn(n,1);
tbl = table(x1, x2, x3, categorical(catVar, 1:3, {'A','B','C'}), y, ...
            'VariableNames', {'x1','x2','x3','Color','y'});

[g, gn] = grp2idx({'Red','Blue','Red','Green'})

[g, gn] = grp2idx(categorical({'Red','Blue','Red','Green'}))

[g, gn] = grp2idx([1, 2, NaN, 1, 2])

[g, gn] = grp2idx([])

[g, gn] = grp2idx(ones(10,1))


D = dummyvar({'Red','Blue','Red','Green'})

D = dummyvar(categorical({'Red','Blue','Red','Green'}))

D = dummyvar([1, 2, 1, 3])

D = dummyvar([1,2; 1,3; 2,1; 2,3])

D_ref = dummyvar([1,2,1,3])
D_full = dummyvar([1,2,1,3], 'full')




mdl = fitlm(tbl, 'y ~ x1 + x2')

mdl = fitlm(tbl, 'y ~ 1')

mdl = fitlm(tbl, 'y ~ x1 + x2 - 1')

mdl = fitlm(tbl, 'y ~ x1*x2')

mdl = fitlm(tbl, 'y ~ x1:x2')

mdl = fitlm(tbl, 'y ~ x1/Color')   % Color is categorical

mdl = fitlm(tbl, 'y ~ (x1 + x2)^2')

mdl = fitlm(tbl, 'y ~ x1^3')

mdl = fitlm(tbl, 'y ~ x1^2 - x1')

mdl = fitlm(tbl, 'y ~ x1 + C(Color)')

mdl = fitlm(tbl, 'y ~ x1 + x2 + x3')

mdl = fitlm(tbl, 'y ~ Color')

mdl = fitlm(tbl, 'y ~ Color * x1')

mdl = fitlm(tbl, 'y ~ x1 + Color')

mdl = fitlm(tbl, 'y ~ x1 + catVar', 'CategoricalVars', 'catVar')

mdl = fitlm(tbl, 'y ~ Color', 'DummyVarCoding', 'full')

mdl = fitlm(tbl, 'y ~ x1 + x2 + Color');




compactMdl = compact(mdl)

mdl.Coefficients

mdl.Rsquared

mdl.RMSE

mdl.DFE

mdl.Formula

mdl.NumCoefficients

mdl.NumEstimatedCoefficients

mdl.MSE

mdl.SSE
mdl.SSR
mdl.SST

mdl.ModelCriterion

mdl.CoefficientCovariance




mdl = fitlm(tbl, 'y ~ x1 + x2 + Color');

Xnew = [1.2, 0.5, categorical(2, 1:3, {'A','B','C'})];
ypred = predict(mdl, Xnew)

[ypred, yci] = predict(mdl, Xnew)

[ypred, yci] = predict(mdl, Xnew, 'Alpha', 0.01)

[ypred, yci] = predict(mdl, Xnew, 'Prediction', 'observation')
[ypred, yci] = predict(mdl, Xnew, 'Prediction', 'curve')

[ypred, yci] = predict(mdl, Xnew, 'Simultaneous', true)

Xnew_tbl = table(1.2, 0.5, categorical(2, 1:3, {'A','B','C'}), ...
                 'VariableNames', {'x1','x2','Color'});
ypred = predict(mdl, Xnew_tbl)

ypred = feval(mdl, Xnew)




mdl = fitlm(tbl, 'y ~ x1 + x2 + Color')
disp(mdl)

mdl = fitlm(tbl, 'y ~ x1 + x2 - 1')
disp(mdl)

X_rd = randn(100,2);
X_rd(:,3) = X_rd(:,1) + X_rd(:,2);
y_rd = X_rd * [1; -1; 0.5] + 0.1*randn(100,1);
mdl_rd = fitlm(X_rd, y_rd)
disp(mdl_rd)

mdl_rob = fitlm(tbl, 'y ~ x1 + x2', 'RobustOpts', 'on')
disp(mdl_rob)






mdl = fitlm(tbl, 'y ~ x1 + x2 + Color');

ci = coefCI(mdl)

p = coefTest(mdl)