LinearModelFit
[m, f, x]m = LinearModelFit[{{2, 1}, {3, 4}, {5, 3}, {7, 6}}, x, x];
m["BasisFunctions"]
m["BestFit"]
m["BestFitParameters"]
m["DesignMatrix"]
m["Function"]
m["Response"]
m["FitResiduals"]
m = LinearModelFit[{{2, 2, 1}, {3, 2, 4}, {5, 6, 3}, {7, 9, 6}}, {Sin[x], Cos[y]}, {x, y}];
m["BasisFunctions"]
m["Function"]
m = LinearModelFit[{{{1, 4}, {1, 5}, {1, 7}}, {1, 2, 3}}];
m["BasisFunctions"]
m["FitResiduals"]