Hi. Just some additional ideas:

data={{2,5},{4,9},{5,16},{7,28}};

LinearModelFit[data,x,x]//Normal

-6.615384615384621+4.692307692307693 x

Full Precision:

PolynomialFit[data[[All,1]],data[[All,-1]],2]

{-(86/13),61/13}

%//N

{-6.615384615384615,4.692307692307693}

Below Code Reference:

http://mathworld.wolfram.com/notebooks/Statistics/LeastSquaresFitting.nb

PolynomialFit[x_List,y_List,n_]:=Module[
{X,i,k},X=Table[Table[x[[i]]^(k-1),{k,n}],{i,Length[x]}];
LinearSolve[Transpose[X].X,Transpose[X].y]
]

HTH Dana

Hi Frank, Thanks for your help, your suggestion worked fine. Now I am having another issue, in this data fitting I am getting the unexpected values of of parameters a & b and now want to fix the domain of variables. How can I do it in FindFit function.

So, i want to fit (X, Y) data set (2, 5), (4, 9) (5, 16), (7, 28) to the equation Y = aX+b to determine the values of a and b but with condition that they lie in the range a1 < a < a2 and b1 < b < b2.

Thanks once again..