Log(y)=A*f1(x) + B*f2(x)

f1(x)=1

f2(x)=log(x)

x	Y	Log(y)	F1	F1^2	F2(x)=log(x)	F2^2	F1*F2	Log(Y)*F1	Log(Y)*F2
2.5 3.5 5 6 7.5 10 12.5 15 17.5 20	7 5.5 3.9 3.5 3.1 2.8 2.6 2.4 2.3 2.3	0.845098040014257 0.740362689494244 0.591064607026499 0.544068044350276 0.491361693834273 0.447158031342219 0.414973347970818 0.380211241711606 0.361727836017593 0.361727836017593	1 1 1 1 1 1 1 1 1 1	1 1 1 1 1 1 1 1 1 1	0.397940008672038 0.544068044350276 0.698970004336019 0.778151250383644 0.8750612633917 1 1.09691001300806 1.17609125905568 1.24303804868629 1.30102999566398	0.158356250501901 0.296010036883134 0.488559066961494 0.605519368473628 0.765732214688678 1 1.20321157663733 1.38319064962718 1.54514359048183 1.69267904961742	0.397940008672038 0.544068044350276 0.698970004336019 0.778151250383644 0.8750612633917 1 1.09691001300806 1.17609125905568 1.24303804868629 1.30102999566398	0.845098040014257 0.740362689494244 0.591064607026499 0.544068044350276 0.491361693834273 0.447158031342219 0.414973347970818 0.380211241711606 0.361727836017593 0.361727836017593	0.336298321371996 0.402807680583044 0.41313643093618 0.423367229004951 0.429971584588904 0.447158031342219 0.455188420520668 0.447163117971726 0.449641463438823 0.47061876492551
				10		9.1384018038726	9.11125988754769	5.17775336777938	4.27535104468402

N=10

Solve for A,B:

A_matrix =

10 9.11125988754769

9.11125988754769 9.1384018038726

b =

5.17775336777938

4.27535104468402

Solve for x.

>> x=inv(A_matrix) * b

x =

0.999234664547637

-0.528422340830939

so, A= 0.999234664547637

B= -0.528422340830939

But A = log10(a)

A

So 10 = a

So a = 9.9823930184707

b= B = -0.528422340830939

so fitting power function is 9.982383 x ^(-0.5284223)

>> plot(x,Y,'o')

>> y=9.982383 * x .^(-0.5284223);

>> y'

6.15111510562453

5.14916183120815

4.26464506030034

3.87294879566411

3.44217022210418

2.95673177595292

2.62786176913272

2.38649968051915

2.19981016237795

2.04993913240556

>> hold on;

>> plot(x,y,'r');

>> legend('observation','power fit');