Power Regression - Matlab vs Excel

Hi Everyone The following code:

x  = [1 2 3 4 5 6 7 8 9 10]';
y  = [2 1 3 5 2 1 3 4 7 9]';

f = fit(x,y,'power1')

Will give

    General model Power1:
     f(x) = a*x^b
     Coefficients (with 95% confidence bounds):
       a =      0.2774  (-0.4832, 1.038)
       b =       1.425  (0.1224, 2.728)

But in Excel, the same data gives us:

y = 1.2519*x ^0.5611
so:
a = 1.2519
b = 0.5611

Why are are both power regression models so different in Matlab and Excel? How can i get the same Excel results in Matlab?

Answer 1

[dpb]

Didn't show your work in Excel so can't judge what went on there, but I don't know why you'd choose that model over the Matlab result after

>> x  = [1 2 3 4 5 6 7 8 9 10]';
y  = [2 1 3 5 2 1 3 4 7 9]';
>> yhM=0.2774*x.^1.425;  % Matlab yhat
>> yhE=1.2519*x.^0.5611; % and Excel...
>> [var(y-yhM) var(y-yhE)]  % fitted residual error
ans =
  3.1309    4.2505
>> plot(x,[y yhM yhE])
>> legend('Data','Matlab','Excel','location','northwest')
>>

The Matlab fitted results has a residual of roughly 30% smaller (albeit given the noise in the input y vector, neither is all that great a fit) and clearly follows the gross overall shape more nearly than does the Excel result.

ADDENDUM After thinking about the results from Excel w/ the power being roughly square root and hence the shape being convex, it came to me that I wonder if transposed the x,y vectors in Excel--so,

>> fit(y,x,'power1')
ans = 
   General model Power1:
   ans(x) = a*x^b
   Coefficients (with 95% confidence bounds):
     a =       2.768  (0.5397, 4.996)
     b =      0.5615  (0.08159, 1.041)
>>

Indeed, the exponents are almost identical so I'm betting that's what went wrong in Excel; you didn't set up the input correctly. Not sure what might've been the actual values such that the multiplier coefficient a is roughly half the size but likely didn't have the data there intended, either.

Answer 2

[Image Analyst]

Try fitnlm() instead.