Why do EXCEL and MATLAB obtain different coefficients of pure quadratic regression? Different algorithm？

I was doing pure quadratic regression for statistics in EXCEL and MATLAB respectively. Basically, there are two input variables, with one group of values each. There are eight output variables, with one group of values each. So, later you will see there are eight rows of coefficients, each row indicates coefficients for one output variable.

I found both EXCEL and MATLAB obtain similar coefficients, but slightly different. I used "Data Analysis" in EXCEL, and "stats = regstats(reg,X,'purequadratic')" in MATLAB. in MATLAB I used "disp" function to show coefficient.

1) I would like to know why are they different?

2) If import statistics of two input variables into regressed functions, I found that there is a huge difference, when using MATLAB coefficients, between predicted values and initial values. But EXCEL coefficients function matches very well with initial output values.

I don't think MATLAB will make mistakes, but who can tell me why?

Thank you so much.

Below are initial statistics, with two rows of input, and eight rows of output.

Input  0.1  0.1  0.1  0.08  0.12;
Input  75  100  125  100  100;
Oouput  1.00   1.00   1.00   1.00   1.00; 
Oouput  1.04   0.98   1.34   1.05   1.11 ;
Oouput  1.19   1.07   1.54   1.09   1.86 ;
Oouput  1.28   1.13   1.94   1.55   2.52 ;
Oouput  1.47   1.41   2.67   1.47   3.64 ;
Oouput  1.63   2.39   3.37   1.55   5.01 ;
Oouput  1.64   3.14   4.26   1.86   6.65 ;
Oouput  1.97   4.20   5.28   2.31   8.57 ;

Below are coefficients from MATLAB.

0.0000   0.0000   0.0000   0.0000   1.0000 ;
0.0000   -0.0600   250.0000   -48.5000   6.0900 ;
0.0000   -0.0900   1012.5000   -183.2500   13.2900 ;
0.0000   -0.1400   2262.5000   -428.2500   27.6900 ;
0.0000   -0.1900   2862.5000   -518.2500   32.7700 ;
0.0000   0.0000   2225.0000   -358.5000   14.2700 ;
0.0000   0.1100   2787.5000   -437.7500   10.7600 ;
0.0000   0.2500   3100.0000   -463.5000   3.7300 ;

Below are coefficients from EXCEL.

0  0  0  0  1;
0.000328417  -0.059704055  243.5669198  -47.21194018  5.955417092;
0.000471708  -0.087383325  1009.858681  -182.7702993  13.267276;
0.000762784  -0.139532918  2250.695149  -425.7704731  27.5291594;
0.001047444  -0.185498787  2856.424299  -516.8874342  32.61387372;
0.000168824  0.00106616  2212.027358  -355.8364858  14.06052536;
-0.000301934  0.112609147  2784.833039  -437.1320185  10.7621216;
-0.00092363  0.251040732  3090.051207  -461.5862656  3.594040508;

[dpb]

What kind of model has 37(!) polynomial coefficients????

As for differences in estimated coefficients, how did you get data into each program to compare--do both start with identical data? How did you do the estimation in each?

For using the coefficients from Matlab, how did you do the evaluation and were these the coefficients in memory or did you try to export them as text as above?

Too many uncertainties to have any specific answers...

[Daixin]

Hi, sorry for too many uncertainties in my question, haha. I will update it right now. Please see it later. Thank you.

Answer 1

[Walter Roberson]

The coefficients are not as different as it might appear at first.

At the MATLAB prompt, give the command

format g

before displaying the coefficients.

[Muthu Annamalai]

Apples to Oranges. Short to Long. How cleverly deceiving!

[Daixin]

Hi Walter,

I don't mean the difference of how it appear. I mean the difference of values. Thank you all the same.