A multiple regression with two independent variables

Question about liner or non linear experimental data fitting with two independent and dependent variable.

I have this eq: Can you perform a multiple regression with two independent variablesa multiple regression with two independent variables but one of them constant ? for example I have this data

How I can get a good fiting for this data in two variables (theta,Length)?

 
Angle (Theta)     Length ratio (%)             Force (kn)                                    
0                      1                          52.1
0.174444444            1                          52.9
0.261666667            1                          53.3
0.348888889            1                          55.5
0.436111111            1                          58.1

[dpb]

Impossible to fit the Length variable when there's no variation- You have a conditional relationship with Angle you can fit but it's only valid for L=1.

[Sulaymon Eshkabilov]

Ibrahim,

Probably in your problem L changes and its change is 1% in each step/iteration. If this is the case, then get the initial value of L and compute its evolving values: L1 = L0+0.01*L0; L2 = L1+0.01*L1, L3 = L2+0.01*L2 .... Then it is feasible to perform a curve fit with cftool() w.r.t. theta and L.

Good luck.

[IBRAHIM BUMADIAN]

Thank you so much

I am still have some confuse.

Could you please give me more details?

[dpb]

You need to give us more details instead...you say one variable is a constant but perhaps as @SE notes (and I didn't) the actual length isn't constant but what you've given is a percentage difference between length observations? IF that is so, then compute the actual Length in whatever units are convenient but also as noted, you've not provided a reference L from which to start -- and is the first observation 1% greater than that value or the initial value?

Very difficult data set to interpret without more information.

IF one assumes each L is 1% greater than the previous and the first is actually the initial length, then

L=L0*(1+r).^[0:numel(L)-1];

where L0 is that reference length and r is the L ratio value converted from per cent to fraction (0.01)

THEN you would at least have two variables to try to fit but the two are going to be colinear and essentially surrogates for each other if not identically linear combinations leading to a singular X'X

[IBRAHIM BUMADIAN]

I am looking to do that:

L will be change from (0 to 1). with incresing 1%

Theta will be change from (0 to 0.436111111), with incresing 1%

to fiiting this eq: F = sin(A*theta)+B*L+C*theta*L*sin(D*L*theta).

For expermintal work that I did:

Angle (Theta) Length ratio (%) Force (kn)

0 0 37.4

0 1 52.1

0.174444444 1 52.9

0.261666667 1 53.3

0.348888889 1 55.5

0.436111111 1 58.1

[dpb]

A 1% increase of L=0 is still 0.

The response variable appears quite discontinuous in behavior between the first two observations -- that implies a 1% L increase made a 40% increase in response but the next four increases were nearly negligible or has a negative correlation with theta, maybe.

You're also more than a little short of data only six observations to fit four parameters--that leaves only two DOF when done.

[IBRAHIM BUMADIAN]

Thank you so much.

This mean I have to do more expermintal work to get a good fiting for L and Theta.

[dpb]

Still didn't answer the two question;

1. What's the first L value as 1% increase in zero is still zero, and
2. What's up with the above observation regarding sensitivity w/ the two variables?

[IBRAHIM BUMADIAN]

The first value of L is 0.1.

The observation when the theta is increseing and L is incresing the Force increseing.

For example: at theta 0.43 and L 1.0 the F= 58.1 Kn.

Also, the mix force should be 60 kn no more that and the min force 37.4 at theta 0 and L =1.

[dpb]

Still doesn't make any sense, but from the best we can tell from what you've described--

L=0.1*[1+0.01].^[0:5]  % initial L==0.1; 1% growth between observations
th=[0 0 .1744444444 .2616666666666 .348888888888 .43611111111];
X=[th;L].';         % design matrix in fitnlm input form by column
F=[37.4 52.1 52.9 53.3 55.5 58.1].';  % response variable
% define the functional form
f=@(b,x) sin(b(1)*x(:,1))+b(2)*x(:,2)+b(3)*x(:,1).*x(:,2).*sin(b(4)*x(:,1).*x(:,2));
% now try to fit the model
>> mdl=fitnlm([th;L].',F,f,ones(4,1))
mdl = 
Nonlinear regression model:
    y ~ sin(b1*x1) + b2*x2 + b3*x1*x2*sin(b4*x1*x2)

Estimated Coefficients:
          Estimate      SE       tStat       pValue  
          ________    ______    ________    _________
    b1     47.365     27.394      1.7291      0.22594
    b2     481.71     43.181      11.156    0.0079398
    b3    -177.03      249.3    -0.71012      0.55126
    b4    -563.44     33.912     -16.615     0.003603

Number of observations: 6, Error degrees of freedom: 2
Root Mean Squared Error: 8.76
R-Squared: 0.419,  Adjusted R-Squared -0.452
F-statistic vs. zero model: 52.4, p-value = 0.0188
>> 
% and see what it looks like
>> [F predict(mdl,X) predict(mdl,X)-F]
ans =
   37.4000   48.1714   10.7714
   52.1000   48.6531   -3.4469
   52.9000   48.2740   -4.6260
   53.3000   51.8218   -1.4782
   55.5000   55.8213    0.3213
   58.1000   56.7851   -1.3149
>> 

As predicted, the overall fit is significant; but the two coefficients b(1) (A) and b(3) (C) are barely significant and note R-sq <0.5 and Adjusted R-sq < 0 -- badly conditioned system. Overall the fit is marginal for applicability/ accuracy in fitting the observed data with the functional form of the desired expression.

This could be bad data for the right model or the wrong model of choice for good data or simply that the explanation is lacking and we don't understand what the data/model really are and are misusing one or both. Particularly this length variable is yet a deep mystery as to what it really is and how to code it--the above was just a wild guess based on Sulaymon's observation/hypothesis of a fractional increase.

Going ahead anyway, as noted from looking at the input data, the first point is an outlier in the model can't fit the gross difference at theta=0.

The model itself looks peculiar, but that's the form as you wrote it.

There's still quite a lot lacking in the explanation here to make any real sense of the problem.