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How can I calculate SAE J1269 least squre method in matlab? (multiple variable function)

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the equation of RR in J1269 is below,
RR = A0 + (A1 * Load) + (A2 / Infl) + (A3 * (Load / Infl)) + (A4 * (Load / (Infl * Infl))))
and I have 6 test result. for load/infl/RR
in SAE J 1269, the variable (A0~4) should be performed by least square method,
(I dont' know why i have to use least square method becaue the polynomial is 6, and variable is 5 (A0~4)
please let me know the code to calculate least square method for this issue
(in matlab document, there can't make the formula like above.)

Accepted Answer

Varun
Varun on 20 Dec 2023
Hi,
While I am unsure what kind of data you are working with, I assume that you have 6 values each for the variables “Load”, “Infl”, and “RR” and need help with framing a matrix equation for the equation you have mentioned.
| Load (N) | Infl (psi) | RR (N) |
|----------|------------|--------|
| 3000 | 35 | 10.5 |
| 3200 | 33 | 10.8 |
| 3100 | 30 | 11.0 |
| 3300 | 32 | 11.2 |
| 3400 | 34 | 11.5 |
| 3500 | 36 | 11.7 |
You can use these variables to frame the required equation as follows:
% Test data
Load = [3000, 3200, 3100, 3300, 3400, 3500]; % Load in Newtons
Infl = [35, 33, 30, 32, 34, 36]; % Inflation in psi
RR = [10.5, 10.8, 11.0, 11.2, 11.5, 11.7]; % Rolling Resistance in Newtons
% Construct the design matrix for the least squares method
X = [ones(size(Load)), ...% Column for A0
Load, ... % Column for A1
1 ./ Infl, ... % Column for A2
Load ./ Infl, ... % Column for A3
Load ./ (Infl .* Infl)]; % Column for A4
After this, you can all the least squares method using the function “lsqr” as seen in the following documentation: https://www.mathworks.com/help/matlab/ref/lsqr.html. I'd be able to help more if I had more idea about the kind of data you were working with, but hope this helps!

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