model spec 'polyijk' o=in fitlm does not work as per MATLAB documentation?

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Jerry Chen 2024-3-22

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评论： Jerry Chen 2024-3-22

Hi, I am trying to use 'polyijk' model spec to specify my linear regression model complexity when using fitlm, but i dont seem to be getting what the documentation suggests i should. As per documentation: 'poly13' has an intercept and x1, x2, x2^2, x2^3, x1*x2, and x1*x2^2 terms. but when i try it, the terms i get are: 1 + x1*x2 + x2^2 + x1:(x2^2) + x2^3. so somehow it is missing the x1 and x2 terms.

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Answer 1

the cyclist 2024-3-22

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编辑：the cyclist 2024-3-22

在 MATLAB Online 中打开

I think you are just misinterpreting the Wilkinson notation of the model spec in the output.

x1*x2 % note the * for interaction, which includes lower-order terms

is short-hand for

x1 + x2 + x1:x2 % note the : for interaction, which does NOT include lower-order terms

Here is an example. Note that all the terms you expect are in the table of estimated coefficients.

load carsmall
X1 = Acceleration;
X2 = Displacement;
X = [X1,X2];
y = Weight;
mdl = fitlm(X,y,"poly13")
mdl = 
Linear regression model:
    y ~ 1 + x1*x2 + x2^2 + x1:(x2^2) + x2^3

Estimated Coefficients:
                    Estimate        SE         tStat      pValue 
                   __________    _________    ________    _______

    (Intercept)        446.97         1693     0.26401    0.79236
    x1                 41.114       81.832     0.50242    0.61656
    x2                  14.69       21.387     0.68685    0.49388
    x1:x2            -0.18481      0.92831    -0.19908    0.84263
    x2^2            -0.026093     0.068886    -0.37878    0.70571
    x1:x2^2         0.0010263    0.0021616     0.47479    0.63605
    x2^3           8.6477e-06    5.822e-05     0.14853    0.88224


Number of observations: 100, Error degrees of freedom: 93
Root Mean Squared Error: 315
R-squared: 0.857,  Adjusted R-Squared: 0.848
F-statistic vs. constant model: 92.9, p-value = 4.46e-37