Real issue with the Matlab user interface for most of the Curve Fitting and Statistics Toolbox stuff -- frequently it is very difficult to get the information back out in human-legible format.
AFAIK, the only way to get the model associated with the numbers is by actually fitting the linear model object and getting the info from it...afaict, while rstool has to have built it internally, there's no way to actually export it from the GUI.
lm=fitlm(X,Y,'purequadratic');
will leave you with the linear model object lm and in it are
>> lm.CoefficientNames
ans =
1×7 cell array
{'(Intercept)'} {'x1'} {'x2'} {'x3'} {'x1^2'} {'x2^2'} {'x3^2'}
>> lm.Formula
ans =
y ~ 1 + x1 + x2 + x3 + x1^2 + x2^2 + x3^2
>>
>> lm.disp
Linear regression model:
y ~ 1 + x1 + x2 + x3 + x1^2 + x2^2 + x3^2
Estimated Coefficients:
Estimate SE tStat pValue
__________ __________ ________ __________
(Intercept) 68.813 11.517 5.9749 5.0652e-08
x1 -0.0089158 0.0062355 -1.4299 0.15638
x2 -0.26388 0.10866 -2.4285 0.017246
x3 -0.43451 0.97939 -0.44365 0.65841
x1^2 7.5652e-07 9.3838e-07 0.8062 0.42235
x2^2 0.00062257 0.00033999 1.8311 0.070547
x3^2 0.0039153 0.030748 0.12733 0.89897
Number of observations: 93, Error degrees of freedom: 86
Root Mean Squared Error: 3.94
R-squared: 0.777, Adjusted R-Squared 0.762
F-statistic vs. constant model: 50, p-value = 5.51e-26
and the coefficients will be the same as those computed independently and returned in regstats.
Having the .disp output table is indeed useful, but that there are all these other methods that do bits and pieces and give only those is very redundant and confusing to use -- and that the GUIs don't export the whole model but just bits 'n pieces in disjointed fashion has always been and remains mind-boggling as to "why?" they were so designed/implemented.
