# Why do i get tstat Inf after a linear regression?

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Jefferson Sola de Haro on 6 Nov 2020
Answered: the cyclist on 6 Nov 2020
Hellow folks,
I saw that the comunity is very active so i hope someone can help me. I am writing down a simple function to estimate and evaluate the beta values for a regression, as well as its respective ANOVA.
If i run my Constraints and Effects algorithm it all works fine, but once i do a simple regression using fitlm(), i cannot evaluate the ANOVA, here is my code and what i get:
Y = [33.2 31.2
4.6 9.6
40.6 39.4
162.4 158.6];
X = [-1 -1
1 -1
-1 1
1 1 ];
Y_mean = mean(Y,2) ;
mdl = fitlm(X,Y_mean,"interactions")
mdl = Linear regression model:
y ~ 1 + x1*x2
Estimated Coefficients:
Estimate SE tStat pValue
________ __ _____ ______
(Intercept) 59.95 0 Inf NaN
x1 23.85 0 Inf NaN
x2 40.3 0 Inf NaN
x1:x2 36.4 0 Inf NaN
Number of observations: 4, Error degrees of freedom: 0
F-statistic vs. constant model: NaN, p-value = NaN
With such result, of course once i call anova(mdl) the answer will be bad.
What could be the root cause?

the cyclist on 6 Nov 2020
The root cause is that your model is "perfect". The model is effectively
y = b1 + b2*x1 + b3*x2 + b4*x1*x2
which means you have 4 free parameters to fit 4 equations.
The estimated coefficients will perfectly fit this sample of (X, Y_mean) data. In this case, the t-statistic is infinite. Off the top of my head, I think the p-values probably is (or "approaches") 0 in this case, but again it is not very meaningful for a perfect fit.