Why do i get tstat Inf after a linear regression?

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

R-squared: 1, Adjusted R-Squared: NaN

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?

Answer 1

[the cyclist]

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.