# Need help with Least Squares Estimator

I am interested in a One-Way ANOVA model:

I wrote the model out as and got $$X$$ as a matrix that looks like:

Which is rank 2 (6 x 4 Matrix, so not full rank)

Does the least squares estimator for β = (µ, α1, α2)^T exist? If it exists, is it unique? Why?

• I see three parameters ($\alpha_1, \alpha_2,\mu$) in your model but four columns in $X.$ What does that extra column represent?? – whuber Feb 11 at 15:35