# Questions tagged [least-squares]

Questions about (linear or nonlinear) least-squares, an estimation method used in statistics, signal processing and elsewhere.

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### OLS assumption, full rank of matrix X

One of the OLS assumptions concerning the X-matrix (with a constant) is that the columns $(1, x_{i1}, · · · , x_{iK})$ are not linearly dependent. This looks intuitive to me, because of the dummy-...
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### Why is the norm the last $m - n$ elements of $Q^Tb$ in least squares?

The answer to this question says that If you're solving the Least Squares problem minimizing $||Ax - b||_2$ then the error, or residual, is the norm of the last m-n elements of the vector $Q^Tb$. ...
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### Matrix equation solving involving vectorization and Kronecker product

I am looking an analytical solution for a least-squares solution of the following equation for $X$: $(A \ (I_{J} \otimes X)) \ \textrm{vec}(X) = b,$ where $A \in \mathbb{R}^{I\times J^2}$, $I_J$ is ...
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### Can I use the least square fitting to obtain a real solution of a complex equation?

I am trying to solve the following equation: $$\omega^{1/3} = p_l \omega_l^{1/3} + (1-p_l)\omega_{\omega}^{1/3} \tag{1}$$ $\omega$, $\omega_l$, and $\omega_w$ are complex numbers and $p_l$ must be ...