# 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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### Understanding error estimate for least squares fit.

I'm reading the following paper link. In it, on page $7011$, the authors apply linear least squares to a system in the form $${\bf A}x = b$$ Where $\bf A$ has $M$ rows and $N$ columns, they state an ...
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### How to optimize the number of data points used to interpolate a fit over an unknown polynomial (with noisy data)?

I'm trying to find the coefficients of an unknown polynomial given that I can choose to extract a coordinate at any point but at a cost. The cost goes up as more points are chosen. When a coordinate ...
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### Find the expected value of the sum of squares of the residuals.

Question: In $\mathbb{R}^2$, it is given $n$ points $(x_i,Y_i)$, where $x_i$ are known constants, and given independent random variables $Y_i\sim U(l_i,r_i)$. Fit a straight line through these $n$ ...
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### Does this proof that $\min_P ||APx||$ is NP-complete (for general $n\times n$ $A$, permutations $P$, and a vector $x$) work?

Let $A$ be some $n×n$ matrix, and $x$ be a column vector of length $n$. I am looking to find the permutation matrix $P$ of size $n×n$ that minimizes the vector norm of $APx$. In a previous question ...
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### A corollary of Frisch-Waugh-Lowell Theorem

The formulation is just a special case of FWL. Say we have a partitioned regression, $Y=X_1\beta_1+X_2\beta_2+\epsilon$ but with $X_2$ be $n\times 1$ and $\beta_2$ a constant. Let $b_1,b_2$ be two OLS ...
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### Estimating parameters in a system of ODE's from data.

I'm trying to model the COVID-19 pandemic in Madrid during the first wave, to model the data I'm using the SIR model. The SIR model stands for suceptible, infected and recovered. It is a compartmental ...
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