# Tagged Questions

Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.

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### Interpolation and mapping between scattered vectors in two unequally dimensioned spaces

Imagine two spaces: An ‘input’ space with dimension $m$. An ‘output’ space with dimension $n$. $m \geq n$ There are points in each of these spaces defined such that some characteristic is defined....
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### How estimate straight line using linear regression with some outliers

I have a data set ...
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### Linear regression using gradient descent: is the whole weight vector updated with the same number?

I'm using gradient descent with mean squared error as error function to do linear regression. Take a look at the equations first. As you can see in eq.1, the prediction is done with a bias term b ...
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### Why the identity $P_X=P_XZ(Z'P_XZ)^{-1}Z'P_X$ with $P_X=X(X'X)^{-1}X'$?

Suppose $X$ and $Z$ are matrices such that $(X,Z)$ and $P_XZ$ both have full column ranks. Here, $P_X=X(X'X)^{-1}X'$. Consider a regression model $$P_Xy=P_XZ\zeta+v\tag{A}$$ where OLS is used to ...
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### Sum of component projection matrices

Show that if $X$ $=$ [$X_1$ $X_2]$ and $X_1'X_2 = 0$, then $P = P_1 + P_2$, where $P$ is defined as $X(X'X)^{-1}X'$, the projection matrix. Don't quite know where to start. I tried evaluating it by ...
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### Variance in the sum of batch-correlated residuals in a regression

I am looking at a regression model of the following form: $Y=intercept+\beta_{Yf.n}X_f+\beta_{Yn.f}X_n +error$ where $X_f$ and $X_n$ are predictors. A value for $Y$ will be sampled from the ...