# Questions tagged [regression]

This tag is for questions on (linear or nonlinear) regression, which is a way of describing how one variable, the outcome, is numerically related to predictor variables. The dependent variable is also referred to as $~Y~$, dependent or response and is plotted on the vertical axis (ordinate) of a graph.

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### What is the difference between regression and classification?

What is the difference between regression and classification, when we try to generate output for a training data set $x$?
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### Derivation of the formula for Ordinary Least Squares Linear Regression

How was the formula for Ordinary Least Squares Linear Regression arrived at? Note I am not only looking for the proof, but also the derivation. Where did the formula come from?
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### Best fit ellipsoid

Given a collection of points $P \subset \mathbb R^3$, a crude characterization of the "shape" of $P$ is sometimes given by the principal components. We construct a covariance matrix, e.g., if $P$ is ...
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### Polynomial fitting where polynomial must be monotonically increasing

Given a set of monotonically increasing data points (in 2D), I want to fit a polynomial to the data which is monotonically increasing over the domain of the data. If the highest x value is 100, I don'...
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### Method of Least Squares-Why is it preferred? [duplicate]

Possible Duplicate: Why do we use a Least Squares fit? To find the normal equations for derivation of the regression line we use the method of least squares, We want to make the error smallest ...
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### Assumption of a Random error term in a regression

In one of my recent statistics courses, our teacher introduced the linear regression model. The typical $y=\alpha + \beta X + \epsilon$, where $\epsilon$ is a "random" error term. The teacher then ...
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### Analytic solution for matrix factorization using alternating least squares

The standard form for ridge regression aims to minimize the following cost function. $$\min\ \ \sum_i(y_i-x_i^T\beta)^2 + \lambda\sum_j\beta^2_j$$ As described here, it's possible to differentiate ...
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### Theoretical basis for overfitting

There are many examples in which making more "precise" predictions gives worse performance (e.g. Runge's phenomenon). My professor implied that there was a sound basis for choosing "simple" functions ...
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### Formula for straight part of a slightly bumpy line

Given a straight line that deviates from the horizontal by at most 15 degrees. On this straight line there are bumps on top at random places on the line. The combined width of the bumps is at most ...
328 views

### Perturbation theory for least squares for very different A, b

Consider the least squares problem $f(x;A,b) = \|Ax-b\|_2^2$ and define $x^*$ the minimizer of $f(x;\hat A,\hat b)$, and $\hat x$ the minimizer of $f(x; A_2, b_2)$. I want to put some bound on \$\|...
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### Can someone explain what plim is?

In my Introductory Econometrics class we discussed a concept of "plim" or "probability limit. I'm not sure what this means though and my professor doesn't explain it well at all. Can someone tell me ...