# 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.

105 questions
Filter by
Sorted by
Tagged with
4k views

19k views

### 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?
11k views

### easy to implement method to fit a power function (regression)

I want to fit to a dataset a power function ($y=Ax^B$). What is the best and easiest method to do this. I need the $A$ and $B$ parameters too. I'm using in general financial data in my project, which ...
195 views

37k views

### Given a data set, how do you do a sinusoidal regression on paper? What are the equations, algorithms?

Most regressions are easy. Trivial once you know how to do it. Most of them involve substitutions which transform the data into a linear regression. But I have yet to figure out how to do a ...
7k views

### 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'...
1k views

### why small L1 norm means sparsity?

I'm trying to understand regularization in machine learning. one way of regularization is adding a l1 norm to the error function. This is said to produce sparsity. But I can't understand. sparsity is ...
5k views

### What is $\operatorname{Cov}(\widehat{Y},Y)$?

If $\hat{Y}$ is the OLS linear regression model for $Y$, what can I say about $\operatorname{Cov}(\hat{Y},Y)$? Is this value $0$?
9k views

3k views

### derivation of simple linear regression parameters

I know there are some proof in the internet, but I attempted to proove the formulas for the intercept and the slope in simple linear regression using Least squares, some algebra, and partial ...
### Why is $E(u)=0$ when an intercept is included in OLS Estimation?
I am reading Wooldridge's graduate econometrics text. There he states that when estimating the equation $y=\mathbf{x\beta}+u$ by OLS, if an intercept (constant term) is included in your $\mathbf{x}$ ...