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## Linear regression - Wikipedia

### Linear Regression Model - CAMO

Regression can help finance and investment professionals as well as professionals in other businesses. Regression can help predict sales for a company based on weather, previous sales, GDP growth or other conditions. The capital asset pricing model (CAPM) is an often-used regression model in finance for pricing assets and discovering costs of capital. The general form of each type of regression is:

The goal is to build a mathematical formula that defines y as a function of the x variable. Once, we built a statistically significant model, it’s possible to use it for predicting future outcome on the basis of new x values.

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LinearRegression will take in its fit method arrays X, y and will store the coefficients of the linear model in its coef_ member:

Simple linear regression is a way to describe a relationship between two variables through an equation of a straight line, called line of best fit , that most closely models this relationship.

Linear regression is a common statistical method, which has been adopted in machine learning and enhanced with many new methods for fitting the line and measuring error. In the most basic sense, regression refers to prediction of a numeric target. Linear regression is still a good choice when you want a very simple model for a basic predictive task. Linear regression also tends to work well on high-dimensional, sparse data sets lacking complexity.

Before moving forward to find the equation for your regression line, you have to identify which of your two variables is* X * and which is* Y* . When doing correlations, the choice of which variable is* X* * * and which is* Y * doesn’t matter, as long as you’re consistent for all the data. But when fitting lines and making predictions, the choice of* X * and* Y * does make a difference.

Fitting a linear regression model returns a results class. OLS has a specific results class with some additional methods compared to the results class of the other linear models.

Regression is a common process used in many applications of statistics in the real world. There are two main types of applications:

Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the "lack of fit" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares cost function as in ridge regression (* L* 2 -norm penalty) and lasso (* L* 1 -norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms "least squares" and "linear model" are closely linked, they are not synonymous.

In the next section, we will extend 1-D linear regression to any-dimensional linear regression - in other words, how to create a machine learning model that can learn from multiple inputs.

Many techniques for carrying out regression analysis have been developed. Familiar methods such as linear regression and ordinary least squares regression are parametric , in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data . Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions , which may be infinite-dimensional .

The number of jobs to use for the computation. If -1 all CPUs are used. This will only provide speedup for n_targets > 1 and sufficient large problems.