Linear Model Regression System

AKA: Linear Regression Software.
Context:
- It can range from being a Simple Linear Regression System to being a Multiple Linear Regression System.
- It can range from being a Least-Squares Linear Regression System, to being Linear Ridge Regression System.
Example(s):
- sklearn.linear_model, a Generalized Linear Model Regression System within Scikit Learn.
- statsmodels.api, a Linear Model Regression System within Statmodels.
- lm an Ordinary Linear Model Regression System within R.
- An One-predictor-variable linear regression online calculator such as: http://onlineregression.sdsu.edu/onlineregression11.php
- A Multiple linear regression online calculator such as: http://onlineregression.sdsu.edu/onlineregression13.php
- A Generalized Linear Model Regression System.
- A Ordinary Linear Model Regression System.
- A Weighted Linear Model Regression System.
- A Regularized Linear Model Regression System.
- …
Counter-Example(s):
- an Analysis of Variance System.
- a Non-Linear Regression System, such as a Logistic Regression System.
- A Regularized Non-Linear Regression System such as a Total Variation Regularization System.
See: Least Supervised Classification System, Linear Least-Squares Regression System, Linear Ridge Regression System, A Linear Bayesian Regression System.

References

(Scikit Learn, 2017) ⇒ http://scikit-learn.org/stable/modules/linear_model.html Retrieved: 2017-30-07.
- QUOTE: The following are a set of methods intended for regression in which the target value is expected to be a linear combination of the input variables. In mathematical notion, if [math]\displaystyle{ \hat{y} }[/math] is the predicted value.
  [math]\displaystyle{ \hat{y}(w, x) = w_0 + w_1 x_1 + \cdots + w_p x_p }[/math]
  Across the module, we designate the vector [math]\displaystyle{ w = (w_1,\cdots, w_p) }[/math] as coef_ and [math]\displaystyle{ w_0 }[/math] as intercept_.

(Redriguez,2017) ⇒ Germán Rodríguez, Princeton University (2017). “Introducing R - 4 Linear Models" http://data.princeton.edu/R/linearModels.html
- QUOTE: To fit an ordinary linear model with fertility change as the response and setting and effort as predictors, try
  lmfit = lm( change ~ setting + effort )
  Note first that lm is a function, and we assign the result to an object that we choose to call lmfit (for linear model fit). This stores the results of the fit for later examination.
  The argument to lm is a model formula, which has the response on the left of the tilde ~ (read "is modeled as") and a Wilkinson-Rogers model specification formula on the right.