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Supervised classification and regression models that assume linear relationship between dependent and explanatory variables.
Linear Models
Linear models describe a continuous response variable as a function of one or more predictor variables. The model describes the relationship between a dependent variable y (also called the response) as a function of one or more independent, or explanatory variables \(X_i\). The general equation for a linear model is: \[y = \beta_0 + \sum_{i=1}^n \beta_iX_i + \epsilon\]
where \(\beta_0 \) is the intercept term (the expected value of Y when X = 0), \(\epsilon \) is an error term that is is independent of X and \(\beta_i \) is the average increase in y associated with a one-unit increase in \(X_i\)
Model assumptions:
- Linearity. The relationship between X and the mean of y is linear.
- Constant variance. The variance of residual is the same for any value of X.
- Normality. For any fixed value of X, Y is normally distributed.
- Independence. Observations are independent of each other.
References:
Modules
- This is a generic solver for Ax = b type of equation
- Elastic Net
- Lasso
- An Interior-Point Method for Large-Scale l1-Regularized Least Squares
- Linear Regression
- Logistic Regression
- Ridge Regression