Linear models for regression

Linear regression models are the most basic type of regression models and are widely used in predictive data analysis. The overall idea of regression models is to examine two things:

1. Does a set of explanatory features / input variables do a good job at predicting an output variable? Is the model using features that account for the variability in changes to the dependent variable (output variable)?
2. Which features in particular are significant ones of the dependent variable? And in what way do they impact the dependent variable (indicated by the magnitude and sign of the parameters)? These regression parameters are used to explain the relationship between one output variable (dependent variable) and one or more input features (independent variables).

A regression equation will formulate the impact of the input variables (independent variables) on the output variable (dependent variable). The simplest form of this equation, with one input variable and one output variable, is defined by this formula y = c + b*x. Here, y = estimated dependent score, c = constant, b = regression parameter/coefficients, and x = input (independent) variable.