for issues related to linear regression modelling approach
Linear Regression is a formalization of relationships between variables in the form of mathematical equations. It describes how one or more random variables are related to one or more other variables. Here the variables are not deterministically but stochastically related.
Example
Height and age are probabilistically distributed over humans. They are stochastically related; when you know that a person is of age 30, this influences the chance of this person being 4 feet tall. When you know that a person is of age 13, this influences the chance of this person being 6 feet tall.
Model 1
heighti = b0 + b1agei + εi, where b0 is the intercept, b1 is a parameter that age is multiplied by to get a prediction of height, ε is the error term, and i is the subject
Model 2
heighti = b0 + b1agei + b2sexi + εi, where the variable sex is dichotomous
In linear regression, user data X is modelled using linear functions Y, and unknown model parameters W are estimated or learned from the data. E.g., a linear regression model for a k-dimensional user data can be represented as :
Y = w1 x1 + w2 x2 + ... + wk xk
Reading Statistical Modeling: The Two Cultures http://projecteuclid.org/download/pdf_1/euclid.ss/1009213726
In scientific software r for statistical computing and graphics, function lm (see lm) implements linear regression.
