# Multiple Linear Regression Calculator

Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variable x is associated with a value of the dependent variable y. The population regression line for p explanatory variables x1, x2, ... , xp is defined to be y = 0 + 1x1 + 2x2 + ... + pxp. This line describes how the mean response y changes with the explanatory variables. The observed values for y vary about their means y and are assumed to have the same standard deviation . The fitted values b0, b1, ..., bp estimate the parameters 0, 1, ..., p of the population regression line.

**References:** In multiple linear regression, the model specification is that the dependent variable, denoted y_i, is a linear combination of the parameters (but need not be linear in the independent x_i variables). As the linear regression has a closed form solution, the regression coefficients can be computed by calling the Regress(Double[] [] ,Double[] ) method only once.

We used Accord.Statistics for this calculator