Mutiple Linear Regression and Estimation

Multiple Linear Regression analysis can be looked upon as an extension of simple linear regression analysis to the situation in which more than one independent variables must be considered.

The general model with response Y and regressors X₁, X₂,... X_p:

Suppose we observe data for n subjects with p variables. The data might be presented in a matrix or table like:

We could then write the model as:

We can think of Y and E as (n x 1) vectors when transposed, and β as a ((p + 1) x 1) vector. X would be:

Thus the general linear regression may be written as:

Or     y_i = x_i^|*β + E_i