Simple Linear Regression

In general, the model looks as follows:

yt = βxt + C + et

t = 1 … T

Or in vector form

y = βx + e

Where:

If the constant C is defined (zero or non-zero value), the model can be converted by substituting Y → Y + C to the classic view: Y =Xβ + ε.

If the constant must be estimated, convert the model to the classic view: Y =Xβ + ε by adding an additional artificial variable with the 1 value in all observations, and therefore, creating the X extended matrix by adding a single column to the X matrix.

Suppose that we replace n → n + 1. To estimate the coefficients β or β = (β, C) use the OLS technique.

Additional characteristics of the model. Determination coefficient:

Where:

Value of the Fisher statistics:

See also:

Library of Methods and Models