In general, the model looks as follows:
yt = βxt + C + et
t = 1 … T
Or in vector form
y = βx + e
Where:
T. Number of observations.
β. Estimated coefficient of the explanatory variable.
xt. Observations of the explanatory variable.
et. Residuals.
yt. Explained variable.
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:
y* = τYi.
e = Y - Ŷ.
.
i. Unit column.
;
τ = 1 if the constant is estimated automatically, τ = 0 if the constant is estimated manually.
Value of the Fisher statistics:
See also: