What is the line of means?

A probabilistic model has both a deterministic and a random error component. For example, suppose we anticipate that sales y are related to advertising spend x by

y = 15x + Random error

General Form of Probabilistic Models:

y = Deterministic component + Ramdom error,

Where, y is the variable of interest we always assume that the mean value of the random mistake is 0. This is comparable to assuming that the mean value of y, E(y), equals the model's deterministic component; that is,

E(y) = Deterministic component.

We know that a basic linear regression equation has the form, where y= β₀+ β₁x is the dependent variable,x is the independent variable, β₀is the intercept, β₁is the slope ε and is an error random variable with mean 0 and variance of . The probabilistic model will then bey= β₀+ β₁x. If we consider E(y), we may determine that

E(y)= β₀+ β₁x.

Every y value is normally distributed with mean values based on x for each value of x. When we plot this E(y) with x, we obtain a straight line with all mean lying on it; this line is known as the line means.