We initially have a response variable Y and a simple linear regression mean function:
Y = β0 + β1 +ϵ
Now, let’s introduce a second variable X2, and aim to understand how Y depends on both X1 and X2 simultaneously. By incorporating X2 into the analysis, we create a mean function that considers the values of both X1 and X2:
Y = β0 + β1 x1 + β2 x2 + ϵ
The primary objective in including X2 is to account for the portion of Y that hasn’t already been explained by X1.
% Diabetes(Predict) ← % Inactivity, % Obesity (Predictors or Factors)
The Generalized Linear Model extends the concept of linear regression by introducing a link function that relates the linear model to the response variable and by permitting the measurement variance to be influenced by the predicted value of each measurement.