Consider a regression analysis with three independent variables x1, x2, and x3. Give the equation for the following regression models:
a. The model that includes as predictors all independent variables but no quadratic or interaction terms;
b. The model that includes as predictors all independent variables and all quadratic terms;
c. All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term;
d. The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model).