Prove Algebraically That

question 7

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Prove algebraically that .

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Definitions:

Intercept

The value of the dependent variable when all independent variables are equal to zero in a regression equation.

Indicator Variable

A variable that takes a value of 1 if a specific condition is true and 0 if it is not.

Interaction Term

A term in a statistical model that captures the effect of two or more variables interacting or influencing each other in a way that their individual effects cannot independently account for.

Stepwise Regression

A method of fitting regression models in which the choice of predictive variables is carried out by an automated procedure, either by adding or removing variables step by step, based on certain criteria.