Question about multiple regression analysis

[sigh1342]

Homework Statement

My question is q.3 in the attachment. I don't really understand the scenario of the question.

The Attempt at a Solution

For (a), if X = 1, will the model become: y = (b_1)(E_1) + epsilon? So (b_i)'s are the slopes of the models? But what is the assumption of the model?

And for the rest of the question, I'm just looking for someone to explain to me a little bit more.

 

[Ray Vickson]

Homework Statement

My question is q.3 in the attachment. I don't really understand the scenario of the question.

The Attempt at a Solution

For (a), if X = 1, will the model become: y = (b_1)(E_1) + epsilon? So (b_i)'s are the slopes of the models? But what is the assumption of the model?

And for the rest of the question, I'm just looking for someone to explain me a little bit more.

The assumption of the model is that the errors are independent of the categories. For example, suppose there are two categories, called 'male' and 'female' and that there is some measured numerical aspect Y of a person. The model is saying that Y_male = m_male + ε and Y_female = m_female + ε, with possibly different means m but identical "noise" ε.

RGV