Question about multiple regression analysis

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SUMMARY

The discussion centers on multiple regression analysis, specifically addressing the assumptions and structure of the model. The participant queries the formulation of the regression equation, particularly when X = 1, and seeks clarification on the model's assumptions regarding error independence across categories. It is established that the model posits different means for distinct categories, such as 'male' and 'female', while maintaining identical error terms (ε).

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sigh1342
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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.
 

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sigh1342 said:

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 Ymale = mmale + ε and Yfemale = mfemale + ε, with possibly different means m but identical "noise" ε.

RGV
 

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