Question about multiple regression analysis

In summary: W5lLCBpZiBYID0gMSwgZm9yIChhKSwgd2lsbCB0aGUgbW9kZWwgYmVjb21lOiB5ID0gKGJfMSkpICsgZXBzaW9uPz8gU28gKGJfaScnIGFyZSB0aGUgc2xvcGVzIG9mIHRoZSBtb2RlbHM/IEFuZCBmb3IgdGhlIHJlc3Qgb2YgdGhlIHF1ZXN0aW9uPyBBbmQgZm9yIHRoZSByZX
  • #1
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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  • #2
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
 

1. What is multiple regression analysis?

Multiple regression analysis is a statistical technique used to examine the relationship between a dependent variable and two or more independent variables. It allows you to determine how much of the variation in the dependent variable can be explained by the independent variables.

2. When should I use multiple regression analysis?

Multiple regression analysis is typically used when you want to understand the impact of multiple independent variables on a single dependent variable. It is often used in social sciences, psychology, and business research to examine complex relationships and make predictions.

3. How do I interpret the results of a multiple regression analysis?

The results of a multiple regression analysis can be interpreted by looking at the coefficients, or beta values, for each independent variable. These coefficients indicate the strength and direction of the relationship between each independent variable and the dependent variable. Additionally, the overall model fit and significance of the independent variables can also be used to interpret the results.

4. What are some common assumptions of multiple regression analysis?

Some common assumptions of multiple regression analysis include the assumption of linearity (that the relationship between the independent and dependent variables is linear), normality (that the residuals are normally distributed), and independence (that the observations are not influenced by each other).

5. Can multiple regression analysis be used for causal inference?

While multiple regression analysis can suggest a relationship between variables, it cannot establish causation. Other methods, such as experimental designs, are better suited for determining causality. However, multiple regression analysis can be used to control for potential confounding variables and make stronger arguments for causality.

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