Linked Questions

6
votes
1answer
12k views

How to “regress out” some variables? [duplicate]

I have been hearing about this term "regress out the variable" all the time and understand that it roughly means that you exclude the effects by that variable. But how does one mathematically do this? ...
3
votes
1answer
11k views

Why do regression coefficients change when excluding variables? [duplicate]

Possible Duplicate: How exactly does one “control for other variables”? In my linear model ...
2
votes
1answer
7k views

What does 'Controlling for' mean in regression? [duplicate]

I am working towards completing my undergrad honours thesis and I am in the process of analyzing and writing up my discussion section that is dealing with some form of multiple regression (can't ...
2
votes
2answers
5k views

How to “statistically adjust” for variables? [duplicate]

I've been trying to understand what means "statistically adjusted" when comparing two variables. For example, when computing the odds ratio for a death after surgery in two hospitals, we compute the ...
1
vote
0answers
1k views

Confusion regarding “regression by successive orthogonalization” [duplicate]

In trying to answer a question here on Cross Validated, I was re-reading Section 3.2.3, specifically Algorithm 3.1 from Elements of Statistical Learning. What I followed from this is that, given a ...
4
votes
1answer
184 views

Frisch-Waugh-Lovell Theorem: Partialing out a set of regressors [duplicate]

I am trying to understand the result of the Frisch-Waugh-Lovell Theorem that we can partial out a set out regressors. The model I am looking at is $y=X_1\beta_1 + X_2\beta_2 +u$ So the first step ...
0
votes
0answers
363 views

Regression anatomy: can a multivariate model with K independent variables be broken down into K bivariate models? [duplicate]

Valerio Filoso (2013) writes: Most econometrics textbooks limit themselves to providing the formula for the $\beta$ vector of the type $$\beta = (X′X)^{-1} X'Y.$$ Although compact and ...
3
votes
0answers
302 views

How does controlling for variables work in multiple regression? [duplicate]

My question is not about statistical programming. We know how to code the software in a regression with many independent variables. My question is about how the computer software controls for all ...
3
votes
1answer
125 views

General expression for a single coefficient $\hat{\beta_1}$ in a multiple linear regression? [duplicate]

Suppose I am trying to estimate a multiple linear regression with $k$ regressors and I have $n$ observations $$Y = X\beta + \epsilon$$ Where $\beta \in \mathbb{R}^k$ and $X \in \mathbb{R}^{k \times ...
3
votes
1answer
131 views

Difference between Multivariate Regression vs Iterative Regression on Residuals [duplicate]

Suppose one has an n × 2 matrix X (the independent variables) and a n × 1 vector y (the dependent variable). In a standard multiple linear regression setting, we solve for the 2 × 1 beta vector that ...
1
vote
0answers
45 views

Concept of performing a t-test while controlling/adjusting for one or more variables? [duplicate]

Could someone please help me understand the concept of performing a t-test while controlling/adjusting for one or more variables? E.g.: Say I have a hypothetical data set, with the following ...
0
votes
0answers
35 views

How to obtain regression coefficients of a multiple linear regression model from simple linear regression models? [duplicate]

Suppose I have a multiple linear regression model $$ Y=\beta_0+\beta_1X_1+\cdots+\beta_pX_p+\epsilon$$ How can I obtain the regression coefficients $\hat{\beta_i}$ by fitting just a series of simple ...
0
votes
1answer
27 views

Capturing effects / Controlling for variables [duplicate]

I understand the idea behind regressions and know how to interpret them, however, when I hear the term "capturing the effect of.." or "controlling for.." so far I've just accepted it without ...
1
vote
0answers
20 views

Obtaining the $j$th component of the OLS - an explanation [duplicate]

In a linear regression setting, I've seen that the $j$th component of the ordinary least square estimator $\hat{\beta}_j$ can be obtained as follows: $$\hat{\beta}_j = Y^T Z^{(j)} / (X^{(j)})^T Z^{(j)}...
0
votes
1answer
16 views

Will an OLS estimator for a regressor differ between a single linear regression and a multiple linear regression? [duplicate]

Thought question that I am having a difficult time formulating mathematically. Knowing that $y = \beta_0 + \beta_1X_1 +\beta_2X_2 + \varepsilon$, where $X_1$ and $X_2$ are non-random and $\beta_2$ ...

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