10k 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? ...
9k views

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

Possible Duplicate: How exactly does one “control for other variables”? In my linear model ...
6k 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 ...
3k 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 ...
817 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 ...
294 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 ...
291 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 ...
44 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 ...
28 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 ...
29 views

### How does multiple regression control for variables? [duplicate]

I've watched videos, read articles, asked around, but I can't seem to get into my head how exactly multiple regression works. I mostly use logistic multiple regression and so I will have a binary ...
25 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 ...
13 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 ...
6 views

### Partailling out approach in multiple linear regression [duplicate]

Assume I run the following regression: $$sales = \beta_{0} + \beta_{1} price + \beta_{2}advert + \beta_{3}advert^2$$ Now I regress sales, price, and advertising separately on advertising_squared ...
In the simple linear regression case $y=\beta_0+\beta_1x$, you can derive the least square estimator $\hat\beta_1=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}$ such that you don't have to ...