Linked Questions

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0answers
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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 ...
0
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0answers
330 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 ...
4
votes
1answer
42 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 ...
1
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0answers
140 views

Hierarchical and sequential regression [duplicate]

I performed a hierarchical multiple regression to study the effect of different variables, above and beyond the apriori selected more important variables. The R script used to perform this regression ...
1
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0answers
60 views

Can we solve multiple linear regression using simple linear regression solver? [duplicate]

Suppose I have a blackbox function that solves simple linear regression. Can I use this function to solve "multiple" linear regression? The blackbox computes the slope and intercept in a simple ...
3
votes
1answer
46 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 ...
0
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0answers
28 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 ...
1
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0answers
19 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
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0answers
7 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 ...
32
votes
5answers
84k views

How to derive the least square estimator for multiple linear regression?

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 ...
31
votes
6answers
15k views

Line graph has too many lines, is there a better solution?

I'm trying to graph the number of actions by users (in this case, "likes") over time. So I have "Number of actions" as my y-axis, my x-axis is time (weeks), and each line represents one user. My ...
43
votes
5answers
49k views

How to make a time series stationary?

Besides taking differences, what are other techniques for making a non-stationary time series, stationary? Ordinarily one refers to a series as "integrated of order p" if it can be made stationary ...
15
votes
3answers
9k views

Utility of the Frisch-Waugh theorem

I am supposed to teach the Frish Waugh theorem in econometrics, which I have not studied. I have understood the maths behind it and I hope the idea too "the coefficient you get for a particular ...
5
votes
2answers
22k views

Getting a second-order polynomial trend line from a set of data

Alright, so I have about a thousand datapoints that I'm plotting on a chart (scatter plot). Here's a few of the records: ...
15
votes
1answer
2k views

How to understand the correlation coefficient formula?

Can anyone help me understand the Pearson correlation formula? the sample $r$ = the mean of the products of the standard scores of variables $X$ and $Y$. I kind of understand why they need to ...

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