# Questions tagged [linear-regression]

For questions about linear regressions, an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables.

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### Results of linear regression with just statistically significant features vs. whole dataset

If I have a dataset, in this case the diabetes toy dataset, and am running a linear regression model, could someone explain what I should expect in terms of performance if I were to conduct the ...
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### PDF Being Invariant Under Orthogonal Transformations

Regarding linear regression, in the (informal) solution manual of T. Hastie's "The Elements of Statistical Learning" book, there is a paragraph (p. 16 in the manual) that goes: "... ...
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### Population OLS coefficient in simple regression?

The population OLS coefficient for some $X_i \in \mathbb{R}^d, Y \in \mathbb{R}$ for the model $Y = \beta’X + e$ is defined as $$\beta =\mathbb{E}[X_iX_i']^{-1}\mathbb{E}[X_iY_i]$$ and if $X$ is a ...
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Let $(\Omega,\Sigma,P)$ be some probability space and let $Y: \Omega \to \mathbb{R}$ be a random variable. Let $x, \beta \in \mathbb{R}^n$. In a linear model we assume something like this: $E(Y|x)=\... • 1,560 0 votes 0 answers 18 views ### Creating a regression model of scaling data from five points for ATAR I am looking to calculate the scaled results for the ATAR (Australian Tertiary Admission Rank) subjects that someone inputs from the recently released 2023 data. For example if someone got a 59.00 in ... 0 votes 0 answers 47 views ### Simpson's Paradox for$R^2$I've been reading about Simpson's Paradox and I understand how if you fit a regression on a per-group basis versus on the entire set, the coefficients in each group can be drastically different from ... 0 votes 0 answers 21 views ### Convergence of coefficients in multivariate regression In this thread, the convergence of coefficient for univariate dependent variable is proven. I wonder, assuming the same setup, how can the convergence be extended to multivariate as: $$Y=XW+\epsilon$$ ... • 253 0 votes 0 answers 61 views ### Proving product of two projection matrices is commutative I’ve been trying to understand the details of orthogonal projections within the context of linear regression models, and I’ve come across the following scenario: Given a linear regression model$Y=\...
In the paper Square Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming they talk about Sqrt-LASSO which is simply just trying to minimize $\|Ax-b\|_2 + \lambda\|x\|_1$ rather than ...