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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Is there a direct interpretation of the least squares solution based on composition of linear operators?

The least squares solution to the problem $$\min_x \|Ax - b\|_2^2$$ is $x = (A^\top A)^{-1}A^\top b$. Is there an interpretation of this solution by directly interpretating $x$ as the output of a ...
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Notation for Dyadic Hierarchical Partitions of $[0, 1)$

For a presentation I'm giving, I need to explain how tree-based regression works. I'm not $100\%$ sure of the notation I'm using, and whether it's consistent. So the basic idea is that we write the ...
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Mistakes in calculating SST SSR SSE

Lets say my three measured data was $y= 2,3,4$ for $x= 1,2,3.$ I want to calculate R-square for checking how well the observed data fits to my model, y=x. (or how well my model explains the data.) ...
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Least square estimators for “no slope” and “no intercept” models.

I'm trying to understand simple linear regression. Here is a problem I'm working on, and I'm trying to understand the answers conceptually. I want to find the least square estimators $b_1$ and $b_0$ ...
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Prove that $\Phi(\Phi^T\Phi)^{-1}\Phi^T=I$ if $\Phi$ has more columns than rows

In linear regression, for a data set $\bar t$, the least-squares solution of the equation $\bar t = \Phi\bar w$ is $$\hat{\bar w} = (\Phi^T\Phi)^{-1}\Phi^T\bar t$$ where $\Phi$ is the design matrix ...
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Bayesian Linear Regression Conjugate Prior

The model is linear regression, that is $$Y=X\beta+\epsilon$$ where $Y$ is the vector of response variable, $X$ is the design matrix, $\beta$ is the vector of regression coefficients and $\epsilon$ ...