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hernandis.me | ||
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www.listendata.com
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| | | | | [AI summary] The user is seeking guidance on performing linear regression analysis in R, including data preparation, model building, and interpretation. They have questions about multicollinearity, variable selection, and package usage. The response should provide step-by-step instructions on installing necessary packages, conducting analysis, and addressing common issues. | |
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bldavies.com
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| | | | | Suppose \(X\) and \(Y\) are random variables with $$\DeclareMathOperator{\E}{E} \DeclareMathOperator{\Cov}{Cov} \DeclareMathOperator{\Var}{Var} \newcommand{\abs}[1]{\lvert#1\rvert} Y=\beta X+u,$$ where \(u\) has zero mean and zero correlation with \(X\). The coefficient \(\beta\) can be estimated by collecting data \((Y_i,X_i)_{i=1}^n\) and regressing the \(Y_i\) on the \(X_i\). Now suppose our data collection procedure is flawed: instead of observing \(X_i\), we observe \(Z_i=X_i+v_i\), where the \(v_i\) are iid with zero mean and zero correlation with the \(X_i\). Then the ordinary least squares (OLS) estimate \(\hat\beta_{\text{OLS}}\) of \(\beta\) obtained by regressing the \(Y_i\) on the \(Z_i\) suffers from attenuation bias: $$\begin{align*} \DeclareMa... | |
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gregorygundersen.com
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| | | | | Gregory Gundersen is a quantitative researcher in New York. | |
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blog.scottlogic.com
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| | | Recently I've been learning about Neural Networks and how they work. In this blog post I write a simple introduction in to some of the core concepts of a basic layered neural network. | ||
