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hernandis.me | ||
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bldavies.com
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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www.listendata.com
[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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www.jeremykun.com
Machine learning is broadly split into two camps, statistical learning and non-statistical learning. The latter we've started to get a good picture of on this blog; we approached Perceptrons, decision trees, and neural networks from a non-statistical perspective. And generally "statistical" learning is just that, a perspective. Data is phrased in terms of independent and dependent variables, and statistical techniques are leveraged against the data. In this post we'll focus on the simplest example of thi... |
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blog.ephorie.de
[AI summary] The blog post explores the connection between logistic regression and neural networks, demonstrating how logistic regression can be viewed as the simplest form of a neural network through mathematical equivalence and practical examples. |
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