4 stats models
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[1]
The process of finding the model that relates \(y\) to \(x\) and best fits the data is called regression analysis.
- The variable \(y\) to be modeled is called the dependent variable (or response variable). Its expected value is denoted \(\Exp(y)\).
General Form of probabilistic Model in Regression is \[ y=E(y)+\varepsilon \]
4.1 Estimation
a statistic whose sampling distribution has the mean around the proposed value and a small variance. If the means are equal: unbiased estimator. No: biased.
4.2 build a model that fits the data
predicted value: \(\hat{y}\), \(\hat{\beta}\), …
- model: \(y=\Exp(y)+\varepsilon\)
[2]
- want to estimate \(f\): \(Y=f(X)+\varepsilon\)
- want to use \(\hat{f}\) to estimate \(f\): \(\hat{Y}=\hat{f}(X)\).