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Merge branch 'main' of https://github.com/s-ccs/summerschool_simtech_2023

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behinger (s-ccs 001) 2023-10-11 11:12:38 +00:00
commit d5357fe3b6
1 changed files with 3 additions and 3 deletions
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material/3_wed/regression/MultipleRegressionBasics.qmd
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@ -152,7 +152,7 @@ Defining the *design matrix*
$$ \mathbf{X} = \left( \begin{array}{cccc}
1 & x_{11} & \ldots & x_{1p} \\
\vdots & \vdots & \ddots & \vdots \\
1 & x_{11} & \ldots & x_{1p}
1 & x_{n1} & \ldots & x_{np}
\end{array}\right) \qquad
(\text{size } n \times (p+1)), $$
@ -177,7 +177,7 @@ regression model, but we provide explicit formulas now:
- estimated standard errors:
$$
\hat s_{\beta_i} = \sqrt{([\mathbf{X}^\top \mathbf{X}]^{-1})_{ii} \frac 1 {n-p} \|\mathbf{y} - \mathbf{X} \beta\|^2}
\hat s_{\beta_i} = \sqrt{([\mathbf{X}^\top \mathbf{X}]^{-1})_{ii} \frac 1 {n-p-1} \|\mathbf{y} - \mathbf{X} \beta\|^2}
$$
- $t$-statistics:
@ -187,7 +187,7 @@ regression model, but we provide explicit formulas now:
- $p$-values:
$$
p\text{-value} = \mathbb{P}(|T| > t_i), \quad \text{where } T \sim t_{n-p}
p\text{-value} = \mathbb{P}(|T| > t_i), \quad \text{where } T \sim t_{n-p-1}
$$
::: {.callout-caution collapse="false"}