From 2089c808df0375ba12f6846d307426a8546e8c6e Mon Sep 17 00:00:00 2001 From: Benda Xu Date: Sat, 27 Jul 2024 13:42:19 +0800 Subject: [PATCH] =?UTF-8?q?pe:=20=E5=BF=8D=E7=97=9B=E8=88=8D=E5=BC=83?= =?UTF-8?q?=E5=A5=87=E6=80=AA=E7=9A=84=20tikz=20=E6=9E=84=E9=80=A0?= =?UTF-8?q?=E3=80=82?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- pd.org | 38 -------------------------------------- 1 file changed, 38 deletions(-) diff --git a/pd.org b/pd.org index a2c6c31..222d793 100644 --- a/pd.org +++ b/pd.org @@ -11987,44 +11987,6 @@ F-statistic: 4632 on 1 and 438 DF, p-value: < 2.2e-16 #+RESULTS: [[file:plot/thermistor-lm.pdf]] -#+beamer: \pause -**** r :BMCOL: -:PROPERTIES: -:BEAMER_col: 0.5 -:BEAMER_opt: t -:END: -#+begin_export latex -\begin{equation*} - \begin{aligned} - &\frac{1}{t/\si{\celsius} + 273.15} = \hat{a} + \hat{b} \log \frac{R}{\si{\kilo\ohm}} \\ - \implies &\frac{t}{\si{\celsius}} = \left(\hat{a} + \hat{b} \log \frac{R}{\si{\kilo\ohm}}\right)^{-1} - 273.15 - \end{aligned} -\end{equation*} -#+end_export - -#+begin_src R :session pd :file plot/thermistor-lm-curve.pdf :results graphics file :width 7 :height 5 :family GB1 :exports code - par(mar = c(4.5, 4.5, 0.8, 0.8)) - plot(1/(温度 + 273.15) ~ log(电阻), d, , cex.lab=2, cex.axis=2) - blue = sort(d$电阻) - lines(blue, 1/predict(lm.therm, data.frame(电阻=blue)) - 273.15, col="blue", lwd=4) -#+end_src - -- 通过电路测得 \(R\) ,即可通过公式转化得到温度 \(t\) 的读数。 - -*** \(\sigma^2\) 的估计 - \[ \hat{y} = \hat{a} + \hat{b} x \] - 一元线性回归模型 - \[ y = a + bx + \epsilon, \epsilon \sim N(0, \sigma^2) \] - - 因随机因素引起的误差称为 *残差平方和* - \[ Q_e = \sum_{i=1}^n (y-\hat{y})^2 \] - #+begin_export latex - \begin{equation*} - \begin{aligned} - & \frac{Q_e}{\sigma^2} \sim \chi^2(n-2) \\ - \implies & \hat{\sigma^2} = \frac{Q_e}{n-2} - \end{aligned} - \end{equation*} - #+end_export *** \(t\) 检验 检验假设 \( \displaystyle{H_0: b=0, H_1: b \neq 0}\) #+attr_beamer: :overlay <+->