COMMunication
RESearch.NET

User Tools

Site Tools

You are here: index » sand_box
Trace: • poisson_distribution • social_network_analysis • collinearity • fedora • linear_regression • anova_note • sand_box • internet_history • sandbox • suppressor_in_multiple_regression
sand_box

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
sand_box [2025/12/07 17:40] – hkimscilsand_box [2026/04/01 01:52] (current) – hkimscil
Line 1: Line 1:
 +{{pasted:20260401-015229.png?300}}
 +{{pasted:20251229-044558.png?300}}
 +<tabbed>
 +  * sand box:code01
 +  * *sand box:output01
 +</tabbed>
 +----
 +  graph TD
 +    A(**mermaid**)-->B((__plugin__))
 +    A-->C(((//for//)))
 +    B-->D[["[[https://www.dokuwiki.org/dokuwiki|Dokuwiki]]"]]
 +    C-->D
 +
 +\begin{eqnarray*} 
 +& & P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}\\
 +& & P(B \mid A) = \dfrac{P(B \cap A)}{P(A)}\\
 +\\
 +& & P(B \vert A) \;\; \text{  vs. } \;\; P(B \mid A) \\
 +& & P(A \cap B) = P(A \mid B) * P(B) \\
 +& & P(B \cap A) = P(B \mid A) * P(A) \\
 +& & P(A \cap B) = P(A, B) \\
 +
 +\\
 +& & \frac{3}{4 \pi} \sqrt{4 \cdot x^2 12} \\ 
 +& & \lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6} \\ 
 +& & {\it f}(x) = \frac{1}{\sqrt{x} x^2} \\ 
 +& & e^{i \pi} + 1 = 0\; 
 +\end{eqnarray*}
 +
 +<WRAP tabs>
 +  * [[:sand box/intro]]
 +  * [[:sand box/body]]
 +  * [[:sand box/conc]]
 +</WRAP>
 +
 +{{tabinclude>sand_box:page1|Top page,sand_box:page2|Second page,*sand_box:page3}}
 +<tabbed>
 +  * *sand_box:page1
 +  * sand_box:page2
 +  * sand_box:page3
 +
 +</tabbed>
 +[{{:r.regressionline3.png}}]
 +
 +\begin{align*}
 +& \;\;\;\; \sum{(Y_i - \hat{Y_i})^2} \\
 +&= \sum{(Y_i - (a + bX_i))^2}  \;\;\; \because \hat{Y_i} = a + bX_i \\
 +&= \text{SSE or SS.residual} \;\;\; \text{(and this should be the least value.)} \\
 +\end{align*}
 +
 +<WRAP box>
 +\begin{align*}
 +&\text{for a (constant)} \\ \\
 +&\dfrac{\text{d}}{\text{dv}} \sum{(Y_i - (a + bX_i))^2} \\
 +&=  \sum \dfrac{\text{d}}{\text{dv}} {(Y_i - (a + bX_i))^2} \\ 
 +&= \sum{2 (Y_i - (a + bX_i))} * (-1) \;\;\;\; \\
 +&\because \dfrac{\text{d}}{\text{dv for a}} (Y_i - (a+bX_i)) = -1 \\
 +& = -2 \sum{(Y_i - (a + bX_i))} \\ 
 +\\
 +&\text{in order to have the least value, the above should be zero} \\ 
 +\\
 +&-2 \sum{(Y_i - (a + bX_i))} = 0 \\
 +&\sum{(Y_i - (a + bX_i))} = 0 \\ 
 +&\sum{Y_i} - \sum{a} - b \sum{X_i} = 0 \\
 +&\sum{Y_i} - n*{a} - b \sum{X_i} = 0 \\
 +&n*{a} = \sum{Y_i} - b \sum{X_i} \\
 +&a = \dfrac{\sum{Y_i}}{n} - b \dfrac{\sum{X_i}}{n} \\
 +&a = \overline{Y} - b \overline{X} \\
 +\end{align*} 
 +</WRAP>
 +
 +<WRAP box>
 +\begin{eqnarray*}
 +\text{for b, (coefficient)} \\ 
 +\\
 +\dfrac{\text{d}}{\text{dv}} \sum{(Y_i - (a + bX_i))^2}  & = & \sum \dfrac{\text{d}}{\text{dv}} {(Y_i - (a + bX_i))^2} \\ 
 +& = & \sum{2 (Y_i - (a + bX_i))} * (-X_i) \;\;\;\; \\
 +& \because & \dfrac{\text{d}}{\text{dv for b}} (Y_i - (a+bX_i)) = -X_i \\
 +& = & -2 \sum{X_i (Y_i - (a + bX_i))} \\
 +\\
 +\text{in order to have the least value, the above should be zero} \\ 
 +\\
 +-2 \sum{X_i (Y_i - (a + bX_i))} & = & 0 \\
 +\sum{X_i (Y_i - (a + bX_i))} & = & 0 \\ 
 +\sum{X_i (Y_i - ((\overline{Y} - b \overline{X}) + bX_i))} & = & 0 \\ 
 +\sum{X_i ((Y_i - \overline{Y}) - b (X_i - \overline{X})) } & = & 0 \\ 
 +\sum{X_i (Y_i - \overline{Y})} - \sum{b X_i (X_i - \overline{X}) } & = & 0 \\ 
 +\sum{X_i (Y_i - \overline{Y})} & = &  b \sum{X_i (X_i - \overline{X})} \\ 
 +b & = & \dfrac{\sum{X_i (Y_i - \overline{Y})}}{\sum{X_i (X_i - \overline{X})}} \\
 +b & = & \dfrac{\sum{(Y_i - \overline{Y})}}{\sum{(X_i - \overline{X})}} \\
 +b & = & \dfrac{ \sum{(Y_i - \overline{Y})(X_i - \overline{X})} } {\sum{(X_i - \overline{X})(X_i - \overline{X})}} \\
 +b & = & \dfrac{ \text{SP} } {\text{SS}_\text{x}} \\
 +\end{eqnarray*} 
 +</WRAP>
 +
 +
 <code> <code>
 library(tidyverse) library(tidyverse)
Line 294: Line 390:
  
 </code> </code>
-<tabbed> 
-  * sand box:code01 
-  * *sand box:output01 
-</tabbed> 
- 
- 
-{{clock}} 
- 
- 
----- 
-  graph TD 
-    A(**mermaid**)-->B((__plugin__)) 
-    A-->C(((//for//))) 
-    B-->D[["[[https://www.dokuwiki.org/dokuwiki|Dokuwiki]]"]] 
-    C-->D 
- 
-\begin{eqnarray*}  
-& & P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}\\ 
-& & P(B \mid A) = \dfrac{P(B \cap A)}{P(A)}\\ 
-\\ 
-& & P(B \vert A) \;\; \text{  vs. } \;\; P(B \mid A) \\ 
-& & P(A \cap B) = P(A \mid B) * P(B) \\ 
-& & P(B \cap A) = P(B \mid A) * P(A) \\ 
-& & P(A \cap B) = P(A, B) \\ 
- 
-\\ 
-& & \frac{3}{4 \pi} \sqrt{4 \cdot x^2 12} \\  
-& & \lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6} \\  
-& & {\it f}(x) = \frac{1}{\sqrt{x} x^2} \\  
-& & e^{i \pi} + 1 = 0\;  
-\end{eqnarray*} 
- 
-<WRAP tabs> 
-  * [[:sand box/intro]] 
-  * [[:sand box/body]] 
-  * [[:sand box/conc]] 
-</WRAP> 
- 
-{{tabinclude>sand_box:page1|Top page,sand_box:page2|Second page,*sand_box:page3}} 
-<tabbed> 
-  * *sand_box:page1 
-  * sand_box:page2 
-  * sand_box:page3 
- 
-</tabbed> 
-[{{:r.regressionline3.png}}] 
- 
-\begin{align*} 
-& \;\;\;\; \sum{(Y_i - \hat{Y_i})^2} \\ 
-&= \sum{(Y_i - (a + bX_i))^2}  \;\;\; \because \hat{Y_i} = a + bX_i \\ 
-&= \text{SSE or SS.residual} \;\;\; \text{(and this should be the least value.)} \\ 
-\end{align*} 
- 
-<WRAP box> 
-\begin{align*} 
-&\text{for a (constant)} \\ \\ 
-&\dfrac{\text{d}}{\text{dv}} \sum{(Y_i - (a + bX_i))^2} \\ 
-&=  \sum \dfrac{\text{d}}{\text{dv}} {(Y_i - (a + bX_i))^2} \\  
-&= \sum{2 (Y_i - (a + bX_i))} * (-1) \;\;\;\; \\ 
-&\because \dfrac{\text{d}}{\text{dv for a}} (Y_i - (a+bX_i)) = -1 \\ 
-& = -2 \sum{(Y_i - (a + bX_i))} \\  
-\\ 
-&\text{in order to have the least value, the above should be zero} \\  
-\\ 
-&-2 \sum{(Y_i - (a + bX_i))} = 0 \\ 
-&\sum{(Y_i - (a + bX_i))} = 0 \\  
-&\sum{Y_i} - \sum{a} - b \sum{X_i} = 0 \\ 
-&\sum{Y_i} - n*{a} - b \sum{X_i} = 0 \\ 
-&n*{a} = \sum{Y_i} - b \sum{X_i} \\ 
-&a = \dfrac{\sum{Y_i}}{n} - b \dfrac{\sum{X_i}}{n} \\ 
-&a = \overline{Y} - b \overline{X} \\ 
-\end{align*}  
-</WRAP> 
- 
-<WRAP box> 
-\begin{eqnarray*} 
-\text{for b, (coefficient)} \\  
-\\ 
-\dfrac{\text{d}}{\text{dv}} \sum{(Y_i - (a + bX_i))^2}  & = & \sum \dfrac{\text{d}}{\text{dv}} {(Y_i - (a + bX_i))^2} \\  
-& = & \sum{2 (Y_i - (a + bX_i))} * (-X_i) \;\;\;\; \\ 
-& \because & \dfrac{\text{d}}{\text{dv for b}} (Y_i - (a+bX_i)) = -X_i \\ 
-& = & -2 \sum{X_i (Y_i - (a + bX_i))} \\ 
-\\ 
-\text{in order to have the least value, the above should be zero} \\  
-\\ 
--2 \sum{X_i (Y_i - (a + bX_i))} & = & 0 \\ 
-\sum{X_i (Y_i - (a + bX_i))} & = & 0 \\  
-\sum{X_i (Y_i - ((\overline{Y} - b \overline{X}) + bX_i))} & = & 0 \\  
-\sum{X_i ((Y_i - \overline{Y}) - b (X_i - \overline{X})) } & = & 0 \\  
-\sum{X_i (Y_i - \overline{Y})} - \sum{b X_i (X_i - \overline{X}) } & = & 0 \\  
-\sum{X_i (Y_i - \overline{Y})} & = &  b \sum{X_i (X_i - \overline{X})} \\  
-b & = & \dfrac{\sum{X_i (Y_i - \overline{Y})}}{\sum{X_i (X_i - \overline{X})}} \\ 
-b & = & \dfrac{\sum{(Y_i - \overline{Y})}}{\sum{(X_i - \overline{X})}} \\ 
-b & = & \dfrac{ \sum{(Y_i - \overline{Y})(X_i - \overline{X})} } {\sum{(X_i - \overline{X})(X_i - \overline{X})}} \\ 
-b & = & \dfrac{ \text{SP} } {\text{SS}_\text{x}} \\ 
-\end{eqnarray*}  
-</WRAP> 
- 
  
sand_box.1765129233.txt.gz · Last modified: by hkimscil
Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki