In AndrewElaryan/Lab1Intro: Introduction to Math 4973

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(Lab1Intro)

Important Links

Here is the link to the webpage containing information on using vignettes to document packages.

This is a link to my GitHub repo.

Formulae in $\LaTeX$

Sample Mean

$$\bar{x}k=\frac{1}{n}\sum^n{j=1}x_{jk}\ \ \ \ k=1,2,...,p$$

Sample Covariance

$$s_{ik}=\frac{1}{n}\sum^n_{j=1}(x_{ji}-\bar{x}i)(x{jk}-\bar{x}_k)\ \ \ \ i=1,2,...,p,\ \ k=1,2,...,p$$

Sample Correlation

$$r_{ik}=\frac{s_{ik}}{\sqrt{s_{ii}}\sqrt{s_{kk}}}=\frac{\sum^n_{j=1}(x_{ji}-\bar{x}i)(x{jk}-\bar{x}k)}{\sqrt{\sum^n{j=1}(x_{ji}-\bar{x}i)^2}\sqrt{\sum^n{j=1}(x_{jk}-\bar{x}_k)^2}}$$

Formula 3-27

$$ \bar{x}=\frac{1}{n}X'1 \S=\frac{1}{n-1}X'(I-\frac{1}{n}11')X $$

Sample Standard Deviation Matrix

$$ D^{1/2}{pxp}= \begin{bmatrix} \sqrt{s{11}} & 0 & ... & 0\ 0 & \sqrt{s_{22}} & ... & 0\ \vdots & \vdots & \ddots & \vdots\ 0 & 0 & ... & \sqrt{s_{pp}} \end{bmatrix} $$

Formula 3-29

$$ R = D^{-1/2}SD^{-1/2} $$

Package Demo

Read in data

library(Lab1Intro)
x = read.table("T1-2.DAT",header=FALSE)

Sample mean for each column

samp_mean(x[,1])
samp_mean(x[,2])
samp_mean(x[,3])

Sample Covariance

samp_cov(x)

Sample Correlation

samp_cor(x)

Assessment Overview

1. Clicker quiz each class and lab (Total 10%)
2. 4 assignments (20% Total)
3. Laboratories (10% Total)
4. 2 exams (10% each, Total 20%)
5. 2(4793) projects (10%)
6. 1 final (30%)

AndrewElaryan/Lab1Intro documentation built on Jan. 30, 2020, 6:25 a.m.