In OUStudent/Lab1Intro: Lab1Intro

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

OU MATH-4793/5793

The R code used to load the package is the following:

library(Lab1Intro)

Package Functions Descriptions

SampleMeanVector

This function takes in a dataframe or matrix, and returns a vector of the means from the columns. Calling the function would look like the following:

SampleBiasedCovarianceMatrix

Given a matrix of data, an algorithm is employed to calculate the sample covariance and variance (biased) matrix. The variance values are located on the diagonal of the matrix, $x_{11}$,$x_{22}$...$x_{pp}$; while the covariance values are located in the other positions. Note: Uses SampleMeanVector function.

SampleCorrelationMatrix

Given a matrix of data, an algorithm is employed to calculate the sample correlation coefficient matrix. Note: Uses SampleBiasedCovarianceVarianceMatrix function.

Lab 1 Work

Web Link

Web Link to GitHub Public Repository Address: https://github.com/OUStudent/Lab1Intro

Latex

Sample Mean (1-1):

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

Sample Covariance (1-4):

$$ s_{jk} = \frac{1}{n} \sum_{j=1}^n (x_{ji}-\bar x_i)(x_{jk}-\bar x_k) $$

Pearson's Product Moment Correlation Coefficient (1-5):

$$ r_{ik}=\frac{S_{ik}}{\sqrt{S_{ii}}\sqrt{S_{kk}}}=\frac{\sum_{j=1}^n (x_{ji}-\bar x_i)(x_{jk}-\bar x_k)}{\sqrt{\sum_{j=1}^n(x_{ji}-\bar x_i)^2}\sqrt{\sum_{j=1}^n(x_{jk}-\bar x_k)^2}} $$

Figure (3-27):

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

Figure (3-28):

$$ D^{1/2}{(p\ x \ p)}= \begin{bmatrix} \sqrt{S{11}} & 0 & \dots & 0 \ \vdots & \sqrt{S_{22}} & \dots & 0\ \vdots & \vdots & \ddots & \vdots \ 0 & 0 & \dots & 0.77\ \end{bmatrix} $$

Figure (3-29):

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

Using Package Functions for data given in Table 1.2

Loading the file and creating the data frame.

x=read.table("Lab1.DAT",header=FALSE)

Sample Mean

Lab1Intro::SampleMeanVector(x)

Sample Covariance (Biased)

Lab1Intro::SampleBiasedCovarianceVariance(x)

Sample Correlation

Lab1Intro::SampleCorrelationMatrix(x)

Assesments

Clicker Quizes 10%

Assignments 20%

Laboratories 10%

Mid Semester Exam 1 10%

Mid Semester Exam 2 10%

Final Exam 30%

Projects 10%

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