In abinashborah/Lab1Intro: Package for Lab1

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Creating a package in R

A package is a fundamental unit of reproducible R code which include reusable R functions along with their documentation and sample data.

Documentation about package making in R can be found at https://r-pkgs.org/

About this exercise

In this Lab1 exercise, I have created an R package "Lab1Intro" that contains three functions to create from a data array X:

1. the sample mean vector : mean_vector(X)
2. the sample (biased) covariance matrix : covariance_matrix(X)
3. the sample correlation matrix : correlation_matrix(X)

My package is available at the github repository https://github.com/abinashborah/Lab1Intro

Following formulae are used in calculating the above quantities:

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

$${s}{ik} = \frac{1}{n}\sum{j=1}^{n} (x_{ji}-\overline{x}i)(x{jk}-\overline{x}_k) \hspace{1cm}i = 1, 2,...,p,\hspace{0.5cm}k = 1, 2,...,p$$

$${r}{ik} = \frac{{s}{ik}}{{\sqrt{{s}{ii}}}{\sqrt{{s}{kk}}}} = \frac{\sum_{j=1}^{n} (x_{ji}-\overline{x}i)(x{jk}-\overline{x}k)} {\sqrt{\sum{j=1}^{n}(x_{ji}-\overline{x}i)^2}\sqrt{\sum{j=1}^{n}(x_{jk}-\overline{x}_k)^2}} \hspace{1cm}i = 1, 2,...,p,\hspace{0.5cm}k = 1, 2,...,p$$

$$\textbf{S} = \frac{1}{n-1}\textbf{X}^/\left(\textbf{I} - \frac{1}{n}\textbf{11}^/\right)\textbf{X}$$

\usepackage{amsmath}

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

$$\textbf{R} = \textbf{D}^{{-1}/{2}}\textbf{S}\textbf{D}^{{-1}/{2}}$$

A demonstration of the package is shown below:

# Loading the package
library(Lab1Intro)

# Loading the data
data("T1_2")

# Finding the mean vector for the data array using the function mean_vector()
Lab1Intro::mean_vector(T1_2)

# Finding the covariance matrix for the data array using the function covariance_matrix()
Lab1Intro::covariance_matrix(T1_2)

# Finding the correlation matrix for the data array using the function correlation_matrix()
Lab1Intro::correlation_matrix(T1_2)

Assessment for this course MATH 5793 is as follows:

1. Clicker quiz, each class and lab (Total 10%)
2. 4 assignments (Total 20%)
3. Laboratories (Total 10%)
4. 2 Mid-term exams (10% each, Total 20%)
5. 3 Projects (More weighting on third project, Total 10%)
6. 1 Final exam (30%)

abinashborah/Lab1Intro documentation built on Jan. 26, 2020, 4:09 a.m.