1 R Markdown

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.

When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:

1.1 Numerical Summary

summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

1.2 Including Plots

You can also embed plots, for example:

Scatter plot of something

Scatter plot of something

1.3 IncludingExternal Images

include_graphics("C:\\peng\\STA321\\LinearReg\\ram.png")
#include_graphics("ram.png")

2 Writing Equations in RMarkdown

2.1 In-line Equations

The linear regression model is defined to be of \(y = \alpha_0 + \alpha_1 x + \epsilon\)

2.2 Standalone Equation

The variance of a given population \(\{ x_1, x_2, \cdots, x_{15}, \cdots, x_n \}\) is given by

\[ \sigma^2= \frac{\sum_{i = 1}^n(x_i-\mu)^2}{N}. \]

The Pearson correlation coefficent is given by

\[ r=\frac{\sum_{i=n}^n(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{(x_i-\bar{x})^2} \times\sqrt{(y_i-\bar{y})^2}} \]

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.