lab1.Rmd

---
title: "Stat 423 Lab1"
author: "Mingwei Tang"
date: "January 1, 2015"
output: pdf_document
---
# An example by 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:


## A chunck contains your code

The basic block of code is called __chunk__, the code in the Chunk will be evaluated and printed
```{r simple}
summary(cars)
```

```{r second}
1+1
```


## Embeds plots
You can also embed plots, for example:

```{r Embeds, echo=FALSE,fig.height=4,fig.width=4}
plot(cars)
```

Note that the `echo = FALSE` parameter was added to the code chunk to **prevent** printing of the R code that generated the plot. `fig.height=4` and `fig.width=4`. Controls the height of your figure. 

## manipulates the results 
Somes times you don't to want to display your result

`results="hide"` to hide the results/output (but here the code would still be displayed).

```{r display1,results='hide'}
cars.lm = lm(dist~speed,data=cars)
cars.lm
```
`include=FALSE` to have the chunk evaluated, but neither the code nor its output displayed.
```{r disply2,include=FALSE}
cars.lm2=lm(speed~dist^2,data=cars)
cars.lm2
```


```{r last}
summary(cars.lm2)
```

### add latex equations
Bivariate samples $(X_1,Y_1),\ldots,(X_n,Y_n)$, the sample covariace for $X,Y$ is defined as 
$$\dfrac{1}{n-1}\sum_{i=1}^n (X_i-\bar{X})(Y_i-\bar{Y})$$