R02_knitr_basic.Rmd

---
title: "Markdown file - a basic example"
author: "Insert your name here"
date: "`r Sys.Date()`"
output:
  html_document:
    df_print: paged
---

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:

```{r}
summary(mtcars)
```

You can hide the `summary(mtcars)` R code from the knitted output:
(this is done using the `echo=FALSE` parameter)  
Note: two empty spaces at the end of a line force a line return

* Lists are insterted using `*`
* Horizontal lines `---`
* Headings are produced using `#`, `##`, etc. 
* Math expression are inserted through `LaTex` syntax: $\hat{\beta}_1$, $\sigma_i^2$

---

# Heading 1
## Heading 2
### Heading 3
#### Another `R` code \& output goes here:


```{r}
summary(cars)
```

Additional information on the data:
```{r, echo=T}
str(mtcars)
```


You can also embed plots, for example:

```{r, echo=T}
plot(mtcars)
```


---

## Linear regression models (LRMs) in R - example

* Using the `mtcars` dataset, we may perform LRM estimation 

* For example, we may estimate a model:

$$ 
\text{MPG}_i = \beta_0 + \beta_1 \text{HP}_i + \beta_2 \text{WT}_i + \varepsilon_i
$$

* In `R`, we use a general syntax `y ~ x1 + x2` to cast the regression equation (the intercept is included by default).


```{r}
lrm1 <- lm(mpg~hp+wt, data=mtcars)
summary(lrm1)
#
# Fitted values 
head(cbind(mtcars$mpg, predict(lrm1)))
```

* The above code is just a basic example of LRM estimation & output syntax.  

* Additional (introductory-level) LRM topics are discussed in `R03_LRM_self_study_material.R`