index.Rmd

---
title: "Applied Econometrics"
site: workflowr::wflow_site
output:  
  html_document
---

```{r eval=T, echo=F, warning=F, message=F}
# Packages
library(knitr)
library(tidyverse)
library(readxl)
library(broom)
library(stargazer)

library(gridExtra)
```

```{r eval=T, echo=F, warning=F}
# Data Import
corr_1 <- read_excel("data/corr_1.xlsx")
cancer_test <- read_excel("data/cancer_test.xlsx")
lag <- read_excel("data/lag.xlsx")
```

# Setting Up

## Packages 
* **tidyverse** - basic package for data wrangling

* **readxl** - allows inputs of excel files

* **readr** - allows inputs of text files

* **broom** - result organization with tidy tibbles

* **stargazer** - better organized regression outputs 


## Output Tables

# Initial Statistics

## Correlation

### One Variable

Correlation is the strength of linear assosciation. It can be sensitive to outliers.
```{r eval=T, echo=T}
cor <- corr_1 %>% 
  summarise(r=cor(X, Y)) %>% 
  pull(r)
cor
```
Correlations can also be visualized through scatterplots which are the foundation of econometric analysis. 
```{r eval=T, echo=T, message=F}
ggplot(corr_1, aes(x=X, y=Y))+
  geom_point(alpha=0.5)+
  geom_smooth(method = "lm", se=F)
```
```{r eval=T, echo=F}
remove(cor)
```

### Multiple Variables

# Simple Linear Regression
Linear regression can be performed by:
```{r eval=T, echo=T}
lm.model <- lm(Cancer_Diagnosis~Median_Income+Median_Age+Percent_Black, data=cancer_test)
lm.res <- augment(lm.model) # visualize all residuals in table form
```

## Least Square Lines
The following code is for two variables:
```{r eval=T, echo=T}
lm.ls <- lm.res %>% 
  summarize(x.sd=sd(Median_Age), y.sd=sd(Cancer_Diagnosis),
            cor=cor(Cancer_Diagnosis, Median_Age)) %>%
  mutate(slope=(x.sd/y.sd)*cor) # Slope = 0.015
```
When we look at the **lm** model, the slope is also 0.015.

## Visualizing Assumptions 

**a.** Linearity (scatterplot + residual plot - residuals needs to be random)

**b.** Nearly normal residuals (histogram of residuals or QQ residual plot)

**c.** Constant variability (residual plot)

[Link](https://gallery.shinyapps.io/slr_diag/) for interactive regression diagnostic test. 

```{r eval=T, echo=T}
a <- ggplot(lm.res, aes(x=.fitted, y=.resid))+
  geom_point()+
  geom_hline(yintercept = 0, linetype="dashed", color="red")+
  labs(title="Residuals vs Fitted Values", x="Fitted Values", y="Residuals")
b <- ggplot(lm.res, aes(x=.resid))+
  geom_density()+
  labs(title="Histogram of residuals", x="Residuals") #geom_density can also be added
c <- ggplot(lm.res, aes(sample=.resid))+
  stat_qq()+
  stat_qq_line()
```
```{r eval=T, echo=F}
grid.arrange(a, b, c, ncol=3)
remove(a,b,c)
```

# Dummy Variables

# Hypothesis Testing

# Lagged Regression
```{r eval=T, echo=T}
lag1 <- lag %>% 
  mutate(Work_1 = lag(Work, 1)) %>% 
  mutate(Work_2 = lag(Work, 2))
kable(head(lag1))
```

Using this we can perform linear regression the normal way:
```{r eval=F, echo=T}
reg <- lm(Income ~ Work+Work_1+Work_2, data=dataset)
```
```{r eval=T, echo=F}
remove(lag, lag1)
```