index.qmd

---
title: "Sample Report - Data Science Capstone"
author: "Student name"
date: '`r Sys.Date()`'
format:
  html:
    code-fold: true
course: STA 6257 - Advanced Statistical Modeling
bibliography: references.bib # file contains bibtex for references
#always_allow_html: true # this allows to get PDF with HTML features
self-contained: true
execute: 
  warning: false
  message: false
editor: 
  markdown: 
    wrap: 72
---

## Introduction

### What is "mehtod"?

This is an introduction to LASSO regression, which is a non-parametric
estimator that estimates the conditional expectation of two variables
which is random. The goal of a kernel regression is to discover the
non-linear relationship between two random variables. To discover the
non-linear relationship, kernel estimator or kernel smoothing is the
main method to estimate the curve for non-parametric statistics. In
kernel estimator, weight function is known as kernel function
[@efr2008]. Cite this paper [@bro2014principal]. The GEE [@wang2014].
The PCA [@daffertshofer2004pca]

This is my work and I want to add more work...

### Related work

This section is going to cover the literature review...

## Methods

The common non-parametric regression model is
$Y_i = m(X_i) + \varepsilon_i$, where $Y_i$ can be defined as the sum of
the regression function value $m(x)$ for $X_i$. Here $m(x)$ is unknown
and $\varepsilon_i$ some errors. With the help of this definition, we
can create the estimation for local averaging i.e. $m(x)$ can be
estimated with the product of $Y_i$ average and $X_i$ is near to $x$. In
other words, this means that we are discovering the line through the
data points with the help of surrounding data points. The estimation
formula is printed below [@R-base]:

$$
M_n(x) = \sum_{i=1}^{n} W_n (X_i) Y_i  \tag{1}
$$ $W_n(x)$ is the sum of weights that belongs to all real numbers.
Weights are positive numbers and small if $X_i$ is far from $x$.

Another equation:

$$
y_i = \beta_0 + \beta_1 X_1 +\varepsilon_i
$$

## Analysis and Results

### Data and Visualization

A study was conducted to determine how...


```{r, warning=FALSE, echo=T, message=FALSE}
# loading packages 
library(tidyverse)
library(knitr)
library(ggthemes)
library(ggrepel)
library(dslabs)
```

```{r, warning=FALSE, echo=TRUE}
# Load Data
kable(head(murders))

ggplot1 = murders %>% ggplot(mapping = aes(x=population/10^6, y=total)) 

  ggplot1 + geom_point(aes(col=region), size = 4) +
  geom_text_repel(aes(label=abb)) +
  scale_x_log10() +
  scale_y_log10() +
  geom_smooth(formula = "y~x", method=lm,se = F)+
  xlab("Populations in millions (log10 scale)") + 
  ylab("Total number of murders (log10 scale)") +
  ggtitle("US Gun Murders in 2010") +
  scale_color_discrete(name = "Region")+
      theme_bw()
  

```

### Statistical Modeling

```{r}

```

### Conclusion

## References