---
title: "Homework 3, CROPS 545, Spring 2020"
author: "Your Name"
date: "March 3, 2020"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Professor: Zhiwu Zhang
## **Due on March 6, 2020, Friday, 3:10PM, PST**

**Hand in:** Email your report (Rmarkdown and knitted .html file) with subject of "CROPS545_HW2" to Zhiwu.Zhang@WSU.edu. Written portions are limited to 500 words or less for each problem. Name your files with the following format: Homework2_firstname_lastname.Rmd and Homework2_firstname_lastname.html

**Objectives:**

1) Simulate phenotypes from genotypes
2) GWAS by correlation
3) Evalueate true and false positives

**Grading Criteria:**

* Problem is adequately addressed
* All code should be bug-free and well commented
* Plots should be properly labeled
* Written portions should be in sentence form and easy to read.

**Remember:** You can use the echo=FALSE chunk option to hide your code in the .html file.

Feel free to add extra sub-problem code chunks as necessary.

### **Problem 1 (20 Pts)**

Sample 10 SNPs as QTNs out of the available SNPs. Simulate QTN effects from a standard normal distribution. Assign genetic effects for each of the 281 individuals. Simulate normal distributed residual effects with appropriate variance to have a heritability of 0.75. Add residual effects to genetic effects to create phenotypes. You can either use the G2P R function or your own custom function. Describe the distribution of genetic effects, residual effects, and phenotypes. Explore the relationships among them.

```{r problem1, echo=FALSE}
# Your code goes here

print('Hello World')
```

THIS IS AN EXAMLE OF WHERE YOUR WRITTEN ANSWERS WILL SHOW UP.

### **Problem, 2 (20 Pts)**

Perform GWAS by using the correlation method. You can either use the GWASbyCor R function or code everything by yourself. Create a Manhattan plot and label the positions of the QTNs.

```{r problem2}
# Your code goes here
```

### **Problem 3 (20 Pts)**

Determine how many QTNs are among the top ten associated SNPs.

```{r problem3}
# Your code goes here
```

### **Problem 4 (20 Pts)**

Count the number of SNPs with P-values smaller than the P-value of the seventh significant QTN.

```{r problem4}
# Your code goes here
```

### **Problem 5 (20 Pts)**

Redo problems 3-4 for 100 replicates. Report the averages and standard deviations.

```{r problem5}
# Your code goes here
```

### **Problem 6 (Extra Credit 20 Pts)**

Simulate phenotypes from genotypes so that the phenotypes have a skewed normal distribution due to genetic effect with a long tail on the right.

```{r problem6}
# Your code goes here
```