Hsuan Lee Exercises

Practicals/Hsuan/Assignment 1/My Info.txt

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+I am from Taiwan, the pronounciation of my name is the same as Shuan.

Practicals/Hsuan/Exercise 1/Exercise_1_HsuanLee.Rmd

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+---
+title: "Exercise 1"
+author: "Hsuan Lee"
+output: 
+  html_document:
+    css: style.css
+---
+
+**8 Monte Carlo Simulation Exercise**
+
+Question a and b
+
+```{r}
+set.seed(9252568)
+
+# n.sample is number of samples that we wanna sample
+# size is the sample size of each sample
+# mean is the sample mean of each sample that we sampled form
+# sd is the sample sd of each sample that we sampled from
+
+sample_samples <- function(n.sample, size, mean, sd){
+
+  # create the matrix to store each values in each sample
+  samples <- matrix(0, nrow = size, ncol = n.sample)
+  colnames(samples) <- c(1:n.sample)
+
+  # create the matrix to store means, absolute bias, SE, 95% CI, sample bias for each sample
+  info_sample <- data.frame(matrix(0, nrow = n.sample, ncol = 6))
+  colnames(info_sample) <- c("means", "abs_bias", "SE", "low_95_CI", "high_95_CI",
+                             "sample_bias")
+
+  # sample samples
+  for (i in 1:n.sample) {
+    samples[,i] <- rnorm(n = size, mean = mean, sd = sd)
+  }
+
+  # display the info of each sample
+  for (i in 1:n.sample) {
+    info_sample[i,1] <- mean(samples[,i])
+    info_sample[i,2] <- abs(info_sample[i,1] - mean)
+    info_sample[i,3] <- sd(samples[,i]) / sqrt(size)
+    info_sample[i,4] <- mean(samples[,i]) - 1.96*info_sample[i,3]
+    info_sample[i,5] <- mean(samples[,i]) + 1.96*info_sample[i,3]
+    info_sample[i,6] <- ifelse((info_sample[i,4] > mean) | (info_sample[i,5] < mean),
+                               "Biased", "Correct")
+  }
+
+  return(info_sample)
+}
+
+# draw the samples
+my_draw <- sample_samples(100, 1000, 2, 0.8) 
+```
+
+Question c
+
+```{r, results='hide', message=F, warning=FALSE}
+library(tidyverse)
+```
+
+```{r, warning = FALSE, message = FALSE, error = FALSE, results='hide', fig.keep = 'all', out.width = "100%", fig.align = 'center'}
+ggplot(data = my_draw, aes(x = 1:100, y = means)) +
+  geom_point(color = "#585858") +
+  geom_errorbar(aes(ymin = low_95_CI, ymax = high_95_CI, colour = sample_bias)) +
+  scale_color_manual(values=c("Blue", "#383838"), name = "Biased Sample", ) +
+  geom_hline(yintercept = 2, color = "Red", linetype = "dashed") +
+  labs(x="Simulations", y = "95% Confident Interval") +
+  theme_classic()
+```
+
+Question d
+
+```{r}
+my_draw %>% filter(sample_bias == "Biased")
+```
+

Practicals/Hsuan/Exercise 1/style.css

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+/* Whole document: */
+body{
+  font-family: Times New Roman;
+  font-size: 16pt;
+}
+/* Headers */
+h1{
+text-align: center;
+font-size: 20pt;
+font-weight: bold;
+}
+h2,h3,h4,h5,h6{
+text-align: center;
+font-size: 16pt;}

Practicals/Hsuan/Exercise 2/HsuanLee_Exercise_2.Rmd

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+---
+title: "Exercise 2"
+author: "Hsuan Lee"
+output: html_document
+---
+
+## Introduction
+
+The study is concerned with whether the number of rat sighting is tied to the population of a city and the waste of food thrown on the streets. 
+
+
+The data analyzed are simulated with 4 variables, they are:
+
+*city_id*: ID number of each city
+*popu*: population of a city in millions.
+*was_food*: the amount of food thrown on the street an year, in tons
+*rat_sight*: the number of rat sighting an year
+
+```{r}
+library(truncnorm) # for function rtruncnorm() that allow to set the max and min for normal dist
+options(scipen = 999)
+```
+
+
+**Simulate the data**
+```{r}
+set.seed(9252568)
+city_id <- c(1:2000)
+popu <- rtruncnorm(n = 2000, a = 0.05, mean = 1, sd = 1)
+was_food <- rtruncnorm(2000, a = 10, mean = 30, sd = 20)
+
+rat_sight <- round(700.5 + 8.7*popu + 12.7*was_food + rnorm(2000, mean = 0.5),1)
+
+rat <- data.frame(city_id, popu, was_food, rat_sight)
+```
+
+**Analysis**
+```{r}
+# operate the linear regression for analyzing
+rat_model <- lm(rat_sight~ popu + was_food, data = rat)
+
+summary(rat_model)
+```
+
+## Replication
+
+**Simulation**
+```{r}
+set.seed(92525568)
+
+city_id <- c(1:2000)
+popu <- rtruncnorm(n = 2000, a = 0.05, mean = 1, sd = 1)
+was_food <- rtruncnorm(2000, a = 10, mean = 30, sd = 20)
+
+rat_sight <- round(700.5 + 8.7*popu + 12.7*was_food + rnorm(2000, mean = 0.5),1)
+
+rat_rep <- data.frame(city_id, popu, was_food, rat_sight)
+```
+
+**Analysis**
+```{r}
+rep <- lm(rat_sight~ popu + was_food, data = rat_rep)
+summary(rep)
+```
+
+The results are quite similar after changing the seed.
+
+```{r}
+sessionInfo()
+```
+
+

Practicals/Hsuan/Exercise 3/HsuanLee_Exercise3.aux

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