---
title: "Statistics 652 - Section 1 or 2: Homework 1"
author: "Prof. Eric A. Suess"
date: " February 17, 2020"
output: html_notebook
---

### Exercise 7.1

Using the [ModernDive](moderndive.com) book, [Chapter 8 Bootstrapping and Confidence Intervals](https://moderndive.com/8-confidence-intervals.html).


```{r}
library(pacman)

p_load(mdsr, tidyverse, mosaicData, infer)
```

```{r}
Gestation
```

```{r}
Gestation %>% select(age) %>%
  drop_na(age) %>%
  summarize( n = n(), age_mean = mean(age, na.rm=TRUE),
             age_sd = sd(age, na.rm=TRUE))
  
```

```{r}
Gestation %>% select(age) %>%
  drop_na(age) %>%
  ggplot(aes(x = age)) +
  geom_histogram(binwidth = 1, color = "white")
  
```

```{r}
x_bar <- Gestation %>% drop_na(age) %>%
  select(age) %>% 
  specify(response = age) %>% 
  calculate(stat = "mean")
x_bar
```

Generate the bootstrap distribution of the sample mean.  Take 1000 random samples with replacement from the original sample and compute the sample mean of each of the bootstrap samples.

```{r}
Gestation_distribution <- Gestation %>% drop_na(age) %>%
  select(age) %>% 
  specify(response = age) %>% 
  generate(reps = 1000, type = "bootstrap") %>%
  calculate(stat = "mean") 
```

Boostrap distribution.

```{r}
Gestation_distribution %>% visualize()

```

Boostrap Confidence Interval

```{r}
Gestation_distribution %>% 
  get_confidence_interval(level = 0.95, type = "percentile")
```

```{r}
percentile_ci <- Gestation_distribution %>%  
  get_confidence_interval(level = 0.95, type = "percentile")
percentile_ci
```


```{r}
Gestation_distribution %>% visualize() + 
  shade_confidence_interval(endpoints = percentile_ci)

```

The traditional on sample confidence interval.

```{r}
standard_error_ci <- Gestation_distribution %>% 
  get_confidence_interval(type = "se", point_estimate = x_bar)
standard_error_ci
```


```{r}
 Gestation_distribution %>% visualize() + 
  shade_confidence_interval(endpoints = standard_error_ci)
```

### Exercise 7.2


```{r}
Gestation %>% select(age) %>%
  drop_na(age) %>%
  summarize( n = n(), age_mean = mean(age, na.rm=TRUE),
             age_sd = sd(age, na.rm=TRUE))
  
```


```{r}
Gestation_distribution <- Gestation %>% drop_na(age) %>% 
  select(age) %>% 
  specify(response = age) %>% 
  generate(reps = 1000, type = "bootstrap") %>%
  calculate(stat = "median") 
```

Boostrap distribution.

```{r}
Gestation_distribution %>% visualize()

```


```{r}
percentile_ci <- Gestation_distribution %>%  
  get_confidence_interval(level = 0.95, type = "percentile")
percentile_ci
```


```{r}
Gestation_distribution %>% visualize() + 
  shade_confidence_interval(endpoints = percentile_ci)

```

### Exercise 7.5

Read [Appendix E Regression modeling](https://mdsr-book.github.io/excerpts/mdsr-regression.pdf)

```{r}
ds
```