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title: "Lab 2"
author: "STAT 302"
date: "Due Date Here"
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---

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

*If you collaborated with anyone, you must include "Collaborated with: FIRSTNAME LASTNAME" at the top of your lab!*

## Part 1. More on Functions (10 points)

**1a.** (3 points) The hard-threshold function is defined as 
$$f_\lambda(x) = \begin{cases} x & |x| \geq \lambda\\ 0 & |x| < \lambda \end{cases}$$
Write an R function that takes two parameters, numeric input `x` and a threshold `lambda`.
Your function should return the value of $f_\lambda(x)$ and work for vector input `x` of any length.

**1b.** (1 point) Set $\lambda = 4$, demonstrate your function on the vector `c(-5, -3, 0, 3, 5)`.

(*Hint: the output should be the vector `-5, 0, 0, 0, 5`*)

**1c.** (1 point) Set $\lambda = 2$, demonstrate your function on the vector `c(-7, -5, -3, 0, 3, 5, 7)`.

**2a.** (3 points) The soft-threshold function is defined as 
$$g_\lambda(x) = \begin{cases} sign(x)(|x| - \lambda) & |x| \geq \lambda\\ 0 & |x| < \lambda \end{cases}$$
Write an R function that takes two parameters, numeric input `x` and a threshold `lambda`.
Your function should return the value of $g_\lambda(x)$ and work for vector input `x` of any length.

**2b.** (1 point) Set $\lambda = 4$, demonstrate your function on the vector `c(-5, -3, 0, 3, 5)`.

(*Hint: the output should be the vector `-1, 0, 0, 0, 1`*)

**2c.** (1 point) Set $\lambda = 2$, demonstrate your function on the vector `c(-7, -5, -3, 0, 3, 5, 7)`.

## Part 2. Lists (6 points)

Many popular functions in R output lists in order to return multiple objects of different types and lengths. Here we will look at the function `lm`, which performs linear regression. 

First, run the following code to create an object of class `lm`.

```{r}
linearMod <- lm(dist ~ speed, data = cars) 
```

**3a.** (2 points) What are the names of the items in the list `linearMod`?

**3b.** (4 points) Store the `coefficients` within `linearMod` as a new variable. What are the coefficients and their interpretations?

## Part 3. Data (4 points)

For problem 5, we will use an adapted version of the weather data from Tidyverse.

```{r}
library(kableExtra)
weather <- data.frame("station" = rep(c("A", "B", "C"), each = 4),
                      "element" = rep(c("temp_min", "temp_max"), 2),
                      "month1"  = c(11.4, 25.6, NA, NA, 17.7, 28.0,
                                    NA, NA, 20.0, 24.9, NA, NA),
                      "month2"  = c(NA, NA, 16.8, 28.7, NA, NA,
                                    11.1, 26.8, NA, NA, 14.7, 33.4))
kable_styling(kable(weather))
```

**4.** (4 points) Use `kable()` to present a tidied up version of this data, without any NA values. Do you prefer the tidied version? Why or why not? (Hint: My table has 4 variables, 6 observations, and no `NA` values. I only kept one of the variables unchanged.)