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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).
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.
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?
For problem 5, we will use an adapted version of the weather data from Tidyverse.
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))| station | element | month1 | month2 |
|---|---|---|---|
| A | temp_min | 11.4 | NA |
| A | temp_max | 25.6 | NA |
| A | temp_min | NA | 16.8 |
| A | temp_max | NA | 28.7 |
| B | temp_min | 17.7 | NA |
| B | temp_max | 28.0 | NA |
| B | temp_min | NA | 11.1 |
| B | temp_max | NA | 26.8 |
| C | temp_min | 20.0 | NA |
| C | temp_max | 24.9 | NA |
| C | temp_min | NA | 14.7 |
| C | temp_max | NA | 33.4 |
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.)