Enter your answers in the empty code chunks. Replace “# your code here” with your code.

Make sure you run this chunk before attempting any of the problems:

library(tidyverse)

2 Basics

Calculate 2+2$2+2$:

2+2

## [1] 4

Calculate 2∗3$2\ast 3$:

# your code here

Calculate (2+2)×(32+5)(6/4)$\frac{(2+2)\times (3^2+5)}{\left(6/4\right)}$:

# your code here

3 dplyr

Let’s work with the data set diamonds:

data(diamonds) # this will load a dataset called "diamonds"

Calculate the average price of a diamond. Use the %>% and summarise() syntax (hint: see lectures).

# your code here

Calculate the average, median and standard deviation price of a diamond. Use the %>% and summarise() syntax.

# your code here

Use group_by() to group diamonds by color, then use summarise() to calculate the average price and the standard deviation in price by color:

# your code here

Use filter() to remove observations with a depth greater than 62, then usegroup_by() to group diamonds by clarity, then use summarise() to find the maximum price of a diamond by clarity:

# your code here

Use mutate() and log() to create a new variable to the data called “log_price”. Make sure you add the variable to the dataset diamonds.

# your code here

(Hint: if I wanted to add a variable called “max_price” that calculates the max price, the code would look like this:)

diamonds = diamonds %>% 
  mutate(max_price = max(price))

4 ggplot2

Continue using diamonds.

Use geom_histogram() to plot a histogram of prices:

# your code here

Use geom_density() to plot the density of log prices (the variable you added to the data frame):

# your code here

Use geom_point() to plot carats against log prices (i.e. carats on the x-axis, log prices on the y-axis):

# your code here

Same as above, but now add a regression line with geom_smooth():

# your code here

Use stat_summary() to make a bar plot of average log price by cut:

# your code here

Same as above but change the theme to theme_classic():

# your code here

5 Inference

Use lm() to estimate the model

log(price)=β0+β1carat+β2table+ε$log\left(\text{price}\right)={\beta }_0+{\beta }_1\text{carat}+{\beta }_2\text{table}+\epsilon$

and store the output in an object called “m1”:

# your code here

Use summary() to view the output of “m1”:

# your code here

Use lm() to estimate the model

log(price)=β0+β1carat+β2table+β3depth+ε$log\left(\text{price}\right)={\beta }_0+{\beta }_1\text{carat}+{\beta }_2\text{table}+{\beta }_3\text{depth}+\epsilon$

and store the output in an object called “m2”:

# your code here

Use summary() to view the output of “m2”:

# your code here