R Practice
Assignment 1
Sal Pollastro
1 Directions
The problem set is worth 100 points.
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## [1] 4Calculate \(2*3\):
2*3## [1] 6Calculate \(\frac{(2+2)\times (3^2 + 5)}{(6/4)}\):
((2+2)*((3^2)+5))/(6/4)## [1] 37.333333 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).
diamonds %>%
summarise(mean(price))## # A tibble: 1 x 1
## `mean(price)`
## <dbl>
## 1 3933.Calculate the average, median and standard deviation price of a diamond. Use the %>% and summarise() syntax.
diamonds %>%
summarise(mean(price), median(price), sd(price))## # A tibble: 1 x 3
## `mean(price)` `median(price)` `sd(price)`
## <dbl> <dbl> <dbl>
## 1 3933. 2401 3989.Use group_by() to group diamonds by color, then use summarise() to calculate the average price and the standard deviation in price by color:
diamonds %>%
group_by(color) %>%
summarise(mean(price), sd(price))## # A tibble: 7 x 3
## color `mean(price)` `sd(price)`
## <ord> <dbl> <dbl>
## 1 D 3170. 3357.
## 2 E 3077. 3344.
## 3 F 3725. 3785.
## 4 G 3999. 4051.
## 5 H 4487. 4216.
## 6 I 5092. 4722.
## 7 J 5324. 4438.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:
diamonds %>%
filter(depth <= 62) %>%
group_by(clarity) %>%
summarise(max(price))## # A tibble: 8 x 2
## clarity `max(price)`
## <ord> <int>
## 1 I1 15223
## 2 SI2 18784
## 3 SI1 18797
## 4 VS2 18823
## 5 VS1 18795
## 6 VVS2 18730
## 7 VVS1 18682
## 8 IF 18806Use mutate() and log() to create a new variable to the data called “log_price”. Make sure you add the variable to the dataset diamonds.
diamonds = diamonds %>%
mutate(log_price = log(price))(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:
diamonds %>%
ggplot(aes(x = price)) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Use geom_density() to plot the density of log prices (the variable you added to the data frame):
diamonds %>%
ggplot(aes(x = log_price)) +
geom_density()
Use geom_point() to plot carats against log prices (i.e. carats on the x-axis, log prices on the y-axis):
diamonds %>%
ggplot(aes(x = carat, y = log_price)) +
geom_point()
Same as above, but now add a regression line with geom_smooth():
diamonds %>%
ggplot(aes(x = carat, y = log_price)) +
geom_point() +
geom_smooth()## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Use stat_summary() to make a bar plot of average log price by cut:
diamonds %>%
ggplot() +
stat_summary(
mapping = aes(x= cut, y = log_price
, fun.y = mean(log_price))
)## Warning: Ignoring unknown aesthetics: fun.y## No summary function supplied, defaulting to `mean_se()`
Same as above but change the theme to theme_classic():
diamonds %>%
ggplot() +
stat_summary(
mapping = aes(x= cut, y = log_price
, fun.y = mean(log_price))
) +
theme_classic()## Warning: Ignoring unknown aesthetics: fun.y## No summary function supplied, defaulting to `mean_se()`
5 Inference
Use lm() to estimate the model
\[ log(\text{price}) = \beta_0 + \beta_1 \text{carat} + \beta_2 \text{table} + \varepsilon \]
and store the output in an object called “m1”:
m1 = lm(log_price ~ carat, table, data = diamonds)Use summary() to view the output of “m1”:
summary(m1)##
## Call:
## lm(formula = log_price ~ carat, data = diamonds, subset = table)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.05975 -0.03780 -0.03780 0.03763 1.41354
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.749561 0.003056 1881.7 <2e-16 ***
## carat 0.973751 0.010504 92.7 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08224 on 53938 degrees of freedom
## Multiple R-squared: 0.1374, Adjusted R-squared: 0.1374
## F-statistic: 8594 on 1 and 53938 DF, p-value: < 2.2e-16Use lm() to estimate the model
\[ log(\text{price}) = \beta_0 + \beta_1 \text{carat} + \beta_2 \text{table} + \beta_3 \text{depth} + \varepsilon \]
and store the output in an object called “m2”:
m2 = lm(log_price ~ carat, table, depth, data = diamonds)Use summary() to view the output of “m2”:
summary(m2)##
## Call:
## lm(formula = log_price ~ carat, data = diamonds, subset = table,
## weights = depth)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -0.4675 -0.2992 -0.2954 0.2941 11.2629
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.747423 0.003092 1858.54 <2e-16 ***
## carat 0.980933 0.010622 92.35 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.646 on 53938 degrees of freedom
## Multiple R-squared: 0.1365, Adjusted R-squared: 0.1365
## F-statistic: 8528 on 1 and 53938 DF, p-value: < 2.2e-16