R Practice
Assignment 1 - BE
Thomas Laffey
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)## Warning: package 'tidyverse' was built under R version 4.1.32 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(avg_price = mean(price))## # A tibble: 1 x 1
## avg_price
## <dbl>
## 1 3933.Calculate the average, median and standard deviation price of a diamond. Use the %>% and summarise() syntax.
diamonds %>%
summarise(avg_price = mean(price), #average price of a diamond
median_price = median(price), #median price of a diamond
sd_price = sd(price)) #standard deviation of diamond price## # A tibble: 1 x 3
## avg_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(avg_price = mean(price), #average price by color
sd_price = sd(price)) #standard deviation by color## # A tibble: 7 x 3
## color avg_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) %>% #Filter our diamonds with depth greater than 62
group_by(clarity) %>% #Group by clarity
summarise(max_price = max(price)) #max diamond price by clarity with depth >62## # A tibble: 8 x 2
## clarity max_price
## <ord> <int>
## 1 I1 18531
## 2 SI2 18804
## 3 SI1 18818
## 4 VS2 18791
## 5 VS1 18500
## 6 VVS2 18768
## 7 VVS1 18777
## 8 IF 18552Use 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)) #Added new variable that is the log of 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() +
labs(x = "Log Prices")
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() +
labs(x = "Carats", y = "Log Price")
Same as above, but now add a regression line with geom_smooth():
diamonds %>%
ggplot(aes(x = carat, y = log_price)) +
geom_point() +
geom_smooth(method = "lm") +
labs(x = "Carats", y = "Log Price")## `geom_smooth()` using formula 'y ~ x'
Use stat_summary() to make a bar plot of average log price by cut:
diamonds %>%
ggplot(aes(x = cut, y = log_price)) +
stat_summary(fun="mean", geom="bar") +
labs(title = "Average Log Price by Cut")
Same as above but change the theme to theme_classic():
diamonds %>%
ggplot(aes(x = cut, y = log_price)) +
stat_summary(fun="mean", geom="bar") +
labs(title = "Average Log Price by Cut") +
theme_classic() #change to classic theme
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(formula = log_price ~ carat + table, data = diamonds)
#log_price as a function carats and tableUse summary() to view the output of “m1”:
summary(m1)##
## Call:
## lm(formula = log_price ~ carat + table, data = diamonds)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.2930 -0.2453 0.0338 0.2571 1.5573
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.4527654 0.0443008 145.658 < 2e-16 ***
## carat 1.9733423 0.0036678 538.015 < 2e-16 ***
## table -0.0041876 0.0007781 -5.382 7.4e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3971 on 53937 degrees of freedom
## Multiple R-squared: 0.8469, Adjusted R-squared: 0.8469
## F-statistic: 1.491e+05 on 2 and 53937 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(formula = log_price ~ carat+table+depth, data = diamonds)
#log price as a function of carat, table, and depthUse summary() to view the output of “m2”:
summary(m2)##
## Call:
## lm(formula = log_price ~ carat + table + depth, data = diamonds)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.2280 -0.2437 0.0328 0.2578 1.5453
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.045098 0.101427 79.32 <2e-16 ***
## carat 1.978928 0.003672 538.99 <2e-16 ***
## table -0.008539 0.000815 -10.48 <2e-16 ***
## depth -0.021810 0.001251 -17.44 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.396 on 53936 degrees of freedom
## Multiple R-squared: 0.8477, Adjusted R-squared: 0.8477
## F-statistic: 1.001e+05 on 3 and 53936 DF, p-value: < 2.2e-16