HW6
Robert Miller
Objective:
You will use R to analyze the built-in airquality dataset, applying descriptive statistics techniques to explore environmental data. The assignment covers measures of central tendency, spread, histograms, boxplots, scatterplots, correlations, and summary tables, aligning with the Week 6 agenda on Descriptive Statistics.
Dataset
Source: Built-in R dataset airquality.
Description: Contains 153 observations of daily air quality measurements in New York from May to September 1973.
Variables (selected for this assignment):
- Ozone: Mean ozone concentration in parts per billion (ppb, numeric).
- Temp: Maximum daily temperature in Fahrenheit (numeric).
- Wind: Average wind speed in miles per hour (numeric).
- Month: Month of the year (5 = May, 6 = June, …, 9 = September, categorical).
Notes
-The airquality dataset has missing values in Ozone and Solar.R. The code uses na.rm = TRUE or use = “complete.obs” to handle them.
-If you encounter errors, check that tidyverse and corrplot are installed and loaded.
-Feel free to modify plot aesthetics (e.g., colors, binwidth) to enhance clarity.
Instructions:
Complete the following tasks using R to analyze the airquality dataset. Submit your Rpubs link that includes code, outputs (tables and plots), and written interpretations for each task. Ensure you load the dataset using data(airquality) and install/load the tidyverse and corrplot packages.
#Load your dataset
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.1 ✔ stringr 1.5.2
## ✔ ggplot2 4.0.0 ✔ tibble 3.3.0
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.1.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(corrplot)## corrplot 0.95 loadeddata("airquality")
airquality## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2
## 3 12 149 12.6 74 5 3
## 4 18 313 11.5 62 5 4
## 5 NA NA 14.3 56 5 5
## 6 28 NA 14.9 66 5 6
## 7 23 299 8.6 65 5 7
## 8 19 99 13.8 59 5 8
## 9 8 19 20.1 61 5 9
## 10 NA 194 8.6 69 5 10
## 11 7 NA 6.9 74 5 11
## 12 16 256 9.7 69 5 12
## 13 11 290 9.2 66 5 13
## 14 14 274 10.9 68 5 14
## 15 18 65 13.2 58 5 15
## 16 14 334 11.5 64 5 16
## 17 34 307 12.0 66 5 17
## 18 6 78 18.4 57 5 18
## 19 30 322 11.5 68 5 19
## 20 11 44 9.7 62 5 20
## 21 1 8 9.7 59 5 21
## 22 11 320 16.6 73 5 22
## 23 4 25 9.7 61 5 23
## 24 32 92 12.0 61 5 24
## 25 NA 66 16.6 57 5 25
## 26 NA 266 14.9 58 5 26
## 27 NA NA 8.0 57 5 27
## 28 23 13 12.0 67 5 28
## 29 45 252 14.9 81 5 29
## 30 115 223 5.7 79 5 30
## 31 37 279 7.4 76 5 31
## 32 NA 286 8.6 78 6 1
## 33 NA 287 9.7 74 6 2
## 34 NA 242 16.1 67 6 3
## 35 NA 186 9.2 84 6 4
## 36 NA 220 8.6 85 6 5
## 37 NA 264 14.3 79 6 6
## 38 29 127 9.7 82 6 7
## 39 NA 273 6.9 87 6 8
## 40 71 291 13.8 90 6 9
## 41 39 323 11.5 87 6 10
## 42 NA 259 10.9 93 6 11
## 43 NA 250 9.2 92 6 12
## 44 23 148 8.0 82 6 13
## 45 NA 332 13.8 80 6 14
## 46 NA 322 11.5 79 6 15
## 47 21 191 14.9 77 6 16
## 48 37 284 20.7 72 6 17
## 49 20 37 9.2 65 6 18
## 50 12 120 11.5 73 6 19
## 51 13 137 10.3 76 6 20
## 52 NA 150 6.3 77 6 21
## 53 NA 59 1.7 76 6 22
## 54 NA 91 4.6 76 6 23
## 55 NA 250 6.3 76 6 24
## 56 NA 135 8.0 75 6 25
## 57 NA 127 8.0 78 6 26
## 58 NA 47 10.3 73 6 27
## 59 NA 98 11.5 80 6 28
## 60 NA 31 14.9 77 6 29
## 61 NA 138 8.0 83 6 30
## 62 135 269 4.1 84 7 1
## 63 49 248 9.2 85 7 2
## 64 32 236 9.2 81 7 3
## 65 NA 101 10.9 84 7 4
## 66 64 175 4.6 83 7 5
## 67 40 314 10.9 83 7 6
## 68 77 276 5.1 88 7 7
## 69 97 267 6.3 92 7 8
## 70 97 272 5.7 92 7 9
## 71 85 175 7.4 89 7 10
## 72 NA 139 8.6 82 7 11
## 73 10 264 14.3 73 7 12
## 74 27 175 14.9 81 7 13
## 75 NA 291 14.9 91 7 14
## 76 7 48 14.3 80 7 15
## 77 48 260 6.9 81 7 16
## 78 35 274 10.3 82 7 17
## 79 61 285 6.3 84 7 18
## 80 79 187 5.1 87 7 19
## 81 63 220 11.5 85 7 20
## 82 16 7 6.9 74 7 21
## 83 NA 258 9.7 81 7 22
## 84 NA 295 11.5 82 7 23
## 85 80 294 8.6 86 7 24
## 86 108 223 8.0 85 7 25
## 87 20 81 8.6 82 7 26
## 88 52 82 12.0 86 7 27
## 89 82 213 7.4 88 7 28
## 90 50 275 7.4 86 7 29
## 91 64 253 7.4 83 7 30
## 92 59 254 9.2 81 7 31
## 93 39 83 6.9 81 8 1
## 94 9 24 13.8 81 8 2
## 95 16 77 7.4 82 8 3
## 96 78 NA 6.9 86 8 4
## 97 35 NA 7.4 85 8 5
## 98 66 NA 4.6 87 8 6
## 99 122 255 4.0 89 8 7
## 100 89 229 10.3 90 8 8
## 101 110 207 8.0 90 8 9
## 102 NA 222 8.6 92 8 10
## 103 NA 137 11.5 86 8 11
## 104 44 192 11.5 86 8 12
## 105 28 273 11.5 82 8 13
## 106 65 157 9.7 80 8 14
## 107 NA 64 11.5 79 8 15
## 108 22 71 10.3 77 8 16
## 109 59 51 6.3 79 8 17
## 110 23 115 7.4 76 8 18
## 111 31 244 10.9 78 8 19
## 112 44 190 10.3 78 8 20
## 113 21 259 15.5 77 8 21
## 114 9 36 14.3 72 8 22
## 115 NA 255 12.6 75 8 23
## 116 45 212 9.7 79 8 24
## 117 168 238 3.4 81 8 25
## 118 73 215 8.0 86 8 26
## 119 NA 153 5.7 88 8 27
## 120 76 203 9.7 97 8 28
## 121 118 225 2.3 94 8 29
## 122 84 237 6.3 96 8 30
## 123 85 188 6.3 94 8 31
## 124 96 167 6.9 91 9 1
## 125 78 197 5.1 92 9 2
## 126 73 183 2.8 93 9 3
## 127 91 189 4.6 93 9 4
## 128 47 95 7.4 87 9 5
## 129 32 92 15.5 84 9 6
## 130 20 252 10.9 80 9 7
## 131 23 220 10.3 78 9 8
## 132 21 230 10.9 75 9 9
## 133 24 259 9.7 73 9 10
## 134 44 236 14.9 81 9 11
## 135 21 259 15.5 76 9 12
## 136 28 238 6.3 77 9 13
## 137 9 24 10.9 71 9 14
## 138 13 112 11.5 71 9 15
## 139 46 237 6.9 78 9 16
## 140 18 224 13.8 67 9 17
## 141 13 27 10.3 76 9 18
## 142 24 238 10.3 68 9 19
## 143 16 201 8.0 82 9 20
## 144 13 238 12.6 64 9 21
## 145 23 14 9.2 71 9 22
## 146 36 139 10.3 81 9 23
## 147 7 49 10.3 69 9 24
## 148 14 20 16.6 63 9 25
## 149 30 193 6.9 70 9 26
## 150 NA 145 13.2 77 9 27
## 151 14 191 14.3 75 9 28
## 152 18 131 8.0 76 9 29
## 153 20 223 11.5 68 9 30Tasks and Questions
Task 1: Measures of Central Tendency and Spread
Using functions you learned this week, compute mean, median, standard deviation, min, and max separately for Ozone, Temp, and Wind.
#Your code for Ozone goes here
mean_ozone <- function() {
mean(airquality$Ozone, na.rm = T)
}
median_ozone <- function() {
median(airquality$Ozone, na.rm = T)
}
sd_ozone <- function() {
sd(airquality$Ozone, na.rm = T)
}
min_ozone <- function() {
min(airquality$Ozone, na.rm = T)
}
max_ozone <- function() {
max(airquality$Ozone, na.rm = T)
}
mean_ozone()## [1] 42.12931median_ozone()## [1] 31.5sd_ozone()## [1] 32.98788min_ozone()## [1] 1max_ozone()## [1] 168#Your code for Temp goes here
mean_temp <- function() {
mean(airquality$Temp, na.rm = T)
}
median_temp <- function() {
median(airquality$Temp, na.rm = T)
}
sd_temp <- function() {
sd(airquality$Temp, na.rm = T)
}
min_temp <- function() {
min(airquality$Temp, na.rm = T)
}
max_temp <- function() {
max(airquality$Temp, na.rm = T)
}
mean_temp()## [1] 77.88235median_temp()## [1] 79sd_temp()## [1] 9.46527min_temp()## [1] 56max_temp()## [1] 97#Your code for Wind goes here
mean_wind <- function() {
mean(airquality$Wind, na.rm = T)
}
median_wind <- function() {
median(airquality$Wind, na.rm = T)
}
sd_wind <- function() {
sd(airquality$Wind, na.rm = T)
}
min_wind <- function() {
min(airquality$Wind, na.rm = T)
}
max_wind <- function() {
max(airquality$Wind, na.rm = T)
}
mean_wind()## [1] 9.957516median_wind()## [1] 9.7sd_wind()## [1] 3.523001min_wind()## [1] 1.7max_wind()## [1] 20.7Question: Compare the mean and median for each variable. Are they similar or different, and what does this suggest about the distribution (e.g., skewness)? What does the standard deviation indicate about variability?
For ozone, the mean exceeds the median, showcasing right-skewedness and the most variability. Temperature has a very similar mean and median, which suggests a roughly symmetric distribution, with moderate variability. Finally, wind shows a very similar mean and median, which also suggests a roughly symmetric distribtuion, with the lowest varaibility.
Task 2: Histogram
Generate the histogram for Ozone.
#Your code goes here
# Histogram for Ozone concentration
ggplot(airquality, aes(x = Ozone)) +
geom_histogram(binwidth = 10, fill = "#1f77b4", color = "black", na.rm = TRUE) +
labs(title = "Histogram of Ozone Concentration",
x = "Ozone (ppb)", y = "Count") +
theme_minimal()
Question: Describe the shape of the ozone distribution (e.g., normal, skewed, unimodal). Are there any outliers or unusual features?
The ozone distribution is skewed right, with an outlier at 168 ppb.
Task 3: Boxplot
Create a boxplot of ozone levels (Ozone) by month, with months
displayed as names (May, June, July, August, September) instead of
numbers (5–9).Recode the Month variable into a new column called
month_name with month names using case_when
from week 4.Generate a boxplot of Ozone by month_name.
# Your code here
airquality <- airquality |>
mutate(month_name = case_when(
Month == 5 ~ "May",
Month == 6 ~ "June",
Month == 7 ~ "July",
Month == 8 ~ "August",
Month == 9 ~ "September"
))
airquality$month_name <- factor(airquality$month_name,
levels = c("May","June","July","August","September"))
ggplot(airquality, aes(x = month_name, y = Ozone, fill = month_name)) +
geom_boxplot(na.rm = TRUE) +
scale_fill_manual(values = c("May"="#1f77b4",
"June"="#ff7f0e",
"July"="#2ca02c",
"August"="#d62728",
"September"="#9467bd"),
guide = "none") +
labs(title = "Boxplot of Ozone by Month",
x = "Month", y = "Ozone (ppb)") +
theme_minimal()
Question: How do ozone levels vary across months? Which month has the highest median ozone? Are there outliers in any month, and what might they indicate?
Ozone levels have a higher average and range of values throughout August and July, and decrease in June, May, and September. July has the highest median ozone. There are outliers in August, June, May, and September. These outliers may indicate months where weather tends to be more sporadic, as hotter temperatures lead to more ground-level ozone.
Task 4: Scatterplot
Produce the scatterplot of Temp vs. Ozone, colored by Month.
# Your code goes here
airquality$month_name <- factor(airquality$month_name,
levels = c("May","June","July","August","September"))
ggplot(airquality, aes(x = Temp, y = Ozone, color = month_name)) +
geom_point(alpha = 0.7, na.rm = TRUE) +
scale_color_manual(values = c("May"="#1f77b4",
"June"="#ff7f0e",
"July"="#2ca02c",
"August"="#d62728",
"September"="#9467bd")) +
labs(title = "Scatterplot of Temperature vs. Ozone",
x = "Temperature (F)", y = "Ozone (ppb)", color = "Month") +
theme_minimal()
Question: Is there a visible relationship between temperature and ozone levels? Do certain months cluster together (e.g., higher ozone in warmer months)? Describe any patterns.
There is a clear positive relationship between temperature and ozone—higher temperatures are associated with higher ozone levels. Warmer months like July and August cluster at the top right, showing elevated ozone during the hottest periods.
Task 5: Correlation Matrix
Compute and visualize the correlation matrix for Ozone, Temp, and Wind.
# Your code goes here
# Compute correlation matrix
cor_matrix <- cor(
airquality[, c("Ozone", "Temp", "Wind")],
use = "complete.obs"
)
cor_matrix## Ozone Temp Wind
## Ozone 1.0000000 0.6983603 -0.6015465
## Temp 0.6983603 1.0000000 -0.5110750
## Wind -0.6015465 -0.5110750 1.0000000# Visualize correlation matrix
corrplot(cor_matrix,
method = "color",
type = "upper",
order = "hclust",
tl.col = "black",
tl.srt = 45,
addCoef.col = "black",
title = "Correlation Matrix: Ozone, Temperature, and Wind")
Question: Identify the strongest and weakest correlations. For example, is ozone more strongly correlated with temperature or wind speed? Explain what the correlation values suggest about relationships between variables.
The strongest correlation is between Ozone and Temperature (r = 0.70), showing that ozone levels tend to rise on warmer days. The weakest is between Temperature and Wind (r = -0.51), while Ozone and Wind (r = -0.60) also show a strong negative relationship—indicating that higher wind speeds are associated with lower ozone concentrations.
Task 6: Summary Table
Generate the summary table grouped by Month.Generate the summary table grouped by Month. It should include count, average mean of ozone, average mean of temperature, and average mean of wind per month.
# your code goes here
summary_table <- airquality %>%
group_by(month_name) %>%
summarise(
count = n(),
avg_ozone = round(mean(Ozone, na.rm = TRUE), 1),
avg_temp = round(mean(Temp, na.rm = TRUE), 1),
avg_wind = round(mean(Wind, na.rm = TRUE), 1),
.groups = "drop"
)
summary_table## # A tibble: 5 × 5
## month_name count avg_ozone avg_temp avg_wind
## <fct> <int> <dbl> <dbl> <dbl>
## 1 May 31 23.6 65.5 11.6
## 2 June 30 29.4 79.1 10.3
## 3 July 31 59.1 83.9 8.9
## 4 August 31 60 84 8.8
## 5 September 30 31.4 76.9 10.2Question: Which month has the highest average ozone level? How do temperature and wind speed vary across months? What environmental factors might explain these differences?
August has the highest average ozone level. Temperature and wind speed showcase an inversely-related trend, as temperature seems to be higher in the months where wind speed is at its lowest, and vice versa. This is supported by seasonal expectations, where summertime has hotter, calmer air, which increases ozone buildup and temperature.
Submission Requirements
Publish it to Rpubs and submit your link on blackboard