HW6
Matthew Hernandez
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 1.2.1 ✔ readr 2.2.0
## ✔ forcats 1.0.1 ✔ stringr 1.6.0
## ✔ ggplot2 4.0.3 ✔ tibble 3.3.1
## ✔ lubridate 1.9.5 ✔ tidyr 1.3.2
## ✔ purrr 1.2.2
## ── 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(airquality$Ozone, na.rm = TRUE)## [1] 42.12931median(airquality$Ozone, na.rm = TRUE)## [1] 31.5sd(airquality$Ozone, na.rm = TRUE)## [1] 32.98788min(airquality$Ozone, na.rm = TRUE)## [1] 1max(airquality$Ozone, na.rm = TRUE)## [1] 168#Your code for Temp goes here
mean(airquality$Temp, na.rm = TRUE)## [1] 77.88235median(airquality$Temp, na.rm = TRUE)## [1] 79sd(airquality$Temp, na.rm = TRUE)## [1] 9.46527min(airquality$Temp, na.rm = TRUE)## [1] 56max(airquality$Temp, na.rm = TRUE)## [1] 97#Your code for Wind goes here
mean(airquality$Wind, na.rm = TRUE)## [1] 9.957516median(airquality$Wind, na.rm = TRUE)## [1] 9.7sd(airquality$Wind, na.rm = TRUE)## [1] 3.523001min(airquality$Wind, na.rm = TRUE)## [1] 1.7max(airquality$Wind, na.rm = TRUE)## [1] 20.7Question: Compare the mean and median for each variable. Are they similar or different, and what does this suggest about the distribution (e.g., skewness)? What does the standard deviation indicate about variability?
For Ozone, since the mean is higher than the median is can suggest that the distribution is right-skewed. For Temp, the values are very close and instead suggest a symmetric distribution. The slightly lower mean could indicate a very minimal left skew. For Wind, the mean is near the same and thus indicates a fairly symmetric distribution.
Task 2: Histogram
Generate the histogram for Ozone.
#Your code goes here
ggplot(airquality, aes(x = Ozone)) +
geom_histogram(binwidth = 10, fill = "orange", color = "magenta", na.rm = TRUE) +
labs(
title = "Distribution of Ozone Levels",
x = "Ozone Concentration",
y = "Frequency"
)
Question: Describe the shape of the ozone distribution (e.g., normal, skewed, unimodal). Are there any outliers or unusual features?
The ozone distribution is right skewed, but an argument could be made that it is also unimodel. However, there appear to be two peaks, leading to speculation. Most ozone measurements are seen at the lower end of the distribution while their are noticeably less observations toward higher ozone concentration levels. The higher value outliers above the 150 level could be the contributors to the higher mean seen previously.
Task 3: Boxplot
Create a boxplot of ozone levels (Ozone) by month, with months
displayed as names (May, June, July, August, September) instead of
numbers (5–9).Recode the Month variable into a new column called
month_name with month names using case_when
from week 4.Generate a boxplot of Ozone by month_name.
# Your code here
airquality <- airquality |>
mutate(
month_name = case_when(
Month == 5 ~ "May",
Month == 6 ~ "June",
Month == 7 ~ "July",
Month == 8 ~ "August",
Month == 9 ~ "September"
)
)
airquality$month_name <- factor(
airquality$month_name,
levels = c("May", "June", "July", "August", "September")
)
ggplot(airquality, aes(x = month_name, y = Ozone)) +
geom_boxplot(fill = "green", color = "black", na.rm = TRUE) +
labs(
title = "Ozone Levels by Month",
x = "Month",
y = "Ozone Concentration"
)
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 vary noticeably by month. July has the highest median ozone level, with August also showing a higher ozone concentration level when compared with May, June, and September. Certain months demonstrate unusually high observations, which may represent certain days in these months when environmental conditions were favorable for ozone formation. This boxplot demonstrates that overall, ozone levels tend to be higher in the summer months.
Task 4: Scatterplot
Produce the scatterplot of Temp vs. Ozone, colored by Month.
# Your code goes here
ggplot(airquality, aes(x = Temp, y = Ozone, color = month_name)) +
geom_point(size = 2.5, alpha = 0.4, na.rm = TRUE) +
labs(
title = "Temperature vs. Ozone Levels",
x = "Temperature",
y = "Ozone Concentration",
color = "Month"
)
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 visible relationship between temperature and ozone levels. As temperature levels increase, ozone levels generally increase as well through a visible upward trend. The warmer months, August and July, tend to cluster more around higher temperatures and ozone measurments.
Task 5: Correlation Matrix
Compute and visualize the correlation matrix for Ozone, Temp, and Wind.
# Your code goes here
cor_matrix <- airquality |>
select(Ozone, Temp, Wind) |>
cor(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 1.0000000Question: 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 Temp. This indicates that there is a moderately strong positive relationship, meaning that higher temperatures can be associated with higher ozone levels. The weakest correlation is between Temp and Wind. This indicates that there is a moderate negative correlation, although similar to the relationship of Wind and Ozone. This means that as wind speed increases, ozone levels and temperature levels are associated with decreasing.
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 = mean(Ozone, na.rm = TRUE),
avg_temp = mean(Temp, na.rm = TRUE),
avg_wind = mean(Wind, na.rm = TRUE)
)
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 8.94
## 4 August 31 60.0 84.0 8.79
## 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, just above July. Temperature increases substantially from May into the summer months of June through September, reaching the highest monthly average in August nearly 84 degrees before decreasing to 76 degrees in September. Wind shows a pattern that is the opposite, where average wind speeds are highest in May, followed by June, with a general decrease through July and August before increasing once again in September. Since July and August have lower average wind speeds, the combination of high temperatures and less air movement may contribute to the higher ozone levels observed during these months. In contrast, cooler temperatures and stronger winds in May and September may help explain their lower ozone concentrations.
Submission Requirements
Publish it to Rpubs and submit your link on blackboard