HW6
Phillip Alexander
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 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 4.0.0 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── 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)## Warning: package 'corrplot' was built under R version 4.3.3## 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 30?airquality## starting httpd help server ... doneTasks 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
ozone <- airquality |>
summarise(
mean(Ozone, na.rm = TRUE),
median(Ozone, na.rm = TRUE),
sd(Ozone, na.rm = TRUE),
min(Ozone, na.rm = TRUE),
max(Ozone, na.rm = TRUE)
)
ozone## mean(Ozone, na.rm = TRUE) median(Ozone, na.rm = TRUE) sd(Ozone, na.rm = TRUE)
## 1 42.12931 31.5 32.98788
## min(Ozone, na.rm = TRUE) max(Ozone, na.rm = TRUE)
## 1 1 168#Your code for Temp goes here
temp <- airquality |>
summarise(
mean(Temp, na.rm = TRUE),
median(Temp, na.rm = TRUE),
sd(Temp, na.rm = TRUE),
min(Temp, na.rm = TRUE),
max(Temp, na.rm = TRUE)
)
temp## mean(Temp, na.rm = TRUE) median(Temp, na.rm = TRUE) sd(Temp, na.rm = TRUE)
## 1 77.88235 79 9.46527
## min(Temp, na.rm = TRUE) max(Temp, na.rm = TRUE)
## 1 56 97#Your code for Wind goes here
wind <- airquality |>
summarise(
mean(Wind, na.rm = TRUE),
median(Wind, na.rm = TRUE),
sd(Wind, na.rm = TRUE),
min(Wind, na.rm = TRUE),
max(Wind, na.rm = TRUE)
)
wind## mean(Wind, na.rm = TRUE) median(Wind, na.rm = TRUE) sd(Wind, na.rm = TRUE)
## 1 9.957516 9.7 3.523001
## min(Wind, na.rm = TRUE) max(Wind, na.rm = TRUE)
## 1 1.7 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?
Ozone: mean: 42.12931, median: 31.5, sd: 32.98788 The ozone’s mean is way greater than the median by 10. This suggest the distribution is skewed right. The standard deviation is 32.98788 indicating that the most ozone data falls within about 32.98788 ppb of the mean.
Temp: mean: 77.88235, median: 79, sd: 9.46527 The temperature’s mean is very close to the median and is less than the median indicating that the distribution is slightly skewed left. The standard deviation is 9.42627 indicating that most temperature data fall within 9.46527 degrees fahrenheit of the mean.
Wind: mean: 9.957516, median: 9.7, sd: 3.523001 The wind’s mean is very close to the median and is greater than the median indicating that the distribution is slightly skewed right. The standard is 3.523001 indicating that most wind data fall within 9.426527 mph of the mean.
Task 2: Histogram
Generate the histogram for Ozone.
#Your code goes here
ggplot(airquality, aes(x = Ozone)) + geom_histogram(binwidth = 20, fill = "#0388fc", color = "#3461eb") +
labs(title = "Histogram of Ozone (ppb)", x = "Ozone (ppb)", y = "Count") +
theme_minimal()## Warning: Removed 37 rows containing non-finite outside the scale range
## (`stat_bin()`).
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. The ozone histogram doesn’t appear to have any unusual features.
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
month_levels <- c("May", "June", "July", "August", "September")
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, month_levels)
ggplot(airquality, aes(x = factor(month_name), y = Ozone)) +
geom_boxplot(fill = "#0388fc", color = "#3461eb") +
labs(title = "Boxplot of Ozone by Month",
x = "Month", y = "Ozone (ppb)") +
theme_minimal()## Warning: Removed 37 rows containing non-finite outside the scale range
## (`stat_boxplot()`).
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?
The ozone levels for July and August are similar because of where their medians are and the Q1 and Q3 of both July and August are not far apart. The min and max are also similar in location. May and September are also similar because their medians are in similar spots and same as the Q1 and Q3. The min and max are also similar in location. June is the only odd one out. June has the highest median. In terms of outliers: May, June, August, and September all have outliers. The outliers probably indicate that the data point is way to far away from the median.
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() +
labs(
title = "Scatterplot of Temperature and Ozone",
x = "Temperature",
y = "Ozone (ppb)",
color = "Month"
) +
scale_color_manual(values = c("May" = "#FF0000",
"June" = "#FFA500",
"July" = "#FFFF00",
"August" = "#008000",
"September" = "#0000FF"))## Warning: Removed 37 rows containing missing values or values outside the scale range
## (`geom_point()`).
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## @ validate: logi TRUEQuestion: 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.
- Yes, temperature and ozone levels have a postive relationship. May (Red) and June (0range) are clustered together, Augsut (Green) and September (Blue) are clustered together, and July (Yellow) and August (Green) are clustered together. Patterns that are visible are May and June tend range around 60 to 70 degrees Fahrenheit with most of them having lower ozone compared to other months. Another is higher temperature leads to having higher ozone.
Task 5: Correlation Matrix
Compute and visualize the correlation matrix for Ozone, Temp, and Wind.
# Your code goes here
cor_matrix <- cor (
airquality |>
select(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 1.0000000corrplot(cor_matrix, method = "color", type = "upper",
tl.col = "black", tl.srt = 45, addCoef.col = "black",
title = "Correlation Matrix of 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 Ozone and Temperature. The weakest correlations are Ozone and wind, and Temperature and Wind. A 0.70 correlation value for Ozone and temperature suggest a positive relationship. On the other hand, the negative values: -0.60 and -0.51 suggest a negative relationship meaning downward slope.
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) |>
summarise(
count = n(),
mean_ozone = mean(Ozone, na.rm = TRUE),
mean_temp = mean(Temp, na.rm = TRUE),
mean_wind = mean(Wind,na.rm = TRUE)
)
summary_table## # A tibble: 5 × 5
## Month count mean_ozone mean_temp mean_wind
## <int> <int> <dbl> <dbl> <dbl>
## 1 5 31 23.6 65.5 11.6
## 2 6 30 29.4 79.1 10.3
## 3 7 31 59.1 83.9 8.94
## 4 8 31 60.0 84.0 8.79
## 5 9 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?
- Month 8 (August) has the highest average ozone level of 59.96154.
- When temperature rise, wind speeds decrease. Environmental factors for this occurence could be since its hot, its harder to produce wind.
Submission Requirements
Publish it to Rpubs and submit your link on blackboard