Relationship Between Ozone & Temperature
Lauren Skelly
2026-09-03
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Let’s Try It!
Data
The atmos data set resides in the
nasaweather package of the R programming language.
It contains a collection of atmospheric variables measured between 1995
and 2000 on a grid of 576 coordinates in the western hemisphere. The
data set comes from the 2006 ASA Data
Expo.
How to make a list
number list:
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mixed list:
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Let’s Try It!
Some of the variables in the atmos data set are:
- temp - The mean monthly air temperature near the surface of the Earth (measured in degrees kelvin (K))
- pressure - The mean monthly air pressure at the surface of the Earth (measured in millibars (mb))
- ozone - The mean monthly abundance of atmospheric ozone (measured in Dobson units (DU))
How to write formulas
alpha is \(\alpha\); \(\beta \neq \alpha\): some other text; another formula: \[\sum_{i}^n X_i / n\].
You can convert the temperature unit from Kelvin to Celsius with the formula
\[ \text{celsius} = kelvin - 273.15 \]
And you can convert the result to Fahrenheit with the formula
\[ fahrenheit = celsius \times \frac{9}{5} + 32 \]
What is a Code Chunk?
2 + 2## [1] 4summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000shortcut to create code chunk: Ctrl + Alt + i
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summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00# will show code but will not run## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000Let’s Try It!
Cleaning
To analyze this data, we will use the following R packages:
library(nasaweather)
library(tidyverse)the value of a is 25.
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For the remainder of the report, we will look only at data from the year 2000. We aggregate our data by location, using the R code below.
# code chunk 4
means <- atmos %>%
filter(year == year) %>%
group_by(long, lat) %>%
summarize(temp = mean(temp, na.rm = TRUE),
pressure = mean(pressure, na.rm = TRUE),
ozone = mean(ozone, na.rm = TRUE),
cloudlow = mean(cloudlow, na.rm = TRUE),
cloudmid = mean(cloudmid, na.rm = TRUE),
cloudhigh = mean(cloudhigh, na.rm = TRUE)) %>%
ungroup()where the year object equals 2000.
Ozone and temperature
Is the relationship between ozone and temperature useful for understanding fluctuations in ozone? A scatterplot of the variables shows a strong, but unusual relationship.
We suspect that group level effects are caused by environmental conditions that vary by locale. To test this idea, we sort each data point into one of four geographic regions:
# code chunk 7
means$locale <- "north america"
means$locale[means$lat < 10] <- "south pacific"
means$locale[means$long > -80 & means$lat < 10] <- "south america"
means$locale[means$long > -80 & means$lat > 10] <- "north atlantic"Model
We suggest that ozone is highly correlated with temperature, but that a different relationship exists for each geographic region. We capture this relationship with a second order linear model of the form
\[ ozone = \alpha + \beta_{1} temperature + \sum_{locales} \beta_{i} locale_{i} + \sum_{locales} \beta_{j} interaction_{j} + \epsilon\]
This yields the following coefficients and relationships.
# code chunk 8
lm(ozone ~ temp + locale + temp:locale, data = means)##
## Call:
## lm(formula = ozone ~ temp + locale + temp:locale, data = means)
##
## Coefficients:
## (Intercept) temp
## 1336.508 -3.559
## localenorth atlantic localesouth america
## 548.248 -1061.452
## localesouth pacific temp:localenorth atlantic
## -549.906 -1.827
## temp:localesouth america temp:localesouth pacific
## 3.496 1.785# code chunk 9
ggplot(means, aes(temp, ozone, color = locale)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE) +
facet_wrap(~ locale)## `geom_smooth()` using formula = 'y ~ x'
Diagnostics
An anova test suggests that both locale and the interaction effect of locale and temperature are useful for predicting ozone (i.e., the p-value that compares the full model to the reduced models is statistically significant).
# code chunk 10
mod <- lm(ozone ~ temp, data = means)
mod2 <- lm(ozone ~ temp + locale, data = means)
mod3 <- lm(ozone ~ temp + locale + temp:locale, data = means)
anova(mod, mod2, mod3)## Analysis of Variance Table
##
## Model 1: ozone ~ temp
## Model 2: ozone ~ temp + locale
## Model 3: ozone ~ temp + locale + temp:locale
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 574 99335
## 2 571 41425 3 57911 706.17 < 2.2e-16 ***
## 3 568 15527 3 25898 315.81 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1