STAT 311 Statistical Analysis Problems

Stat 311 Winter 2023 Quiz 1Quiz 1 consists of four problems, due uploaded to Gradescope by 11:30 PM PST February 1st. Do not wait
until the last minute to upload as no late quizzes will be allowed.
The quiz is written for about 1 hour and 45 minutes assuming you studied but you may complete the quiz
anytime during the open window (since there is so much supplementary material for Problems 1 and 2, I
decided against a timed quiz); just be sure to leave yourself time to upload your answers before the deadline.
This quiz is open Stat 311 notes, textbook, homework, homework solutions and posted supplementary
materials only. All responses must be your own. If I suspect that you collaborated with other people or put
down answers that match something you found on the internet, your quiz score will be zero and I will file a
report with the Student Conduct office. By uploading your quiz to Gradescope, you are acknowledging that
you adhered to the rules and academic conduct standards set by the University of Washington.
Pay attention to sentence or word length requirements. We will not read more than the allowed limits.
Also, always keep context in mind and report units when applicable. If we say bullets okay, then you may
answer using a bulleted list instead of using full sentences.
If you have questions about any of the questions, you may post a private message on Ed Discussion. Do note
that I can only guarantee responses during daytime hours on Monday and Tuesday. I may not answer any
questions after 5 PM PST on Wednesday, February 1st (and I have limited availability during the day on
Wednesday).
Problem 1 (10 points): Read the short UW News article for an overview of a study that showed that areas
with historical redlining were associated with more air pollution. Then look at the published journal article
that provides more details about the study. The news and journal articles can be found in the Quiz 1
assignment on Canvas. Use the news article to get a short overview before diving into the journal article. Use
information from the journal article to answer parts (a) – (f). Except for part (f), limit your responses to at
most two sentences or bullet points as indicated.
a) Was this an experiment or observational study. Briefly explain. (1 point)
b) What is meant by the term redlining that is used in the two articles? (1 point)
c) What were the main sources of data for this study based on the journal article? (1.5 points)
d) Race and ethnicity were combined into aggregate groups for this study. What are the groups? Include the
HOLC percentages of each group (bullets points instead of complete sentences okay). (2 points)
e) What are the main two pollutants that were investigated in this study and why did they focus on just these
two (bullets points instead of complete sentences okay)? (1.5 point)
f) Figure 1 of the journal article shows population weighted distributions for both pollutants. Summarize
what you can glean from the top left plot [Unadjusted NO2 national aggregation]. Be sure to speak to the
HOLC grades and race/ethnicity and relate to the reported mean and median NO2 values. Limit your
response to at most 150 words. (3 points)
1
Stat 311 Winter 2023 Quiz 1
Problem 2 (10 points): Five measurements were taken on two species of fish from a single lake (𝑛𝑛 = 35
Bream and 𝑛𝑛 = 33 Perch). For this problem, fish weight is the response (𝑦𝑦) and cross length, height and
diagonal width are possible predictors of fish weight. This problem does not require any coding; rather, we
are providing summary graphs, summary tables, and lm output in the supplementary handout,
Quiz1Problem2.pdf, posted in the Quiz 1 assignment page on Canvas. Use the information in this handout to
answer parts (a) – (g).
a) Look at the density plot in the last row of Figure 2 and the histograms in Figure 5 of the supplementary
handout (pages 3 and 6) and describe the overall distribution of the observed sample widths ignoring
species and then compare the sample distributions for widths individually for Bream and Perch. Limit
your answer to no more than three sentences. (1.5 points)
b) Look at Figure 2 (page 3) of the supplementary handout and interpret the overall joint relationship
between Weight and Width. Also comment on the relationship when considering species. [Hint: make
clear, specific observations regarding the relationships]. Limit your answer to no more than three
sentences. (1.5 points)
c) Using Figure 2 (page 3), what is the overall sample correlation between height and weight. What are the
correlations for height and weight by species? How do correlations by species compare with the overall
correlation? Why are the correlations so different when comparing all the data to correlations by species?
Limit your answer to no more than three sentences. (2 points)
d) Write out the regression equation for Weight on Height. In one sentence, interpret the estimated slope
parameter for this regression in the context of the problem. (1 point)
e) In one sentence report and interpret the coefficient of determination for the regression of Weight on
Height in the context of the problem. (1 point)
f) We have provided the output for simple linear regressions of Weight on the two predictor variables we
are considering (Height and Width). Of the two models, which model do you think is the best single
predictor model for fish weight? Use all the information (scatterplots, lm outputs, residual plots, and
histograms of the residuals) to support your choice. We are looking for written answers that are in the
context of the problem and that use more than a single piece of information to support your answer. Limit
your answer to a maximum of 100 words. You may use bullet points instead of complete sentences if that
helps you to better organize your answer. (2 points)
g) On pages 11 and 12 of the supplementary handout, we provide regression output for Weight that includes
Width and the additional categorical variable Species. This is like HW3 Problem 5, however, this
time we considered an additional model that allows for the possibility of different slopes for each of the
two species of fish. Of the three models for Weight on Width (single regression all species, differing
intercepts by species (parallel lines), or different slopes by species), which model do you think is best?
Use the information from the regression outputs and Figure 6 (page 9) to justify your answer. Limit your
answer to a maximum of 100 words. You may use bullet points instead of complete sentences if that
helps you to better organize your answer. (1 point)
2
Stat 311 Winter 2023 Quiz 1
Problem 3 (12 points; 1.5 points each): True or False. If the statement is True, then indicate True and
nothing else. If the statement is False, then indicate False and carefully explain using no more than three
sentences why the statement is false. For statements with numbers that you deem to be false, show any
calculations to support your answer.
a) A researcher is interested in administering a survey to gauge attitudes of Catholic Church members
regarding the current Pope. A random sample of five Catholic Churches in King County are selected and
all church members of those five churches are surveyed. This type of sample is called a stratified sample.
b) A student is collecting data on movie preferences for a class project. The student stands outside a
neighborhood theater and asks people exiting the theater if they would be willing to take a brief survey.
The student can get 50 people willing to participate over the course of six hours. The 50 completed
surveys are an example of a simple random sample.
c) A study compared a group of men who had heart attacks with a similar group of controls. The proportion
of men with male pattern baldness was compared between the two groups. This is an example of an
observational study.
d) A sample of households in a community is selected at random from the telephone directory. In this
community, 4% of households have no telephone, 10% have only cell phones, and another 25% have
unlisted telephone numbers. The largest issue with this sampling scenario is response bias.
e) The contingency table shown below is from a Pew Research Center study, published in May 2022, that
looked at use of video conferencing services (Zoom, Webex or other) for three levels of work from home
status.
Use of Video Conferencing for Work
Work from home
status
Often
Sometimes
Hardly Ever
Never
Total
All or most of the time
66
17
7
11
101
Sometimes
49
28
16
7
100
Rarely or never
35
30
18
17
100
Total
150
75
41
35
301
The joint percentage of people that sometimes work from home and never use video conferencing for
work is 2.3% (rounded to one decimal place), and among people that sometimes use video conferencing
for work, 16.8% (rounded to one decimal place) work from home all or most of the time, 28% sometimes
work from home and 30% rarely or never work from home.
f) The UW sent out a survey to a random sample of 1200 students with sophomore standing to obtain
information of interest in several majors on campus. Of the 750 that were returned, 150 students
indicated they were interested in the Economics major. The population proportion of students interested
in an Economics major is estimated to be 0.20 and the survey nonresponse rate is 37.5%.
g) Adult female Dalmatians weigh an average of 50 pounds with a standard deviation of 3.3 pounds. Adult female
Boxers weigh an average of 57.5 pounds with a standard deviation of 1.7 pounds. One statistics teacher owns an
underweight Dalmatian and an underweight Boxer. The Dalmatian weighs 45 pounds, and the Boxer weighs 52
pounds. Based on the given information, the Dalmatian is more underweight.
h) A statistics class with 30 students took a quiz that had a mean score of 72. A couple of days later a TA
noticed that one score was entered incorrectly. A student received a 50 that should have been a 90. The
correct mean for the quiz is 73.3, rounded to one decimal place.
3
5/1/22, 12:23 PM
More air pollution present in areas with historical redlining | UW News
March 9, 2022
More air pollution present in areas with historical
redlining
UW News staff
POSTED UNDER: POPULATION HEALTH, PUBLIC HEALTH, RESEARCH, SCIENCE, UW NEWS BLOG
Despite dramatic improvements in air
quality over the past 50 years, people of
color at every income level in the United
States are exposed to higher-than-average
levels of air pollution. While this disparity
has been widely studied, the links between
today’s air pollution disparities and historic
patterns of racially segregated planning are
still being uncovered.
Researchers at the UW and UC Berkeley have found that
Now a new study from a team of
housing discrimination practices dating from the 1930s still
researchers at UC Berkeley and the
drive air pollution disparities in hundreds of American cities
today. Sarah McQuate/University of Washington
University of Washington has found that
housing discrimination practices dating
from the 1930s still drive air pollution
disparities in hundreds of American cities today. In this study — the first to do a national-level analysis
of modern urban air pollution and historical redlining — the team examined more than 200 cities and
found a strong correlation between present-day air pollution levels and historical patterns of redlining.
The researchers published their findings March 9 in Environmental Science & Technology Letters.
“Racism from the 1930s, and racist actions by people who are no longer alive, are still influencing
inequality in air pollution exposure today,” said co-author Julian Marshall, a UW professor of civil and
environmental engineering. “The problems underlying environmental inequality by race are larger than
any one city or political administration. We need solutions that match the scale of the problem.”
The term “redlining” describes a widespread federally backed discriminatory mortgage appraisal
practice in the 1930s. This process color-coded city areas red if they included high concentrations of
Black, Asian, immigrant or working-class residents, deeming these areas hazardous and excessively
https://www.washington.edu/news/2022/03/09/more-air-pollution-present-in-areas-with-historical-redlining/?utm_source=UW_News_Subscribers&utm…
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5/1/22, 12:23 PM
More air pollution present in areas with historical redlining | UW News
risky for investment. Redlining blocked access to favorable lending and other services. Historically
redlined areas have been cumulatively affected by a low prevalence of home ownership, uneven
economic development, displacement of residents, community disintegration and lack of access to
education and economic opportunities.
Mapping Inequality
map options
+
–
The population is made up of white people who are employed as
white-collar workers, skilled mechanics or small business men.
B6
The property is predominantly occupied by home owners of
moderate means. No racial problems in this area.
B12 North Broadway and Capitol Hill
A redlining map of Seattle. Click on a neighborhood or a grade for more details. Credit: Mapping Inequality
The researchers compared year-2010 levels of two regulated air pollutants — nitrogen dioxide (NO2; a
short-lived gas emitted by traffic, industry and other sources), and fine particulate matter (PM2.5;
longer-lived, tiny particles found in dust, soot, smoke and other emissions or formed in the
atmosphere) — to redlining maps in 202 U.S. cities.
https://www.washington.edu/news/2022/03/09/more-air-pollution-present-in-areas-with-historical-redlining/?utm_source=UW_News_Subscribers&utm…
2/4
5/1/22, 12:23 PM
More air pollution present in areas with historical redlining | UW News
In these cities, redlined areas consistently had higher levels of pollution today than areas that received
favorable treatment. In fact, air pollution disparities associated with redlining status were even larger
than those associated with race and ethnicity.
The study highlights the “distinct inequities that affect people in all neighborhoods, regardless of
redlining grade,” said lead author Haley Lane, a doctoral student in civil and environmental engineering
at UC Berkeley. “It also emphasized the importance of identifying and improving conditions in those
neighborhoods which have been systematically isolated from financial investment through practices
like redlining while being subjected to increased environmental exposures for decades.”
The long-lasting implications of historical segregation on present-day disparities are striking, according
to the researchers.
The team also found racial disparities within redlined neighborhoods, suggesting that housing
discrimination is one of many factors propelling environmental racism. In other words, white people
who happen to live in redlined neighborhoods still have lower air pollution exposure than people of
color in the same community. That trend held across non-redlined and redlined neighborhoods alike,
the researchers said.
“This study underscores how the past is still very much present when it comes to air pollution
disparities,” said senior author Joshua Apte, assistant professor in the Department of Civil &
Environmental Engineering and the School of Public Health at UC Berkeley. “Redlining is a good
predictor of air pollution disparities but it’s only one of the things that drive the racial and ethnic
disparities in air pollution. It’s not the only source of disparity that we need to be worried about.”
The research goes “a long way toward highlighting the
lasting consequences of structural racism on community
See a related story in The
health,” said co-author Rachel Morello-Frosch, a
Washington Post.
professor of Public Health and Environmental Science,
Policy and Management at UC Berkeley and co-author of
the study. “These results can point the way toward
targeted approaches for regulating emission sources and
reducing exposures, as well as longer-term strategies to address discriminatory land-use decisionmaking that adversely impacts communities of color.”
This publication was developed as part of the Center for Air, Climate, and Energy Solutions (CACES),
which is funded by the U.S. Environmental Protection Agency (R835873).
For more information, contact Marshall at jdmarsh@uw.edu and Apte at jsapte@berkeley.edu.
https://www.washington.edu/news/2022/03/09/more-air-pollution-present-in-areas-with-historical-redlining/?utm_source=UW_News_Subscribers&utm…
3/4
5/1/22, 12:23 PM
More air pollution present in areas with historical redlining | UW News
Adapted from a release from UC Berkeley.
813
Tagged with: College of Engineering, Department of Civil & Environmental Engineering, Julian Marshall, population
health
https://www.washington.edu/news/2022/03/09/more-air-pollution-present-in-areas-with-historical-redlining/?utm_source=UW_News_Subscribers&utm…
4/4
Handout with Supplementary Material for Quiz 1 Problem 2
Problem 2 uses a fish data set that has multiple measurements for multiple species of fish. We
will restrict our analysis to two species, Bream and Perch, and three continuous measurements as
describe in the Table 1 below. We are not completely sure of the origin of this data set, but it
appears like one based on a 1917 study of fish caught in Lake Laengelmavesi near Tampere in
Finland.
Table 1. Fish variables for Quiz 1 Problem 2.
Variable
Weight
Height
Width
Species
Description
Weight of fish in grams (g)
Height of fish in cm
Diagonal width of fish in cm
Categorical variable, either Bream or Perch
For this analysis, we want to determine which of fish height or diagonal width is the best single
predictor of fish weight. We also want to explore differences between the two species. Figure 1
shows you images of typical Bream and Perch for reference.
A stock Bream
Picture from
https://depositphotos.com/stockphotos/sea-bream.html
A yellow Perch
Picture from
https://wiki.fishingplanet.com/Yellow_Perch/en
Figure 1. Images of a typical Bream and a typical Perch.
1
Handout with Supplementary Material for Quiz 1 Problem 2
Exploratory Data Analysis
Pages 3 – 7 provide various EDA output for the fish data set. All EDA includes information on
the three quantitative variables overall and split out by species.
Figure 2, shown on the next page, is a pairs plot for three continuous variables along with density
plots for each variable. All plots also include a third variable, Species, which is color coded
(Bream pink and Perch blue). For our analysis, Weight is the response and Height and Width are
possible predictors. For each pair, three correlations are shown, one overall, one for Bream only
and one for Perch only. The first plot in row 1 shows the density plots for Weight by species.
The remaining information in row 1 are correlations between Weight and each explanatory
variable overall (black), Bream (pink), and Perch (blue). Each following row is for one of the
explanatory variables and with a color-coded scatterplot for Weight on each of the explanatory
variables. The correlations in row 2 are between Height and Length3 and Width and Length3.
Some annotations have been added to Figure 2 to help you understand how to read it.
Pages 8 – 10 show linear model output, including diagnostic plots for the single variable models
for Weight on each of the predictors for all data, ignoring species.
Pages 11 and 12 show output for a regression that includes a single quantitative variable (only
presented for Width) with the addition of the categorical variable Species. The first model is like
Problem 5 in HW3. The second regression shows you the extension to allow for two lines,
different slopes. Interpretation of the output is included on these pages.
2
Handout with Supplementary Material for Quiz 1 Problem 2
Width on
Weight
Figure 2. Pairs plot showing scatterplots, density plots and correlations for all pairwise
combinations of Weight, Height, and Width. Pink indicates the species Bream and light blue
indicate Perch.
3
Handout with Supplementary Material for Quiz 1 Problem 2
Figures 3 – 5 show individual histograms and boxplots (univariate summaries) for each variable
altogether and split out by species. Table 2 shows summary statistics for each of the variables as
well.
Figure 3. Histograms and boxplots for each of Weight overall and Weight by species.
4
Handout with Supplementary Material for Quiz 1 Problem 2
Figure 4. Histograms and boxplots for each of Height overall and Height by species.
5
Handout with Supplementary Material for Quiz 1 Problem 2
Figure 5. Histograms and boxplots for each of Width overall and Width by species.
6
Handout with Supplementary Material for Quiz 1 Problem 2
Table 2. Seven number summary statistics for the Weight (y) and possible predictors (x).
The total sample size is 68 fish, 35 Bream and 33 Perch.
Variable
Weight (g)
All
Bream
Perch
Height (cm)
All
Bream
Perch
Width (cm)
All
Bream
Perch
Min
Q1
Median
Q3
Max
Mean
SD
145
242
145
340
462.5
250
615
610
650
825
717
850
1100
1000
1100
599.0
617.8
579.0
273.55
209.21
330.72
6.3
11.5
6.3
10.6
14.0
7.3
12.5
15.0
10.6
15.0
16.4
11.7
19.0
19.0
12.8
12.5
15.2
9.7
3.51
1.96
2.33
3.7
4.0
3.7
4.7
4.9
4.3
5.5
5.3
6.3
6.4
6.1
7.2
8.1
6.7
8.1
5.6
5.4
5.8
1.16
0.72
1.48
7
Handout with Supplementary Material for Quiz 1 Problem 2
Single Variable Linear Model Output
Weight on Height
Call:
lm(formula = Weight ~ Height, data = FDatSub2)
Coefficients:
Estimate Std. Error
(Intercept)
-26.48
95.50
Height
50.04
7.36
t value
-0.277
6.799
Pr(>|t|)
0.782
3.68e-09
Residual standard error: 211.4 on 66 degrees of freedom
Multiple R-squared: 0.4119
Weight on Diagonal Width
Call:
lm(formula = Weight ~ Width, data = FDatSub2)
Coefficients:
Estimate Std. Error
(Intercept) -611.79
67.03
Width
215.27
11.67
t value
-9.127
18.440
Pr(>|t|)
2.59e-13
< 2e-16 Residual standard error: 111.1 on 66 degrees of freedom Multiple R-squared: 0.8375 8 Handout with Supplementary Material for Quiz 1 Problem 2 Scatterplots with Regression Lines Figure 6 shows scatterplots of Weight on each the two predictor variables with regression lines. The two scatterplots in the top row have three lines. The colored lines are the regression lines fit to individual species (these were done in ggplot2). The black lines are the regression lines for the single variable regressions on the previous page. The scatterplot of Weight on Width has two additional color-coded dashed lines. These are the regression lines for each species if we assume a common slope (parallel lines) and only change the intercept. The solid color-coded lines allow for different slopes, which also implies different intercepts (some of the dashed lines are hard to see as they practically coincide with the solid lines). How to set up these different regressions will be explained on the last two pages of this document. We chose to include this to show you there is more you can do than single variable regression. Figure 6. Scatterplots of Weight on each of the predictors with fitted regression lines. Left plot shows overall regression (black) and results for a model allowing two slopes (salmon and cyan). The right plot shows overall regression (black), same intercepts (dashed lines) and different slopes (solid salmon and cyan). Residual Diagnostic Plots Figure 7 shows residuals plots and histograms of the residuals for each of the univariate regressions (black lines in Figure 6). 9 Handout with Supplementary Material for Quiz 1 Problem 2 Figure 7. Residual plots and histograms of residuals for each of the two overall regressions, ignoring species (page 8). 10 Handout with Supplementary Material for Quiz 1 Problem 2 Linear Model Output Accounting for Species Weight on Width and Species allowing for different intercepts only (same slope/parallel lines) This regression is similar to HW3, Problem 5b. In this regression, we add a second categorical variable to the model. This allows us to fit two lines, one for each species. Remember that in R, the first level of the category is included in the y-intercept. Coefficients for the other levels show up in the output. Thus, in the output below, we have an additional line for the Perch species (SpeciesPerch) Since Species is categorical, this coefficient is added to the y-intercept to get the intercept for Perch. The two regression lines that result from this model are shown underneath the output. When we simply add a categorical variable, we are assuming parallel line, so only one overall slope for Width and different y-intercepts for each Species. Call: lm(formula = Weight ~ Width + Species, data = FDatSub2) Coefficients: Estimate Std. Error (Intercept) -604.299 54.799 Width 225.169 9.692 SpeciesPerch -130.145 22.385 Residual standard error: 90.82 on 65 degrees of freedom Adjusted R-squared: 0.8898 Regression equation for Bream: 𝑦𝑦� = −604.299 + 225.169(𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊ℎ) Regression equation for Perch: 𝑦𝑦� = (−604.299 − 130.145) + 225.169(𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊ℎ) or 𝑦𝑦� = −734.444 + 225.169(𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊ℎ) 11 Handout with Supplementary Material for Quiz 1 Problem 2 Weight on Width and Species allowing for different slopes (and thus different intercepts) This is an extension of what was done in HW3, Problem 5. In this regression, when we add a second categorical variable to the model, we use an asterisk instead of a plus. This allows us to fit two lines, one for each species, but allowing for different slopes for each species. Thus, in the output below, we have two additional lines for the Perch species: 1) SpeciesPerch, which is used to get the y-intercept for Perch, and 2) Width:SpeciesPerch, which allows us to fit a different slope for Perch. This is called in interaction term. The two regression lines that result from this model are shown underneath the output. You can see how the y-intercept and SpeciesPerch were combined to get the y-intercept for the Perch line and Width and Width:SpeciesPerch were combined to the slope for the Perch line. Call: lm(formula = Weight ~ Width * Species, data = FDatSub2) Coefficients: (Intercept) Width SpeciesPerch Width:SpeciesPerch Estimate Std. Error -838.39 114.42 268.30 20.90 167.45 130.69 -54.02 23.39 Residual standard error: 87.94 on 64 degrees of freedom Adjusted R-squared: 0.8967 Regression equation for Bream: 𝑦𝑦� = −838.39 + 268.30(𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊ℎ) Regression equation for Perch: 𝑦𝑦� = (−838.39 + 167.45) + (268.30 − 54.02)(𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊ℎ) or 𝑦𝑦� = −670.94 + 214.28(𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊ℎ) 12 pubs.acs.org/journal/estlcu Letter Historical Redlining Is Associated with Present-Day Air Pollution Disparities in U.S. Cities Haley M. Lane, Rachel Morello-Frosch, Julian D. Marshall, and Joshua S. Apte* Cite This: Environ. Sci. Technol. Lett. 2022, 9, 345−350 Downloaded via 76.121.191.128 on May 1, 2022 at 19:22:11 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. ACCESS Metrics & More Read Online Article Recommendations sı Supporting Information * ABSTRACT: Communities of color in the United States are systematically exposed to higher levels of air pollution. We explore here how redlining, a discriminatory mortgage appraisal practice from the 1930s by the federal Home Owners’ Loan Corporation (HOLC), relates to present-day intraurban air pollution disparities in 202 U.S. cities. In each city, we integrated three sources of data: (1) detailed HOLC security maps of investment risk grades [A (“best”), B, C, and D (“hazardous”, i.e., redlined)], (2) year-2010 estimates of NO2 and PM2.5 air pollution levels, and (3) demographic information from the 2010 U.S. census. We find that pollution levels have a consistent and nearly monotonic association with HOLC grade, with especially pronounced (>50%) increments in NO2 levels between the most
(grade A) and least (grade D) preferentially graded neighborhoods. On a national basis, intraurban disparities for NO2 and PM2.5 are
substantially larger by historical HOLC grade than they are by race and ethnicity. However, within each HOLC grade, racial and
ethnic air pollution exposure disparities persist, indicating that redlining was only one of the many racially discriminatory policies
that impacted communities. Our findings illustrate how redlining, a nearly 80-year-old racially discriminatory policy, continues to
shape systemic environmental exposure disparities in the United States.
KEYWORDS: air pollution, redlining, NO2, PM2.5
■
INTRODUCTION
In the United States, communities of color are exposed to
higher levels of air pollution at every income level.1−4 As with
other environmental justice (EJ) issues, the causes of systemic
racial/ethnic air pollution exposure disparities are complex and
rooted in part in historical patterns of exclusion and
discrimination. While air quality has improved in the United
States over the past several decades,5−7 people of color (POC),
particularly Black and Hispanic Americans, are still exposed to
higher-than-average levels of air pollution.8−11 We examine
here how redlining, a historical, racially discriminatory 1930s
federal mortgage appraisal policy, is associated with presentday air pollution disparities in 202 U.S. cities.
Racial/ethnic air pollution exposure disparities persist in part
because the underlying sociological, economic, and policy
drivers typically evolve on generational time scales. Multiple
legacies of discrimination, including redlining and land use
decision-making, have shaped the current spatial distributions
of pollution sources among diverse communities.12−18 The
resulting locations of emissions infrastructure, including roads,
rail lines, industrial facilities, ports, and other major sources of
pollution, are typically long-lived. Similarly, while housing
discrimination was deemed unconstitutional more than 50
years ago, many areas in the United States remain racially
segregated.19−22
© 2022 The Authors. Published by
American Chemical Society
Redlining has emerged as an area of interest because it is
well documented and was explicit in its discriminatory
implementation, widespread, and carried out by the federal
government. Beginning in the 1930s, the federally sponsored
Home Owners’ Loan Corporation (HOLC) drew maps
characterizing neighborhood security for emergency home
lending for several hundred U.S. cities in the wake of the Great
Depression.23,24 These maps, which are digitized for 202 U.S.
cities,25 graded neighborhoods on a four-point scale: A (most
desirable), B (still desirable), C (definitely declining), and D
(hazardous, i.e., redlined). Many neighborhoods received the
worst grade due to the presence of Black and immigrant
communities and/or known environmental pollution sources.25,26 For example, racist language provided to HOLC
agents describes “infiltration of foreign-born, Negro, or lowergrade population” as cause for a lower neighborhood grade.25
Homes in D neighborhoods were typically ineligible for
federally backed loans or favorable mortgage terms. This
Received: December 22, 2021
Revised: February 18, 2022
Accepted: February 22, 2022
Published: March 9, 2022
345
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Figure 1. Population-weighted distributions of NO2 and PM2.5 levels within HOLC-mapped areas at the census block level. Bars represent 25th and
75th percentiles. Medians are indicated with horizontal lines, and means by the dot marker; the overall mean is indicated by the dotted line.
Unadjusted national distributions are presented for (a) NO2 and (b) PM2.5. Adjusted distributions (c and d) report the national distributions of
intraurban differences for census blocks within a given HOLC grade relative to the PWM level within each city. In each panel, pollution level
distributions are reported by both HOLC grade (left cluster) and race/ethnicity (right cluster). Vertical lines between these clusters reflect the
pollution range of the group means: the difference in the population-weighted mean between groups A and D (left line) and between the highestexposed and lowest-exposed racial/ethnic group. Panels c and d illustrate how intraurban disparities are consistently higher by historical HOLC
grade than by race/ethnicity.
industry, power generation, and other high-temperature
combustion processes. Urban areas tend to exhibit spatially
sharp NO2 gradients because primary traffic emissions are a
major source of NO2.40−43 In contrast, PM2.5 varies more on a
regional scale because it has an atmospheric lifetime of days to
weeks and is influenced strongly by both a broad array of
emission sectors and multiple secondary formation processes.44−47
This paper explores associations between historical redlining
and year-2010 air pollution levels and census demographics for
202 U.S. cities home to 65% of the U.S. urban population. We
find monotonic and highly consistent associations between
pollution levels and HOLC grades for both pollutants, with
larger intraurban disparities associated with NO2. To the best
of our knowledge, this study is the first full-scale examination
of air pollution disparities relative to historical redlining and
advances our understanding of the origins and persistence of
inequities in air pollution exposures in the United States.
practice isolated communities of color, restricting their ability
to build wealth through home ownership, and informed later
local government land use decisions that placed hazardous
industries in and near D neighborhoods.24 The discriminatory
practices captured by the HOLC maps continued until 1968,
when the Fair Housing Act banned racial discrimination in
housing, yet the legacy of explicit racial discrimination still
shapes patterns of racial residential segregation today.27
A growing body of scholarship finds associations between
redlining and present-day environmental health disparities in
U.S. cities. For example, in 64% of grade D neighborhoods, a
majority (>50%) of the population is POC (i.e., not nonHispanic White); in 74% of grade D neighborhoods, the
median income is low to moderate.27 Redlining designations
are associated with a variety of exposures, including greenspace
prevalence,28 tree canopy,29−31 urban-heat exposure disparities,29,32,33 and health effects, including asthma,34 cancer,35,36
adverse birth outcomes,37,38 and overall urban health.39 To
date, limited research has investigated air pollution exposure
and redlining,31,34 despite its importance as an environmental
risk factor.
We focus here on two key air pollutants that are significant
causes of ill health and premature mortality, nitrogen dioxide
(NO2) and fine particulate matter (PM2.5), and have distinct
sources, atmospheric behavior, and spatial patterns. NO2 is a
relatively short-lived, localized pollutant emitted by traffic,
■
MATERIALS AND METHODS
Demographic and HOLC Data. We used georeferenced
1930s era HOLC maps developed by the University of
Richmond’s Mapping Inequality project to identify HOLC
codes in 202 cities (148 U.S. census urbanized areas) across
the United States, shown in Figure S1.25 Mapped neighborhoods were categorized by HOLC into one of four grades: A,
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for the 45 million people residing in HOLC-mapped areas,
versus 10.9 ppb (NO2) and 9.9 μg m−3 (PM2.5) for the
corresponding CUAs.
Unadjusted national statistics show that redlining is strongly
associated with NO2 and more weakly but detectably
associated with PM2.5 (Figure 1a,b). PWM NO2 pollution
levels are 6.0 ppb (56%) higher in the D-grade (“hazardous”)
than in the A-grade census blocks (16.8 ppb vs 10.8 ppb).
PWM concentrations increase monotonically across HOLC
grades. For PM2.5, this monotonic association also holds, but
the PWM difference between A and D groups is smaller, 0.4 μg
m−3 (4%; 10.7 μg m−3 vs 10.3 μg m−3). The smaller difference
for PM2.5 aligns with existing research showing comparatively
smaller intraurban pollution variations that are superimposed
on a larger regional (mostly secondary) background.50,51
Redlining is also associated with intraurban pollution
gradients. PWM NO2 pollution levels for each HOLC zone,
relative to that city’s average level (Figure 1), are 1.0 and 0.1
ppb higher for D and C areas, respectively, and 0.8 and 2.0 ppb
lower for B and A areas, respectively (Figure 1c). Therefore,
the PWM intraurban difference between the D and A grades is
∼3 ppb NO2. Intraurban differences are smaller for PM2.5 than
for NO2 (Figure 1d): maximum of 0.1 μg m−3 (D grade) and
minimum of −0.3 μg m−3 (A grade), for a net 0.4 μg m−3
difference.
We find a high degree of city-to-city consistency in
intraurban disparities. PWM NO2 levels are higher in D
neighborhoods than overall (i.e., considering all HOLCmapped areas) in 80% of the 202 cities and are lower in A
neighborhoods than overall in 84% of cities. Disparities exist
not only for the average (PWM) but also throughout the
distribution. Indeed, in most (52%) cities, the interquartile
ranges (IQRs) for NO2 exhibited no overlap for the A and D
neighborhoods (i.e., the A group 75th percentile was lower
than the D group 25th percentile). For PM2.5, disparities are
again in the same direction though more modest. PWM PM2.5
levels were higher than average for D neighborhoods in 55% of
cities and lower than average for A neighborhoods in 68% of
the cities, and the A and D IQRs exhibit no overlap in 20% of
cities. Overall, trends associated with redlining hold across city
size (Figure S5), across geographical region (Figure S6), and
for the most recent-year (2015) CACES model predictions
(Figure S7).
HOLC security maps were drawn on the basis of the
demographic makeup of neighborhoods, reflecting preexisting
racial residential segregation. However, redlining further
solidified and accelerated those patterns that exist today. In
addition, areas graded as C or D often hosted industrial
facilities, railroads, and other pollution sources. We find that,
within HOLC-mapped areas, D-grade neighborhoods are more
likely to be near industrial sources and that the average number
of sources nearby increases from A to D (Figure S8).
Additionally, the portion of people living near railroads and
primary roadways increases monotonically by HOLC grade
from A to D (Figure S9). While U.S. rail infrastructure was
largely constructed before the 1930s, limited-access highways
were constructed almost entirely after the 1930s and were
preferentially constructed through Black and brown communities in U.S. cities. This comparison using rail lines and
highways emphasizes that racial disparities in air pollution
exposure reported here reflect infrastructure placement that
occurred both before and after HOLC redlining.52,53
best; B, still desirable; C, definitely declining; or D, hazardous
for mortgage appraisal. We linked HOLC maps to individual
U.S. Census blocks from the most recent available decennial
census (2010);48 census blocks provide a spatial resolution at
approximately the scale of a city block in urban areas
(geospatial procedures are described in the Supporting
Information). The resulting data set incorporates 45 million
people in 202 U.S. cities (n = 562,078 census blocks; average
population of 80 people per block).
Because of urban expansion post-1930, the HOLC areas
represent only a subset of the overall present-day urban
footprint in most metropolitan areas: the present-day urban
core. To provide context and comparison, we also separately
extend our analysis to the full U.S. Census urbanized areas
(CUA; n = 148) that contain the HOLC-mapped neighborhoods. These 148 CUAs had a year-2010 population of 161
million people (∼65% of the full U.S. population residing in
urbanized areas in 2010).
We combine race/ethnicity data to develop four aggregate
groupings for analysis: people who are Hispanic of any race
[24% of HOLC population (Table S1)], non-Hispanic White
(henceforth White, 43%), non-Hispanic Black (Black, 23%),
and non-Hispanic Asian (Asian, 7%). The remaining 3% of the
HOLC population (Other) includes Pacific Islander, Native
American, and populations self-identifying as belonging to two
or more races. The broader CUA population demographics are
as follows: 56% White, 15% Black, 7% Asian, and 19%
Hispanic.
Air Pollution Data. We characterized NO2 and PM2.5
levels using empirical (i.e., land-use regression) models
developed by the Center for Air, Climate and Energy Solutions
(CACES; www.caces.us/data).5 This data set provides annual
ambient concentration predictions for census blocks for 1979−
2015. We employ year-2010 pollution data here to align with
the most recent available (2010) decennial census. This model
surface and its predecessors are commonly used for disparity
analyses1,2,49 and predict NO2 and PM2.5 at U.S. EPA
monitoring sites with high fidelity (R2 = 0.81 and 0.84,
respectively).1 Our core results are expressed as populationweighted statistics [i.e., population-weighted mean (PWM)
and other percentiles from the population distribution of
exposures].
We first aggregate data in terms of unadjusted statistics (e.g.,
the national PWM concentration for all blocks in the D grade).
Next, to isolate associations between redlining and intraurban
gradients, we present adjusted statistics that hold constant for
city-to-city differences in air pollution and therefore reveal only
within-urban disparities. This adjusted statistic is computed as
the national PWM of the intraurban concentration difference,
i.e., the difference between census block levels and the
corresponding urban PWM across all HOLC areas in a CUA
(see section S1.2 of the Supporting Information). An example
of the input data sets for Atlanta, GA, is included in Figure S2,
and population demographics are outlined in Table S1 and
Figure S3.
■
RESULTS AND DISCUSSION
Associations between Concentration and HOLC
Category. Because HOLC-mapped areas tend to cover only
city centers and exclude suburban areas, air pollution levels in
the HOLC-mapped areas tend to be higher than in the
corresponding overall CUAs (Figure S4). Year-2010 PWM
concentrations were 15.0 ppb (NO2) and 10.6 μg m−3 (PM2.5)
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Disparities by Race/Ethnicity. We further stratified our
results by comparing each HOLC-grade PWM concentration
for individual racial/ethnic groups. Consistent with the
substantial literature on racial/ethnic disparities for air
pollution, we find that people of color experience higherthan-average NO2 and PM2.5 levels and are overrepresented
within C and D neighborhoods, consistent with prior redlining
research (Figure 1). For example, on average, PWM intraurban
pollution differences for NO2 (Figure 1c) are greater than
average for Hispanic, Asian, and Black populations (0.8, 0.4,
and 0.2 ppb higher than the urban average, respectively) and
below average for the White population (−0.6 ppb).
Differences for PM2.5 are proportionally smaller (Figure 1d)
but reflect similar racial disparities (PWMs of −0.1 μg m−3 for
White and Asian populations and 0.1 μg m−3 for Black and
Hispanic populations). Overall, intraurban PWM differences
by HOLC grade are larger than by race/ethnicity (Figure 1).
We find a substantially larger PWM differences between D and
A HOLC grades (3.0 ppb NO2 and 0.4 μg m−3 PM2.5) than
between the most- and least-exposed racial/ethnic groups [1.3
ppb NO2 and 0.26 μg m−3 PM2.5 (see Figure 1c,d)].
Next, we examined how racial/ethnic disparities interact
with historical HOLC grade. Figure 2 illustrates PWM
Letter
not. To explore the sensitivity of our overall results to racial/
ethnic segregation (i) between and (ii) within each HOLC
grade, we used stylized demographic scaling factors to
mathematically redistribute the populations in every city to
(as a counterfactual approach) eliminate intraurban racial/
ethnic segregation first between, and then within, HOLC
grades (details in section S1.3). The reduction in racial/ethnic
disparity from removing between-grade segregation was larger
for NO2 than for PM2.5. However, both results were modest
relative to the reductions produced by removing within-grade
segregation (Figure S10). These findings may reflect various
factors, including changes in demographics since the 1930s
(e.g., gentrification), within-grade gradients of proximity to
undesirable/polluting land uses (potentially preceding redlining), and later emission source placement (e.g., highways).
Figure S11 offers a complementary insight. Intraurban air
pollution disparities show distinct relationships with demographics, but there is also a stratified gradient from HOLC
grade A to D for nearly any level of demographic composition.
This suggests redlining disparity effects are one of multiple
factors that contribute to intraurban racial/ethnic disparities in
pollution exposure. Importantly, if one could remove all
between-grade disparities, that would only modestly change
the overall, because within-grade disparities are the larger
contributor to overall racial/ethnic disparities.
Broader Implications. Converging lines of evidence from
our analysis suggest the following key points. First, redlining is
associated with substantial intraurban air pollution disparities
for NO2 and PM2.5. These findings are consistent with a broad
body of evidence that adverse historical HOLC designations
are associated with worse present-day local environmental
quality and health outcomes, including air pollution, green
space, 28 tree canopy, 29−31 COVID risk, 54 and urban
heat.29,32,33 Second, for the 45 million Americans who live in
HOLC-mapped areas, NO2 and PM2.5 disparities by grade are
larger than those by race/ethnicity. Third, despite the
substantial association between HOLC redlining and aggregate
pollution disparities, we find that intraurban racial/ethnic
disparities in NO2 and PM2.5 are only moderately correlated
with historical HOLC status; most of the disparities we
observe are within grade rather than between grade. This
finding likely reflects that historical redlining is only one of
many racially discriminatory policies that have contributed to
disparate environmental exposures for people of color.
Findings here highlight that present-day disparities in U.S.
urban pollution levels reflect a legacy of structural racism in
federal policy-makingand resulting investment flows and
land use decisionsapparent in maps drawn more than 80
years ago. NO2 and PM2.5 are considered “short-lived”
pollutants (atmospheric lifetimes of approximately hours and
days, respectively), yet the systems that created these
disparities span more than a human lifetime. Results from
this work55 can support decision-makers in their efforts to
improve air pollution policy in ways that address exposure
inequities. Future work should propose, evaluate, and implement solutions that can benefit disparately impacted
communities. Fully addressing exposure inequities will require
transformations sustained across generations.
Figure 2. Population-weighted mean annual intraurban PWM levels
by HOLC grade and race/ethnicity for (a) NO2 and (b) PM2.5. All
race/ethnicity groups demonstrate monotonic increases by HOLC
grade. Disparities by HOLC grade were larger than those associated
with differences between racial/ethnic groups (100% higher for NO2
and 50% higher for PM2.5).
intraurban disparities that exist by race/ethnicity along the
A−D HOLC grade gradient. Smaller, but still substantial,
intraurban racial/ethnic disparities exist for PM2.5 and NO2
within each historical HOLC grade. On average, the withingrade white population experiences lower than average levels of
NO2 and PM2.5 while the Hispanic population experiences
above average levels. The Black population experiences
consistently above HOLC-grade-average PM2.5 levels while
the Asian population experiences above HOLC-grade-average
NO2 levels. These within-grade disparities are nearly as large as
the overall racial/ethnic disparity for the HOLC-mapped areas,
implying that a substantial portion of the racial/ethnic
exposure disparity within the study areas exists independently
of historical HOLC status.
Racial/ethnic air pollution disparities reported here are
subdivided next into two distinct effects: those that are
associated with historical HOLC redlining and those that are
■
ASSOCIATED CONTENT
sı Supporting Information
*
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.estlett.1c01012.
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Detailed description of materials and methods, supporting demographic tables, and supporting figures S1−S11
(PDF)
AUTHOR INFORMATION
Corresponding Author
Joshua S. Apte − Department of Civil and Environmental
Engineering and School of Public Health, University of
California, Berkeley, California 94720, United States;
orcid.org/0000-0002-2796-3478; Email: apte@
berkeley.edu
Authors
Haley M. Lane − Department of Civil and Environmental
Engineering, University of California, Berkeley, California
94720, United States
Rachel Morello-Frosch − School of Public Health and
Department of Environmental Science, Policy, and
Management, University of California, Berkeley, California
94720, United States
Julian D. Marshall − Department of Civil and Environmental
Engineering, University of Washington, Seattle, Washington
98195, United States; orcid.org/0000-0003-4087-1209
Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.estlett.1c01012
Notes
The authors declare no competing financial interest.
Extended data 55 are available at doi:10.6084/m9.figshare.19193243.
■
ACKNOWLEDGMENTS
This publication was developed as part of the Center for Air,
Climate and Energy Solutions (CACES), which was supported
under Assistance Agreement No. R835873 awarded by the U.S.
Environmental Protection Agency. It has not been formally
reviewed by EPA. The views expressed in this document are
solely those of authors and do not necessarily reflect those of
the Agency. EPA does not endorse any products or commercial
services mentioned in this publication.
■
Letter
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