Spurious correlation #1,938 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Detroit and the second variable is Arson in Michigan. The chart goes from 1985 to 2022, and the two variables track closely in value over that time.

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Detroit and the second variable is Arson in Michigan. The chart goes from 1985 to 2022, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As air quality worsened, it became harder for people to see through the haze, providing the perfect cover for amateur firefighters to practice their hobby. After all, when the air is already smoky, who's going to notice a few extra plumes here and there? It's like a real-life game of SimCity: Detroit edition, where the pollution level unlocks the 'arsonist' character for some fiery urban revitalization.

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image in the style of a black-and-white newspaper illustration, depicting a hazy Detroit skyline filled with smog and pollution. In the foreground, include firefighters rushing to extinguish flames in a building, with smoke billowing into the already polluted air. The scene should be dramatic and convey a sense of urgency and environmental impact. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.

This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: Poor air quality in Detroit and Arson in Michigan. Given these, which of the following image style descriptions seems most appropriate? Pick the one that seems to be related to one of the variables at hand. Please respond with only one of the following potential descriptions: Low poly An image that looks like it is a scene from 'Star Wars' A black-and-white newspaper illustration Cyberpunk Cutsy graphics
ChatGPT: A black-and-white newspaper illustration

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Poor air quality in Detroit and Arson in Michigan together. Keep the description simple.
ChatGPT: In Detroit, a hazy skyline filled with smog and pollution hangs over the city while firefighters rush to extinguish flames in a building, with smoke billowing into the already polluted air.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ A black-and-white newspaper illustration ] and depicting this scene: In Detroit, a hazy skyline filled with smog and pollution hangs over the city while firefighters rush to extinguish flames in a building, with smoke billowing into the already polluted air. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image in the style of a black-and-white newspaper illustration, depicting a hazy Detroit skyline filled with smog and pollution. In the foreground, include firefighters rushing to extinguish flames in a building, with smoke billowing into the already polluted air. The scene should be dramatic and convey a sense of urgency and environmental impact.

*Variations in the User Prompts from chart to chart are just the result of random number generation in Python. I wrote a few arrays of various styles and methods to ask questions to change up the results. Every time this site writes an explanation or generates an image, the script picks from each at random.

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.
^{Show prompt for explanation} Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how increases in Air pollution in Detroit positively influenced Arson in Michigan. Make it feel plausible.

AI academic paper

(Because p < 0.01)

Aerial Arson: Analyzing the Air Pollution-Arson Association in Michigan

The Journal of Environmental Emissions and Criminal Behavior

Jan 2024

Reminder: This paper is AI-generated. Not real!

^{Show prompt used to generate this paper} Quick note: This sequence is long and repetitive. That's how the prompt engineering works for this one. I manage the output in Python to format it into this PDF.

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft a literature review section of an academic research paper, that starts out dry for the first few sentences but then becomes hilarious and goofy.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up a literature review section of an academic research paper presenting the findings of the connection between Air pollution in Detroit and Arson in Michigan. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

Speak in the present tense for this section (the authors find...), as is common in academic research paper literature reviews. Name the sources in a format similar to this: In "Book," the authors find lorem and ipsum.

Make up the lorem and ipsum part, but make it sound related to the topic at hand.

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then name some movies that you watched that are tangentially related to the topic.

Here is the title and abstract of the paper:
[[TITLE]]
Aerial Arson: Analyzing the Air Pollution-Arson Association in Michigan

[[ABSTRACT]]
Our study delves into the relationship between air pollution levels in Detroit and incidence of arson cases across Michigan. Using data sourced from the Environmental Protection Agency and FBI Criminal Justice Information Services, we rigorously evaluated the potential link between these seemingly disparate phenomena over a period spanning from 1985 to 2022.

Our findings reveal a robust correlation coefficient of 0.7716042, indicating a significantly positive association between air pollution levels in Detroit and the occurrence of arson statewide. The statistical significance, with p < 0.01, underscores the strong evidence pointing to the influence of air quality on arson propensity.

Interestingly, our analysis suggests that as air pollution worsens, there is a proportional increase in arson incidents. It seems that when the air is smoggy, some individuals ignite a fiery passion for mischief. *Cue the dad joke drumroll!*

In conclusion, our study offers compelling evidence linking air pollution in Detroit to the occurrence of arson in Michigan, shedding light on a previously unexplored connection. These findings not only enrich the understanding of environmental criminology but also provide a lighthearted reminder that when things get heated, puns are always a safe bet.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Introduction
The connection between environmental factors and criminal behavior has long intrigued researchers and policymakers alike. In particular, the relationship between air pollution and criminal activities, such as arson, has garnered increasing attention in recent years. As we delve into the depths of this intriguing correlation, we cannot help but be reminded of the old adage, "Where there's smoke, there's fire." And where there's fire, well, there's often a perpetrator with a questionable sense of humor.
The city of Detroit, known for its rich industrial history, has also faced its fair share of environmental challenges, including elevated levels of air pollution. On the other hand, arson, the deliberate setting of fires, presents a pressing concern for law enforcement and public safety in Michigan. It seems that the air in the Motor City may not be the only thing igniting passions – *pun intended* – in the region.
Our investigation sets out to explore the potential nexus between these two seemingly disparate phenomena. Leveraging comprehensive data from the Environmental Protection Agency and the FBI Criminal Justice Information Services, we aim to unravel the mysteries behind the relationship between air pollution in Detroit and the incidence of arson across the state of Michigan. After all, who wouldn't be curious to uncover whether smoggy skies in Detroit might be fueling fiery misdeeds elsewhere?
In the following sections, we will discuss the research methodology, data analysis, and, of course, the flaming hot results of our study. But for now, let us stoke the fire of curiosity and embark on this academic adventure to investigate the intriguing interplay of air pollution and arson. After all, who knew that environmental science could set our research ablaze in such unexpected ways!

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The relationship between air pollution and criminal behavior has been a topic of substantial interest in recent decades. Smith et al. (2015) presented evidence suggesting a potential link between air pollution levels and various types of crime, including arson, in urban areas. Similarly, Doe and Jones (2018) conducted a comprehensive study examining the effects of environmental factors on criminal activities, noting a correlation between air quality degradation and an uptick in arson incidents.

Now, let's take a detour to the real world of literature and cinema, where the smoky allure of arson meets the fiery embrace of pollution. In "The Air We Breathe: Understanding Pollution in Urban Settings" by Environmental Scientist Jane Smith, the author highlights the detrimental impact of air pollution on human health and the environment, inadvertently setting the stage for an unforeseen crime thriller. Then, in "Fire in the City: A History of Arson in Michigan" by Historian John Doe, the narrative unfolds into a vivid portrayal of arson's historical significance, mirroring the blaze of urban development and industrialization.

As we venture into the realm of fiction, one cannot help but wonder about the potential intersection of air pollution and arson in the imaginative works of literature. Enter "Smoke Signals" by Mystery Writer Sarah Jones, a gripping novel that blurs the line between environmental catastrophe and criminal intrigue. And who can forget "The Dystopian Blaze" by Sci-Fi Author Chris Smith, a futuristic tale where air pollution and arson intertwine in a fiery dystopia.

Bringing the convergence of air pollution and arson to the big screen, the movie "Burning Bridges" captures the tension between environmental degradation and criminal impulsivity, painting a vivid portrait of the incendiary effects of pollution on human behavior. Meanwhile, "Smoke and Mirrors: A Tale of Arson and Alibis" provides a cinematic escape into the murky world of crime and environmental calamity, fueling the audience's imagination with smoldering suspense.

As we navigate through this eclectic landscape of literature and film, it becomes clear that the entanglement of air pollution and arson transcends the boundaries of reality, extending its reach into the realms of imagination and entertainment. Who would have thought that the air we breathe and the flames that ignite could become the unlikely protagonists of a compelling narrative, leaving us with an unexpected plot twist and a comedic reminder that, sometimes, academic research can be a real "fire"house of surprises!

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the methodology section of an academic research paper.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the methodology section of an academic research paper presenting the findings of the connection between Air pollution in Detroit and Arson in Michigan. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and FBI Criminal Justice Information Services . You used data from 1985 to 2022

Make up the research methods you don't know. Make them a bit goofy and convoluted.

Here is the title, abstract, and introduction of the paper:
[[TITLE]]
Aerial Arson: Analyzing the Air Pollution-Arson Association in Michigan

[[ABSTRACT]]
Our study delves into the relationship between air pollution levels in Detroit and incidence of arson cases across Michigan. Using data sourced from the Environmental Protection Agency and FBI Criminal Justice Information Services, we rigorously evaluated the potential link between these seemingly disparate phenomena over a period spanning from 1985 to 2022.

Our findings reveal a robust correlation coefficient of 0.7716042, indicating a significantly positive association between air pollution levels in Detroit and the occurrence of arson statewide. The statistical significance, with p < 0.01, underscores the strong evidence pointing to the influence of air quality on arson propensity.

Interestingly, our analysis suggests that as air pollution worsens, there is a proportional increase in arson incidents. It seems that when the air is smoggy, some individuals ignite a fiery passion for mischief. *Cue the dad joke drumroll!*

In conclusion, our study offers compelling evidence linking air pollution in Detroit to the occurrence of arson in Michigan, shedding light on a previously unexplored connection. These findings not only enrich the understanding of environmental criminology but also provide a lighthearted reminder that when things get heated, puns are always a safe bet.

[[INTRODUCTION]]
Introduction
The connection between environmental factors and criminal behavior has long intrigued researchers and policymakers alike. In particular, the relationship between air pollution and criminal activities, such as arson, has garnered increasing attention in recent years. As we delve into the depths of this intriguing correlation, we cannot help but be reminded of the old adage, "Where there's smoke, there's fire." And where there's fire, well, there's often a perpetrator with a questionable sense of humor.
The city of Detroit, known for its rich industrial history, has also faced its fair share of environmental challenges, including elevated levels of air pollution. On the other hand, arson, the deliberate setting of fires, presents a pressing concern for law enforcement and public safety in Michigan. It seems that the air in the Motor City may not be the only thing igniting passions – *pun intended* – in the region.
Our investigation sets out to explore the potential nexus between these two seemingly disparate phenomena. Leveraging comprehensive data from the Environmental Protection Agency and the FBI Criminal Justice Information Services, we aim to unravel the mysteries behind the relationship between air pollution in Detroit and the incidence of arson across the state of Michigan. After all, who wouldn't be curious to uncover whether smoggy skies in Detroit might be fueling fiery misdeeds elsewhere?
In the following sections, we will discuss the research methodology, data analysis, and, of course, the flaming hot results of our study. But for now, let us stoke the fire of curiosity and embark on this academic adventure to investigate the intriguing interplay of air pollution and arson. After all, who knew that environmental science could set our research ablaze in such unexpected ways!

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

To begin our investigation, we harnessed a blend of traditional research methods and cutting-edge statistical techniques. First, we collected historical air pollution data from the Environmental Protection Agency, scrutinizing the levels of pollutants such as particulate matter, sulfur dioxide, and nitrogen dioxide. We then combed through the FBI Criminal Justice Information Services database to identify and analyze arson incidents in Michigan, meticulously documenting the time, location, and circumstances of each case. It was a process that required patience, keen attention to detail, and an unwavering willingness to resist the urge to crack puns about literal data "burning up" our time.

Once data collection was complete, we embarked on a classic rendezvous with statistical analysis. Employing rigorous quantitative methods, we calculated correlation coefficients and conducted regression analyses to unveil the potential relationship between air pollution levels in Detroit and the prevalence of arson across various regions in Michigan. Our approach aimed to unveil any hidden connections, like finding the proverbial needle in a haystack – although in this case, the "haystack" was the data and the "needle" was the elusive link between air quality and criminal behavior. Spoiler alert: we found more than just snoozy statistical significance – we ignited a flame of scientific curiosity that blazed its way into intriguing findings. *Insert obligatory dad joke wink here.*

Furthermore, we employed time-series analysis to explore the temporal dynamics of air pollution and arson incidents. This involved considering different time lags to assess whether changes in air quality could predict future changes in arson rates, or if it was just a case of correlation without causation. It was a bit like trying to predict the spark of inspiration that leads to a dad joke – sometimes it's evident, and other times, it seemingly emerges out of thin air. But I digress.

In addition to quantitative analyses, we embarked on qualitative investigations, conducting interviews with local authorities and experts in environmental science and law enforcement. Their insights helped to paint a comprehensive picture of the environmental and social factors intertwining with arson incidents, providing valuable context to complement our statistical findings. It was like adding a splash of color to a monochromatic canvas, bringing depth and dimension to our understanding of the relationship between air pollution and arson. All in all, our research methodology was as meticulous as it was multifaceted, leaving no stone unturned in our quest to uncover the intriguing connection between environmental quality and criminal behavior.

In the next section, we will delve into the scorching hot results of our data analysis, providing a comprehensive overview of the findings that emerged from our investigation. So, grab your metaphorical marshmallows, because things are about to get lit!

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the discussion section of an academic research paper.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the discussion section of an academic research paper presenting the findings of the connection between Air pollution in Detroit and Arson in Michigan. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Limit your response to 500 tokens.

Here are the title, abstract, literature review, and results sections. Please harken back to 1-2 of the goofy items in the literature review, but pretend to take them completely seriously. Discuss how your results supported the prior research.

Do not write a conclusion. I will add a conclusion after this.

[[TITLE]]
Aerial Arson: Analyzing the Air Pollution-Arson Association in Michigan

[[ABSTRACT]]
Our study delves into the relationship between air pollution levels in Detroit and incidence of arson cases across Michigan. Using data sourced from the Environmental Protection Agency and FBI Criminal Justice Information Services, we rigorously evaluated the potential link between these seemingly disparate phenomena over a period spanning from 1985 to 2022.

Our findings reveal a robust correlation coefficient of 0.7716042, indicating a significantly positive association between air pollution levels in Detroit and the occurrence of arson statewide. The statistical significance, with p < 0.01, underscores the strong evidence pointing to the influence of air quality on arson propensity.

Interestingly, our analysis suggests that as air pollution worsens, there is a proportional increase in arson incidents. It seems that when the air is smoggy, some individuals ignite a fiery passion for mischief. *Cue the dad joke drumroll!*

In conclusion, our study offers compelling evidence linking air pollution in Detroit to the occurrence of arson in Michigan, shedding light on a previously unexplored connection. These findings not only enrich the understanding of environmental criminology but also provide a lighthearted reminder that when things get heated, puns are always a safe bet.

[[LITERATURE REVIEW]]
The relationship between air pollution and criminal behavior has been a topic of substantial interest in recent decades. Smith et al. (2015) presented evidence suggesting a potential link between air pollution levels and various types of crime, including arson, in urban areas. Similarly, Doe and Jones (2018) conducted a comprehensive study examining the effects of environmental factors on criminal activities, noting a correlation between air quality degradation and an uptick in arson incidents.
Now, let's take a detour to the real world of literature and cinema, where the smoky allure of arson meets the fiery embrace of pollution. In "The Air We Breathe: Understanding Pollution in Urban Settings" by Environmental Scientist Jane Smith, the author highlights the detrimental impact of air pollution on human health and the environment, inadvertently setting the stage for an unforeseen crime thriller. Then, in "Fire in the City: A History of Arson in Michigan" by Historian John Doe, the narrative unfolds into a vivid portrayal of arson's historical significance, mirroring the blaze of urban development and industrialization.
As we venture into the realm of fiction, one cannot help but wonder about the potential intersection of air pollution and arson in the imaginative works of literature. Enter "Smoke Signals" by Mystery Writer Sarah Jones, a gripping novel that blurs the line between environmental catastrophe and criminal intrigue. And who can forget "The Dystopian Blaze" by Sci-Fi Author Chris Smith, a futuristic tale where air pollution and arson intertwine in a fiery dystopia.
Bringing the convergence of air pollution and arson to the big screen, the movie "Burning Bridges" captures the tension between environmental degradation and criminal impulsivity, painting a vivid portrait of the incendiary effects of pollution on human behavior. Meanwhile, "Smoke and Mirrors: A Tale of Arson and Alibis" provides a cinematic escape into the murky world of crime and environmental calamity, fueling the audience's imagination with smoldering suspense.
As we navigate through this eclectic landscape of literature and film, it becomes clear that the entanglement of air pollution and arson transcends the boundaries of reality, extending its reach into the realms of imagination and entertainment. Who would have thought that the air we breathe and the flames that ignite could become the unlikely protagonists of a compelling narrative, leaving us with an unexpected plot twist and a comedic reminder that, sometimes, academic research can be a real "fire"house of surprises!

[[RESULTS]]
The statistical analysis of the relationship between air pollution levels in Detroit and incidents of arson across Michigan yielded a robust correlation coefficient of 0.7716042. This positive correlation suggests that as air pollution levels in Detroit increased, so did the occurrence of arson incidents across the state. It seems that where there's smog, there's likely to be a surge in fiery shenanigans.
The strong correlation coefficient was further supported by an r-squared value of 0.5953731, signifying that approximately 59.5% of the variation in arson incidents can be explained by variations in air pollution levels in Detroit. In other words, the air pollution in Detroit appears to be a significant factor in heating up the rate of arson in Michigan.
The statistical significance of the correlation was confirmed by the p-value of less than 0.01, providing strong evidence of the association between air pollution and arson. It's safe to say that the association between air pollution and arson is no mere smokescreen – it's statistically significant and not just hot air.
Figure 1, a scatterplot illustrating the relationship between air pollution levels in Detroit and arson incidents in Michigan, visually encapsulates the compelling correlation uncovered by our analysis. The scatterplot showcases how as air pollution levels increase, so too does the occurrence of arson, giving a whole new meaning to the phrase "adding fuel to the fire."
In summary, the results of this study reveal a noteworthy association between air pollution in Detroit and the incidence of arson statewide. These findings not only contribute to the burgeoning field of environmental criminology but also serve as a reminder that even in the realm of academia, unexpected connections can ignite new avenues of research.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The findings of our study corroborate prior research by Smith et al. (2015) and Doe and Jones (2018), who laid the groundwork for exploring the connection between air pollution and criminal behavior, specifically arson. Our robust correlation coefficient of 0.7716042 aligns with the established evidence, indicating a strong positive association between air pollution levels in Detroit and the occurrence of arson across Michigan. It appears that the proverbial sparks from Detroit's air pollution have been igniting more than just fireworks in Michigan – cue the *Dad joke drumroll*.

While our literature review may have ventured into literary and cinematic realms, the statistical results have firmly grounded our findings in empirical reality. As air pollution worsens, there is a proportional increase in arson incidents, echoing the ominous warning: when the air is smoggy, some individuals develop a burning desire for mischief. *Cue the groans from fellow academics*.

The r-squared value of 0.5953731 further reinforces the substantial influence of air pollution in Detroit on arson incidents statewide. Approximately 59.5% of the variation in arson incidents can be attributed to variations in air pollution levels in Detroit, providing compelling evidence of the impact of smog on incendiary activities. In essence, it seems that when it comes to arson in Michigan, "where there's smoke, there's fire" – both literally and figuratively.

Moreover, the statistical significance of the correlation, with a p-value of less than 0.01, underscores the robustness of the association between air pollution and arson. It's a reminder that this correlation is not just a figment of statistical wildfire; it's a statistically significant and real manifestation of the influence of air pollution on criminal intent.

The scatterplot illustrating the relationship between air pollution levels in Detroit and arson incidents provides a vivid visual representation of our findings. The plot graphically captures how as air pollution levels soar, so too do the occurrences of arson, offering a captivating depiction of the proverbial "adding fuel to the fire."

In essence, our study provides empirical support for the link between air pollution in Detroit and the incidence of arson in Michigan. These findings not only offer valuable insight for environmental criminology but also serve as a lighthearted reminder that when it comes to research, uncovering unexpected connections can lead to some truly "fire"y revelations.

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the discussion section of goofy academic research papers that sounds like it belongs based on the title and abstract provided.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up a short conclusion of an academic research paper presenting the findings of the connection between Air pollution in Detroit and Arson in Michigan. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Limit your response to 300 tokens. At the very end, assert that no more research is needed in this area.

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
Aerial Arson: Analyzing the Air Pollution-Arson Association in Michigan

[[ABSTRACT]]
Our study delves into the relationship between air pollution levels in Detroit and incidence of arson cases across Michigan. Using data sourced from the Environmental Protection Agency and FBI Criminal Justice Information Services, we rigorously evaluated the potential link between these seemingly disparate phenomena over a period spanning from 1985 to 2022.

Our findings reveal a robust correlation coefficient of 0.7716042, indicating a significantly positive association between air pollution levels in Detroit and the occurrence of arson statewide. The statistical significance, with p < 0.01, underscores the strong evidence pointing to the influence of air quality on arson propensity.

Interestingly, our analysis suggests that as air pollution worsens, there is a proportional increase in arson incidents. It seems that when the air is smoggy, some individuals ignite a fiery passion for mischief. *Cue the dad joke drumroll!*

In conclusion, our study offers compelling evidence linking air pollution in Detroit to the occurrence of arson in Michigan, shedding light on a previously unexplored connection. These findings not only enrich the understanding of environmental criminology but also provide a lighthearted reminder that when things get heated, puns are always a safe bet.

[[INTRDUCTION]]
Introduction
The connection between environmental factors and criminal behavior has long intrigued researchers and policymakers alike. In particular, the relationship between air pollution and criminal activities, such as arson, has garnered increasing attention in recent years. As we delve into the depths of this intriguing correlation, we cannot help but be reminded of the old adage, "Where there's smoke, there's fire." And where there's fire, well, there's often a perpetrator with a questionable sense of humor.
The city of Detroit, known for its rich industrial history, has also faced its fair share of environmental challenges, including elevated levels of air pollution. On the other hand, arson, the deliberate setting of fires, presents a pressing concern for law enforcement and public safety in Michigan. It seems that the air in the Motor City may not be the only thing igniting passions – *pun intended* – in the region.
Our investigation sets out to explore the potential nexus between these two seemingly disparate phenomena. Leveraging comprehensive data from the Environmental Protection Agency and the FBI Criminal Justice Information Services, we aim to unravel the mysteries behind the relationship between air pollution in Detroit and the incidence of arson across the state of Michigan. After all, who wouldn't be curious to uncover whether smoggy skies in Detroit might be fueling fiery misdeeds elsewhere?
In the following sections, we will discuss the research methodology, data analysis, and, of course, the flaming hot results of our study. But for now, let us stoke the fire of curiosity and embark on this academic adventure to investigate the intriguing interplay of air pollution and arson. After all, who knew that environmental science could set our research ablaze in such unexpected ways!

[[RESULTS]]
The statistical analysis of the relationship between air pollution levels in Detroit and incidents of arson across Michigan yielded a robust correlation coefficient of 0.7716042. This positive correlation suggests that as air pollution levels in Detroit increased, so did the occurrence of arson incidents across the state. It seems that where there's smog, there's likely to be a surge in fiery shenanigans.
The strong correlation coefficient was further supported by an r-squared value of 0.5953731, signifying that approximately 59.5% of the variation in arson incidents can be explained by variations in air pollution levels in Detroit. In other words, the air pollution in Detroit appears to be a significant factor in heating up the rate of arson in Michigan.
The statistical significance of the correlation was confirmed by the p-value of less than 0.01, providing strong evidence of the association between air pollution and arson. It's safe to say that the association between air pollution and arson is no mere smokescreen – it's statistically significant and not just hot air.
Figure 1, a scatterplot illustrating the relationship between air pollution levels in Detroit and arson incidents in Michigan, visually encapsulates the compelling correlation uncovered by our analysis. The scatterplot showcases how as air pollution levels increase, so too does the occurrence of arson, giving a whole new meaning to the phrase "adding fuel to the fire."
In summary, the results of this study reveal a noteworthy association between air pollution in Detroit and the incidence of arson statewide. These findings not only contribute to the burgeoning field of environmental criminology but also serve as a reminder that even in the realm of academia, unexpected connections can ignite new avenues of research.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In summation, our analysis has illuminated a compelling relationship between air pollution levels in Detroit and the occurrence of arson statewide in Michigan. The robust correlation coefficient and statistical significance underscore the influence of air quality on arson propensity, demonstrating that when the air is smoggy, some individuals ignite a fiery passion for mischief. *ba-dum-tss!*

These findings contribute to the growing body of knowledge in environmental criminology, shedding light on a previously unexplored connection and emphasizing the broader impact of environmental factors on criminal behavior. It seems that when it comes to crime, the adage "where there's smoke, there's fire" takes on a whole new meaning in the context of air pollution and arson. *Insert obligatory nod of scholarly acknowledgment here*

As we wrap up this fiery investigation, let our findings serve as a reminder that in the realm of research, unexpected connections can ignite new avenues of exploration. And when it comes to understanding the interplay between environmental elements and criminal activities, well, there's always more than meets the eye. *Cue the dramatic academic mic drop*

In conclusion, our study offers a flame-worthy contribution to the understanding of air pollution's impact on arson in Michigan, highlighting the need for continued interdisciplinary research at the intersection of environmental science and criminology. However, in the spirit of a well-placed dad joke, after this scorching analysis, we confidently assert that no more research is needed in this area. It's time to let this topic cool down and let these findings smolder in scholarly memory. *Oh, the things we do for punny conclusions!*

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of academic journals. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding research, scientific, or academic journal that would publish a paper entited Aerial Arson: Analyzing the Air Pollution-Arson Association in Michigan. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental Emissions and Criminal Behavior

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of nonprofit research organizations and associations. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding nonprofit, academic, or scientific association or organization that would sponsor research that resulted in a paper entited Aerial Arson: Analyzing the Air Pollution-Arson Association in Michigan. Respond only with the name of a fictional organization.

ChatGPT:

The Institute for Atmospheric Arson Analysis

Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled Aerial Arson: Analyzing the Air Pollution-Arson Association in Michigan with an abstract of Our study delves into the relationship between air pollution levels in Detroit and incidence of arson cases across Michigan. Using data sourced from the Environmental Protection Agency and FBI Criminal Justice Information Services, we rigorously evaluated the potential link between these seemingly disparate phenomena over a period spanning from 1985 to 2022.
Our findings reveal a robust correlation coefficient of 0.7716042, indicating a significantly positive association between air pollution levels in Detroit and the occurrence of arson statewide. The statistical significance, with p < 0.01, underscores the strong evidence pointing to the influence of air quality on arson propensity.
Interestingly, our analysis suggests that as air pollution worsens, there is a proportional increase in arson incidents. It seems that when the air is smoggy, some individuals ignite a fiery passion for mischief. *Cue the dad joke drumroll!*
In conclusion, our study offers compelling evidence linking air pollution in Detroit to the occurrence of arson in Michigan, shedding light on a previously unexplored connection. These findings not only enrich the understanding of environmental criminology but also provide a lighthearted reminder that when things get heated, puns are always a safe bet.

ChatGPT:

air pollution, arson, Detroit, Michigan, correlation coefficient, environmental criminology, EPA data, FBI Criminal Justice Information Services, air quality, arson incidents, smoggy air, environmental influences on crime

*There is a bunch of Python happening behind the scenes to turn this prompt sequence into a PDF.

Random correlation

Discover a new correlation

View all correlations

View all research papers

Report an error

Data details

Air pollution in Detroit
Detailed data title: Percentage of days 'unhealthy' or worse air quality in Detroit-Warren-Dearborn, MI
Source: Environmental Protection Agency
See what else correlates with Air pollution in Detroit

Arson in Michigan
Detailed data title: The arson rate per 100,000 residents in Michigan
Source: FBI Criminal Justice Information Services
See what else correlates with Arson in Michigan

Correlation r = 0.7716042 (Pearson correlation coefficient)
Correlation is a measure of how much the variables move together. If it is 0.99, when one goes up the other goes up. If it is 0.02, the connection is very weak or non-existent. If it is -0.99, then when one goes up the other goes down. If it is 1.00, you probably messed up your correlation function.

r² = 0.5953731 (Coefficient of determination)
This means 59.5% of the change in the one variable (i.e., Arson in Michigan) is predictable based on the change in the other (i.e., Air pollution in Detroit) over the 38 years from 1985 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.4E-8.^Show 0.0000000142200199518639570000
The p-value is a measure of how probable it is that we would randomly find a result this extreme.^Note More specifically the p-value is a measure of how probable it is that we would randomly find a result this extreme if we had only tested one pair of variables one time.

But I am a p-villain. I absolutely did not test only one pair of variables one time. I correlated hundreds of millions of pairs of variables. I threw boatloads of data into an industrial-sized blender to find this correlation.

Who is going to stop me? p-value reporting doesn't require me to report how many calculations I had to go through in order to find a low p-value!
On average, you will find a correaltion as strong as 0.77 in 1.4E-6% of random cases. Said differently, if you correlated 70,323,389 random variables^Note You don't actually need 70 million variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

p-value calculations are useful for understanding the probability of a result happening by chance. They are most useful when used to highlight the risk of a fluke outcome. For example, if you calculate a p-value of 0.30, the risk that the result is a fluke is high. It is good to know that! But there are lots of ways to get a p-value of less than 0.01, as evidenced by this project.

In this particular case, the values are so extreme as to be meaningless. That's why no one reports p-values with specificity after they drop below 0.01.

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 37 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 37 because we have two variables measured over a period of 38 years. It's just the number of years minus ( the number of variables minus one ), which in this case simplifies to the number of years minus one.
you would randomly expect to find a correlation as strong as this one.

[ 0.6, 0.88 ] 95% correlation confidence interval (using the Fisher z-transformation)
^{Read more about the confidence interval} The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

This one is a bit more complciated than the other calculations, but I include it because many people have been pushing for confidence intervals instead of p-value calculations (for example: NEJM. However, if you are dredging data, you can reliably find yourself in the 5%. That's my goal!

All values for the years included above: ^Note If I were being very sneaky, I could trim years from the beginning or end of the datasets to increase the correlation on some pairs of variables. I don't do that because there are already plenty of correlations in my database without monkeying with the years.

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.

	1985	1986	1987	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
Air pollution in Detroit (Bad air quality days)	1.36986	3.56164	3.56164	9.01639	4.65753	2.73973	7.12329	1.91257	1.36986	3.0137	3.28767	3.55191	3.28767	3.83562	3.83562	0.819672	4.10959	6.0274	2.46575	0.273224	4.65753	0.821918	2.46575	0.273224	0.273973	0.547945	0.821918	0.819672	0	0	0.273973	0	0	0.547945	0	0.546448	0	0
Arson in Michigan (Arson rate)	43.1	60.7	59.8	55.1	49.6	48	50.6	47.8	44.9	43.5	41.9	47.1	55.6	51	46.3	23.4	42.5	48.8	40.7	36.9	31.8	32.1	29.7	28.6	26.8	30.4	27	24.5	20.2	17.2	20.4	17.9	19.6	17.7	16.8	18.4	14.9	13

Why this works

Data dredging: I have 25,153 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 632,673,409 correlation calculations! This is called “data dredging.” Instead of starting with a hypothesis and testing it, I instead abused the data to see what correlations shake out. It’s a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random.
Lack of causal connection: There is probably^Note Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple^Note Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
p-value calculation does not take this into account, so mathematically it appears less probable than it really is.

Try it yourself

You can calculate the values on this page on your own! Try running the Python code to see the calculation results. ^{Show the steps to do this.} Step 1: Download and install Python on your computer.

Step 2: Open a plaintext editor like Notepad and paste the code below into it.

Step 3: Save the file as "calculate_correlation.py" in a place you will remember, like your desktop. Copy the file location to your clipboard. On Windows, you can right-click the file and click "Properties," and then copy what comes after "Location:" As an example, on my computer the location is "C:\Users\tyler\Desktop"

Step 4: Open a command line window. For example, by pressing start and typing "cmd" and them pressing enter.

Step 5: Install the required modules by typing "pip install numpy", then pressing enter, then typing "pip install scipy", then pressing enter.

Step 6: Navigate to the location where you saved the Python file by using the "cd" command. For example, I would type "cd C:\Users\tyler\Desktop" and push enter.

Step 7: Run the Python script by typing "python calculate_correlation.py"

If you run into any issues, I suggest asking ChatGPT to walk you through installing Python and running the code below on your system. Try this question:

"Walk me through installing Python on my computer to run a script that uses scipy and numpy. Go step-by-step and ask me to confirm before moving on. Start by asking me questions about my operating system so that you know how to proceed. Assume I want the simplest installation with the latest version of Python and that I do not currently have any of the necessary elements installed. Remember to only give me one step per response and confirm I have done it before proceeding."

# These modules make it easier to perform the calculation
import numpy as np
from scipy import stats

# We'll define a function that we can call to return the correlation calculations
def calculate_correlation(array1, array2):

    # Calculate Pearson correlation coefficient and p-value
    correlation, p_value = stats.pearsonr(array1, array2)

    # Calculate R-squared as the square of the correlation coefficient
    r_squared = correlation**2

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([1.36986,3.56164,3.56164,9.01639,4.65753,2.73973,7.12329,1.91257,1.36986,3.0137,3.28767,3.55191,3.28767,3.83562,3.83562,0.819672,4.10959,6.0274,2.46575,0.273224,4.65753,0.821918,2.46575,0.273224,0.273973,0.547945,0.821918,0.819672,0,0,0.273973,0,0,0.547945,0,0.546448,0,0,])
array_2 = np.array([43.1,60.7,59.8,55.1,49.6,48,50.6,47.8,44.9,43.5,41.9,47.1,55.6,51,46.3,23.4,42.5,48.8,40.7,36.9,31.8,32.1,29.7,28.6,26.8,30.4,27,24.5,20.2,17.2,20.4,17.9,19.6,17.7,16.8,18.4,14.9,13,])
array_1_name = "Air pollution in Detroit"
array_2_name = "Arson in Michigan"

# Perform the calculation
print(f"Calculating the correlation between {array_1_name} and {array_2_name}...")
correlation, r_squared, p_value = calculate_correlation(array_1, array_2)

# Print the results
print("Correlation Coefficient:", correlation)
print("R-squared:", r_squared)
print("P-value:", p_value)

Reuseable content

You may re-use the images on this page for any purpose, even commercial purposes, without asking for permission. The only requirement is that you attribute Tyler Vigen. ^Note Attribution can take many different forms. If you leave the "tylervigen.com" link in the image, that satisfies it just fine. If you remove it and move it to a footnote, that's fine too. You can also just write "Charts courtesy of Tyler Vigen" at the bottom of an article.

You do not need to attribute "the spurious correlations website," and you don't even need to link here if you don't want to. I don't gain anything from pageviews. There are no ads on this site, there is nothing for sale, and I am not for hire.

For the record, I am just one person. Tyler Vigen, he/him/his. I do have degrees, but they should not go after my name unless you want to annoy my wife. If that is your goal, then go ahead and cite me as "Tyler Vigen, A.A. A.A.S. B.A. J.D." Otherwise it is just "Tyler Vigen."

When spoken, my last name is pronounced "vegan," like I don't eat meat.

Full license details.
For more on re-use permissions, or to get a signed release form, see tylervigen.com/permission.

Download images for these variables:

High resolution line chart ^Note The image linked here is a Scalable Vector Graphic (SVG). It is the highest resolution that is possible to achieve. It scales up beyond the size of the observable universe without pixelating. You do not need to email me asking if I have a higher resolution image. I do not. The physical limitations of our universe prevent me from providing you with an image that is any higher resolution than this one.

If you insert it into a PowerPoint presentation (a tool well-known for managing things that are the scale of the universe), you can right-click > "Ungroup" or "Create Shape" and then edit the lines and text directly. You can also change the colors this way.

Alternatively you can use a tool like Inkscape.
High resolution line chart, optimized for mobile
Alternative high resolution line chart
Scatterplot
Portable line chart (png)
Portable line chart (png), optimized for mobile
Line chart for only Air pollution in Detroit
Line chart for only Arson in Michigan
AI-generated correlation image
The spurious research paper: Aerial Arson: Analyzing the Air Pollution-Arson Association in Michigan

View another random correlation

How fun was this correlation?

Cheers to you for rating this correlation!

Correlation ID: 1938 · Black Variable ID: 20549 · Red Variable ID: 20050


Problem variable:
Issue:
Additional details: Optional
Confirm you are a human: