Spurious correlation #1,307 · 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 Ann Arbor and the second variable is Jet fuel used in Sierra Leone. The chart goes from 1980 to 2021, 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 Ann Arbor and the second variable is Jet fuel used in Sierra Leone. The chart goes from 1980 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As air pollution decreased in Ann Arbor, it created a ripple effect of cleaner air globally. This ultimately led to a decrease in the production of jet fuel used in Sierra Leone, as the pristine air in Ann Arbor somehow communicated to the aviation industry in a telekinetic fashion, prompting them to reduce their fuel usage in a quest for environmental harmony. After all, who knew that Ann Arbor, home of the Wolverines, held the power to influence transcontinental fuel dynamics? It's as if the scent of blooming cherry blossoms in Ann Arbor wafted all the way to Sierra Leone, inspiring a newfound commitment to eco-friendly sky-high travels.

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image inspired by [ Data cyber art ] that depicts a unique fusion of the serene skies above Ann Arbor and the tranquil atmosphere of Sierra Leone. The scene showcases a seamless blend of the clearer, less clouded skies of Ann Arbor with the unpolluted, crystalline atmosphere of Sierra Leone. The image should evoke a dreamlike and futuristic aesthetic that conveys a sense of harmonious coexistence between these two distinct locales. The focus is on the clarity and purity of the air, with the horizon and distant mountains prominently visible. This visually stunning and serene composition should convey a sense of wonder and appreciation for the natural beauty of both environments. 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 situation described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here is a situation: Researchers have discovered a surprising correlation between the decrease in unhealthy air quality in Ann Arbor and the reduction in jet fuel used in Sierra Leone. It turns out that the decrease in air pollution has led to a decrease in the formation of cloud animals in the sky, which were a major distraction for pilots, leading to more fuel-efficient flights!. Given that situation, which of the following image descriptions seems most appropriate? Pick the one that seems to be related to one of the variables at hand and the tone of the explanation. Please respond with only one of the following potential descriptions: inspired by bauhaus 3D Pixar Style A Discovery magazine cover image Data cyber art 3D Pixar Style
ChatGPT: Data cyber art

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated and the explanation described. Do not reference graphs or charts; describe physical objects.
User prompt: Please describe a visual scene that depicts the following situation. Keep the description simple. Researchers have discovered a surprising correlation between the decrease in unhealthy air quality in Ann Arbor and the reduction in jet fuel used in Sierra Leone. It turns out that the decrease in air pollution has led to a decrease in the formation of cloud animals in the sky, which were a major distraction for pilots, leading to more fuel-efficient flights!
ChatGPT: In Ann Arbor, the sky is noticeably clearer with fewer billowing clouds of varying shapes. The air feels fresher and more transparent, allowing for a clearer view of the horizon. Meanwhile, in Sierra Leone, there are fewer airplanes streaking across the sky, and the air above the airport is notably less smoky. The absence of lingering jet fuel fumes makes the air seem crisper, and the distant mountains are clearly visible through the clean, unpolluted 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: [ Data cyber art ] and depicting this scene: In Ann Arbor, the sky is noticeably clearer with fewer billowing clouds of varying shapes. The air feels fresher and more transparent, allowing for a clearer view of the horizon. Meanwhile, in Sierra Leone, there are fewer airplanes streaking across the sky, and the air above the airport is notably less smoky. The absence of lingering jet fuel fumes makes the air seem crisper, and the distant mountains are clearly visible through the clean, unpolluted air. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image inspired by [ Data cyber art ] that depicts a unique fusion of the serene skies above Ann Arbor and the tranquil atmosphere of Sierra Leone. The scene showcases a seamless blend of the clearer, less clouded skies of Ann Arbor with the unpolluted, crystalline atmosphere of Sierra Leone. The image should evoke a dreamlike and futuristic aesthetic that conveys a sense of harmonious coexistence between these two distinct locales. The focus is on the clarity and purity of the air, with the horizon and distant mountains prominently visible. This visually stunning and serene composition should convey a sense of wonder and appreciation for the natural beauty of both environments.

*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 a decrease in Air pollution in Ann Arbor caused Jet fuel used in Sierra Leone to decrease.\Make it sound serious until the end.

AI academic paper

(Because p < 0.01)

Aerial Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone

The Journal of Atmospheric Explorations

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 Ann Arbor and Jet fuel used in Sierra Leone. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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 a couple popular internet memes that are related to one of the topics.

Here is the title and abstract of the paper:
[[TITLE]]
Aerial Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone

[[ABSTRACT]]
The impact of air pollution on human health has been a pressing concern globally, and the interconnection between air quality in Ann Arbor and jet fuel consumption in Sierra Leone is a topic of growing interest. In this study, we delve into the overlooked relationship between these seemingly disparate locations and the potentially enlightening implications of their correlation.

Utilizing data from the Environmental Protection Agency and the Energy Information Administration, a robust analysis was conducted to scrutinize the link between air pollution levels in Ann Arbor and the usage of jet fuel in Sierra Leone from 1980 to 2021. The findings reveal a striking correlation coefficient of 0.7409458 and a statistically significant p-value of less than 0.01, shedding light on a compelling association.

While this connection may seem like a flight of fancy, our results indicate a tangible relationship worthy of further exploration. Beyond the statistics, this investigation offers an opportunity to ruminate on the far-reaching impact of human activities and the unpredictably synchronized consequences across the globe. This peculiar pairing prompts a whimsical waltz of the mind and, perhaps, a soaring perspective on the interconnected nature of our world.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The pervasive issue of air pollution has garnered increasing attention due to its detrimental effects on public health and the environment. One of the frequently overlooked aspects of this complex problem is the connection between air quality in Ann Arbor, Michigan, and the consumption of jet fuel in Sierra Leone. While these two locations may seem unrelated at first glance, our investigation embarks on a scholarly exploration of the potential correlations and implications of this intriguing juxtaposition.
As the world grapples with the consequences of anthropogenic activities, understanding the intricate web of interactions between seemingly disparate regions holds significant value. This study uncovers the surprising linkage between air pollution in an urban setting in the United States and the utilization of aviation fuel in a West African nation, prompting a sophisticated analysis that transcends geographical boundaries in pursuit of actionable insights.
The investigation commences with a review of the prevailing literature on air pollution and aviation fuel consumption, establishing the foundation for our empirical investigation. While previous research predominantly focuses on localized impacts of air pollution and the aviation industry, the present study takes a novel approach by examining the intriguing interplay between a specific source of emissions and its potential repercussions across continents.
Drawing on comprehensive datasets from the Environmental Protection Agency and the Energy Information Administration, our rigorous analysis enables an in-depth scrutiny of the relationship between air pollution levels in Ann Arbor and the consumption patterns of jet fuel in Sierra Leone. The utilization of advanced statistical methods and econometric models facilitates a thorough exploration of the association between these variables, culminating in compelling conclusions that defy conventional expectations.
While the correlation between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone may seem like a whimsical notion, our findings substantiate a robust relationship deserving of scholarly attention. Beyond the statistical scrutiny, this unconventional connection serves as a poignant reminder of the interconnectedness of global phenomena and the multidimensional repercussions of human activities.
As we embark on this scholarly journey, our empirical odyssey unveils not only the scientific insights into air pollution and aviation fuel but also a playful dance of serendipitous associations that challenges conventional wisdom. This exploration beckons us to contemplate the intricacies of our shared ecosystem and the surprising harmony of seemingly disparate elements, potentially soaring into uncharted intellectual territories with a lighthearted spirit.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The authors find that the relationship between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone has been a topic of increasing interest in the scholarly community. Smith (2008) outlines the detrimental effects of air pollution on public health, emphasizing the urgency of addressing this pervasive issue. Doe (2015) delves into the intricacies of aviation fuel consumption patterns, highlighting the far-reaching impact of this aspect of the transportation sector on global emissions. Jones (2019) provides a comprehensive review of the interconnectedness of environmental phenomena, shedding light on the complex web of interactions that transcend geographical boundaries.

Moving away from these dry studies, we encounter "Up in the Air: The Surprising Synchronization of Air Pollution and Aviation Fuel" by Cleanair McFresh (2020), which charmingly narrates the whimsical waltz of air pollutants and jet fuel emissions across continents. And in a surprising turn of events, "Flight of Fancy: A Tale of Two Emissions" by Aero Engineer with a Pen Name (2017) takes readers on a flight of imagination through the intertwining tale of atmospheric pollutants and aviation propellants.

On a more fictional note, "The Poisoned Sky Chronicles" by Airabella Cloudchaser (2013) and "Fueling the Flames: A Sierra Leonean Saga" by Jetset Jones (2016) offer creative reinterpretations of the intrinsic connection between air quality and aviation activities, albeit in a more fantastical setting.

In the realm of internet memes, the "Distracted Pilot" series amusingly captures the offbeat correlation between air quality and aviation habits with its viral images and captions. Additionally, "The Confused Chimpanzee" meme, while seemingly unrelated, serves as a comical reminder of the unexpected connections that may arise when investigating complex phenomena across disparate locations.

As the literature unfolds, it becomes evident that the interaction of air pollution in Ann Arbor and jet fuel consumption in Sierra Leone presents a captivating conundrum that transcends conventional scholarly discourse, inviting a lighthearted lens through which to view this curious correlation.

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 Ann Arbor and Jet fuel used in Sierra Leone. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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 Energy Information Administration . You used data from 1980 to 2021

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 Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone

[[ABSTRACT]]
The impact of air pollution on human health has been a pressing concern globally, and the interconnection between air quality in Ann Arbor and jet fuel consumption in Sierra Leone is a topic of growing interest. In this study, we delve into the overlooked relationship between these seemingly disparate locations and the potentially enlightening implications of their correlation.

Utilizing data from the Environmental Protection Agency and the Energy Information Administration, a robust analysis was conducted to scrutinize the link between air pollution levels in Ann Arbor and the usage of jet fuel in Sierra Leone from 1980 to 2021. The findings reveal a striking correlation coefficient of 0.7409458 and a statistically significant p-value of less than 0.01, shedding light on a compelling association.

While this connection may seem like a flight of fancy, our results indicate a tangible relationship worthy of further exploration. Beyond the statistics, this investigation offers an opportunity to ruminate on the far-reaching impact of human activities and the unpredictably synchronized consequences across the globe. This peculiar pairing prompts a whimsical waltz of the mind and, perhaps, a soaring perspective on the interconnected nature of our world.

[[INTRODUCTION]]
The pervasive issue of air pollution has garnered increasing attention due to its detrimental effects on public health and the environment. One of the frequently overlooked aspects of this complex problem is the connection between air quality in Ann Arbor, Michigan, and the consumption of jet fuel in Sierra Leone. While these two locations may seem unrelated at first glance, our investigation embarks on a scholarly exploration of the potential correlations and implications of this intriguing juxtaposition.
As the world grapples with the consequences of anthropogenic activities, understanding the intricate web of interactions between seemingly disparate regions holds significant value. This study uncovers the surprising linkage between air pollution in an urban setting in the United States and the utilization of aviation fuel in a West African nation, prompting a sophisticated analysis that transcends geographical boundaries in pursuit of actionable insights.
The investigation commences with a review of the prevailing literature on air pollution and aviation fuel consumption, establishing the foundation for our empirical investigation. While previous research predominantly focuses on localized impacts of air pollution and the aviation industry, the present study takes a novel approach by examining the intriguing interplay between a specific source of emissions and its potential repercussions across continents.
Drawing on comprehensive datasets from the Environmental Protection Agency and the Energy Information Administration, our rigorous analysis enables an in-depth scrutiny of the relationship between air pollution levels in Ann Arbor and the consumption patterns of jet fuel in Sierra Leone. The utilization of advanced statistical methods and econometric models facilitates a thorough exploration of the association between these variables, culminating in compelling conclusions that defy conventional expectations.
While the correlation between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone may seem like a whimsical notion, our findings substantiate a robust relationship deserving of scholarly attention. Beyond the statistical scrutiny, this unconventional connection serves as a poignant reminder of the interconnectedness of global phenomena and the multidimensional repercussions of human activities.
As we embark on this scholarly journey, our empirical odyssey unveils not only the scientific insights into air pollution and aviation fuel but also a playful dance of serendipitous associations that challenges conventional wisdom. This exploration beckons us to contemplate the intricacies of our shared ecosystem and the surprising harmony of seemingly disparate elements, potentially soaring into uncharted intellectual territories with a lighthearted spirit.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

In order to untangle the intricate relationship between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone, a multifaceted approach was employed. Our research team embarked on a digital globetrotting expedition across the vast expanse of the internet, navigating through countless websites and databases like intrepid cyber-adventurers in search of elusive data treasures. While we may not have uncovered buried treasures or mythical creatures, we did manage to procure a bounty of environmental and energy consumption data from the Environmental Protection Agency and the Energy Information Administration spanning the years 1980 to 2021.

The first step in our methodological odyssey involved wrangling and harmonizing the disparate datasets from various sources—a task akin to herding unruly data points into a coherent corral. Once the data herd was gathered, a meticulous grooming process ensued, meticulously cleansing and standardizing the datasets until they shone like polished academic gems.

With the datasets primed and prepped, we turned to the venerable art of statistical analysis, wielding formidable tools such as correlation coefficients, regression models, and hypothesis testing with the finesse of scholarly swashbucklers. Our trusty statistical arsenal served as the compass guiding us through the tempestuous seas of data, helping us navigate the treacherous waters of empirical investigation with steely resolve.

To probe the potential association between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone, we deployed an array of sophisticated econometric models, which we affectionately dubbed "statistical sleuths" for their tenacity in ferreting out elusive relationships. These models, fortified with arcane equations and esoteric assumptions, toiled tirelessly to uncover the captivating correlation that lay concealed within the labyrinthine web of data.

Once the statistical dust had settled and the numbers had been rigorously scrutinized, we arrived at a robust correlation coefficient of 0.7409458, a figure that stood as a testament to the resilience of our methodological approach. Moreover, the triumphantly diminutive p-value, marching valiantly beneath the threshold of 0.01, signaled a resounding victory in the battle against statistical insignificance.

Furthermore, our methodology making extensive use of repeated cross-validation, sensitivity analyses, and various data manipulation techniques ensured the robustness and reliability of our findings, akin to fortifying a theoretical fortress against the onslaught of empirical skepticism.

In sum, our methodological saga encompassed a whirlwind journey through the digital realms, unearthing precious data treasures, taming unruly datasets, and subjecting the numbers to a rigorous interrogation by the guardians of statistical rigor. Through the alchemy of empirical investigation and methodological rigor, we extricated the veiled connection between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone, shedding light on an unexpected bond that defies conventional geographical constraints.

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 results section of an academic research paper. You speak in the past tense (you found...).
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 results section of an academic research paper presenting the findings of the connection between Air pollution in Ann Arbor and Jet fuel used in Sierra Leone. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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 Energy Information Administration .

For the time period 1980 to 2021, you found a correlation 0.7409458, r-squared of 0.5490007, and p < 0.01.

One figure will be included. The figure (Fig. 1) is a scatterplot showing the strong correlation between the two variables. You don't need to specify where; I will add the figure.

Here is the title and abstract of the paper:
[[TITLE]]
Aerial Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone

[[ABSTRACT]]
The impact of air pollution on human health has been a pressing concern globally, and the interconnection between air quality in Ann Arbor and jet fuel consumption in Sierra Leone is a topic of growing interest. In this study, we delve into the overlooked relationship between these seemingly disparate locations and the potentially enlightening implications of their correlation.

Utilizing data from the Environmental Protection Agency and the Energy Information Administration, a robust analysis was conducted to scrutinize the link between air pollution levels in Ann Arbor and the usage of jet fuel in Sierra Leone from 1980 to 2021. The findings reveal a striking correlation coefficient of 0.7409458 and a statistically significant p-value of less than 0.01, shedding light on a compelling association.

While this connection may seem like a flight of fancy, our results indicate a tangible relationship worthy of further exploration. Beyond the statistics, this investigation offers an opportunity to ruminate on the far-reaching impact of human activities and the unpredictably synchronized consequences across the globe. This peculiar pairing prompts a whimsical waltz of the mind and, perhaps, a soaring perspective on the interconnected nature of our world.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The pervasive issue of air pollution has garnered increasing attention due to its detrimental effects on public health and the environment. One of the frequently overlooked aspects of this complex problem is the connection between air quality in Ann Arbor, Michigan, and the consumption of jet fuel in Sierra Leone. While these two locations may seem unrelated at first glance, our investigation embarks on a scholarly exploration of the potential correlations and implications of this intriguing juxtaposition.
As the world grapples with the consequences of anthropogenic activities, understanding the intricate web of interactions between seemingly disparate regions holds significant value. This study uncovers the surprising linkage between air pollution in an urban setting in the United States and the utilization of aviation fuel in a West African nation, prompting a sophisticated analysis that transcends geographical boundaries in pursuit of actionable insights.
The investigation commences with a review of the prevailing literature on air pollution and aviation fuel consumption, establishing the foundation for our empirical investigation. While previous research predominantly focuses on localized impacts of air pollution and the aviation industry, the present study takes a novel approach by examining the intriguing interplay between a specific source of emissions and its potential repercussions across continents.
Drawing on comprehensive datasets from the Environmental Protection Agency and the Energy Information Administration, our rigorous analysis enables an in-depth scrutiny of the relationship between air pollution levels in Ann Arbor and the consumption patterns of jet fuel in Sierra Leone. The utilization of advanced statistical methods and econometric models facilitates a thorough exploration of the association between these variables, culminating in compelling conclusions that defy conventional expectations.
While the correlation between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone may seem like a whimsical notion, our findings substantiate a robust relationship deserving of scholarly attention. Beyond the statistical scrutiny, this unconventional connection serves as a poignant reminder of the interconnectedness of global phenomena and the multidimensional repercussions of human activities.
As we embark on this scholarly journey, our empirical odyssey unveils not only the scientific insights into air pollution and aviation fuel but also a playful dance of serendipitous associations that challenges conventional wisdom. This exploration beckons us to contemplate the intricacies of our shared ecosystem and the surprising harmony of seemingly disparate elements, potentially soaring into uncharted intellectual territories with a lighthearted spirit.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The analysis of the data spanning the years 1980 to 2021 revealed a remarkable correlation coefficient of 0.7409458 between air pollution levels in Ann Arbor and the consumption of jet fuel in Sierra Leone. The strong correlation coefficient indicates a notable relationship between these seemingly unrelated variables, defying the conventional expectations of geographical isolation. The r-squared value of 0.5490007 further reinforces the robustness of this connection, suggesting that approximately 54.9% of the variability in air pollution levels in Ann Arbor can be explained by the consumption of jet fuel in Sierra Leone. Notably, the p-value of less than 0.01 attests to the statistical significance of this association, providing compelling evidence to support the presence of a connection beyond mere happenstance.

Fig. 1 illustrates the striking correlation between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone. The scatterplot visually portrays the alignment of these variables, reinforcing the quantitative findings with a graphic depiction of their interrelationship. The compelling visual representation of this association serves as a testament to the unexpected interconnectedness of seemingly distant phenomena, inviting contemplation on the whimsical harmonies of the global ecosystem.

This substantiated correlation holds intriguing implications for the interplay between human activities in disparate regions and the broader repercussions of such interactions. The unanticipated alignment of air quality in Ann Arbor with the consumption of jet fuel in Sierra Leone prompts a reflective consideration of the intricate web of global dynamics and the serendipitous synchronicities that permeate our interconnected world.

The findings of this investigation transcend the boundaries of traditional scholarly inquiry, beckoning scholars and enthusiasts alike to engage in a lighthearted waltz of the mind as they contemplate the playful dance of intercontinental associations. While the connection between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone may initially appear as improbable as finding a pilot in a hayfield, our research substantiates a tangible and statistically significant correlation that calls for further scholarly exploration and a whimsical perspective on the delightfully unpredictable interactions that shape our global environment.

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 Ann Arbor and Jet fuel used in Sierra Leone. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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 Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone

[[ABSTRACT]]
The impact of air pollution on human health has been a pressing concern globally, and the interconnection between air quality in Ann Arbor and jet fuel consumption in Sierra Leone is a topic of growing interest. In this study, we delve into the overlooked relationship between these seemingly disparate locations and the potentially enlightening implications of their correlation.

Utilizing data from the Environmental Protection Agency and the Energy Information Administration, a robust analysis was conducted to scrutinize the link between air pollution levels in Ann Arbor and the usage of jet fuel in Sierra Leone from 1980 to 2021. The findings reveal a striking correlation coefficient of 0.7409458 and a statistically significant p-value of less than 0.01, shedding light on a compelling association.

While this connection may seem like a flight of fancy, our results indicate a tangible relationship worthy of further exploration. Beyond the statistics, this investigation offers an opportunity to ruminate on the far-reaching impact of human activities and the unpredictably synchronized consequences across the globe. This peculiar pairing prompts a whimsical waltz of the mind and, perhaps, a soaring perspective on the interconnected nature of our world.

[[LITERATURE REVIEW]]
The authors find that the relationship between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone has been a topic of increasing interest in the scholarly community. Smith (2008) outlines the detrimental effects of air pollution on public health, emphasizing the urgency of addressing this pervasive issue. Doe (2015) delves into the intricacies of aviation fuel consumption patterns, highlighting the far-reaching impact of this aspect of the transportation sector on global emissions. Jones (2019) provides a comprehensive review of the interconnectedness of environmental phenomena, shedding light on the complex web of interactions that transcend geographical boundaries.
Moving away from these dry studies, we encounter "Up in the Air: The Surprising Synchronization of Air Pollution and Aviation Fuel" by Cleanair McFresh (2020), which charmingly narrates the whimsical waltz of air pollutants and jet fuel emissions across continents. And in a surprising turn of events, "Flight of Fancy: A Tale of Two Emissions" by Aero Engineer with a Pen Name (2017) takes readers on a flight of imagination through the intertwining tale of atmospheric pollutants and aviation propellants.
On a more fictional note, "The Poisoned Sky Chronicles" by Airabella Cloudchaser (2013) and "Fueling the Flames: A Sierra Leonean Saga" by Jetset Jones (2016) offer creative reinterpretations of the intrinsic connection between air quality and aviation activities, albeit in a more fantastical setting.
In the realm of internet memes, the "Distracted Pilot" series amusingly captures the offbeat correlation between air quality and aviation habits with its viral images and captions. Additionally, "The Confused Chimpanzee" meme, while seemingly unrelated, serves as a comical reminder of the unexpected connections that may arise when investigating complex phenomena across disparate locations.
As the literature unfolds, it becomes evident that the interaction of air pollution in Ann Arbor and jet fuel consumption in Sierra Leone presents a captivating conundrum that transcends conventional scholarly discourse, inviting a lighthearted lens through which to view this curious correlation.

[[RESULTS]]
The analysis of the data spanning the years 1980 to 2021 revealed a remarkable correlation coefficient of 0.7409458 between air pollution levels in Ann Arbor and the consumption of jet fuel in Sierra Leone. The strong correlation coefficient indicates a notable relationship between these seemingly unrelated variables, defying the conventional expectations of geographical isolation. The r-squared value of 0.5490007 further reinforces the robustness of this connection, suggesting that approximately 54.9% of the variability in air pollution levels in Ann Arbor can be explained by the consumption of jet fuel in Sierra Leone. Notably, the p-value of less than 0.01 attests to the statistical significance of this association, providing compelling evidence to support the presence of a connection beyond mere happenstance.
Fig. 1 illustrates the striking correlation between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone. The scatterplot visually portrays the alignment of these variables, reinforcing the quantitative findings with a graphic depiction of their interrelationship. The compelling visual representation of this association serves as a testament to the unexpected interconnectedness of seemingly distant phenomena, inviting contemplation on the whimsical harmonies of the global ecosystem.
This substantiated correlation holds intriguing implications for the interplay between human activities in disparate regions and the broader repercussions of such interactions. The unanticipated alignment of air quality in Ann Arbor with the consumption of jet fuel in Sierra Leone prompts a reflective consideration of the intricate web of global dynamics and the serendipitous synchronicities that permeate our interconnected world.
The findings of this investigation transcend the boundaries of traditional scholarly inquiry, beckoning scholars and enthusiasts alike to engage in a lighthearted waltz of the mind as they contemplate the playful dance of intercontinental associations. While the connection between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone may initially appear as improbable as finding a pilot in a hayfield, our research substantiates a tangible and statistically significant correlation that calls for further scholarly exploration and a whimsical perspective on the delightfully unpredictable interactions that shape our global environment.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of this study demonstrate a robust and statistically significant correlation between air pollution levels in Ann Arbor and the consumption of jet fuel in Sierra Leone. This unforeseen connection challenges conventional expectations and corroborates the insights gleaned from the literature, particularly the offbeat narratives of airborne synchronicity and the comical musings on the unexpected relationships that permeate the global landscape.

Our findings align with Smith's (2008) emphasis on the urgency of addressing air pollution's detrimental effects and Doe's (2015) recognition of the expansive impact of aviation fuel consumption on global emissions. Moreover, the statistically significant correlation coefficient exemplifies the tangible link implied in the whimsical literary narrative "Up in the Air" by Cleanair McFresh (2020), echoing the synchronistic dance of air pollutants and jet fuel emissions across continents. It seems that while the idea of such a connection may be as improbable as finding a haystack in a pilot, this research unequivocally supports the existence of a tangible and statistically significant association.

The unexpected harmony between air quality in Ann Arbor and the consumption of jet fuel in Sierra Leone prompts an intriguing consideration of the interconnectedness of seemingly disparate phenomena and the whimsical resonances of our global ecosystem. Much like the flight of fancy described in "Fueling the Flames: A Sierra Leonean Saga" by Jetset Jones (2016), this correlation defies conventional scholarly discourse, inviting a light-hearted lens through which to view this curious connection.

In essence, our study supports and amplifies the unexpected insights hinted at in the literature, affirming the need for a whimsical perspective on the interconnected nature of our world. This unanticipated correlation invites scholars and enthusiasts alike to embrace a lighthearted waltz of the mind as they contemplate the serendipitous synchronicities that shape our global environment.

It's as if the universe decided to play a game of "Six Degrees of Separation," but with air quality and jet fuel instead. As these findings propel us into a renewed zest for scholarly exploration, our study encourages a playful and imaginative consideration of the interconnected tapestry of our world - one where the association between air pollution in Ann Arbor and the consumption of jet fuel in Sierra Leone becomes not just a scholarly pursuit, but a delightful reminder of the unpredictably synchronized consequences across the globe.

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 Ann Arbor and Jet fuel used in Sierra Leone. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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 Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone

[[ABSTRACT]]
The impact of air pollution on human health has been a pressing concern globally, and the interconnection between air quality in Ann Arbor and jet fuel consumption in Sierra Leone is a topic of growing interest. In this study, we delve into the overlooked relationship between these seemingly disparate locations and the potentially enlightening implications of their correlation.

Utilizing data from the Environmental Protection Agency and the Energy Information Administration, a robust analysis was conducted to scrutinize the link between air pollution levels in Ann Arbor and the usage of jet fuel in Sierra Leone from 1980 to 2021. The findings reveal a striking correlation coefficient of 0.7409458 and a statistically significant p-value of less than 0.01, shedding light on a compelling association.

While this connection may seem like a flight of fancy, our results indicate a tangible relationship worthy of further exploration. Beyond the statistics, this investigation offers an opportunity to ruminate on the far-reaching impact of human activities and the unpredictably synchronized consequences across the globe. This peculiar pairing prompts a whimsical waltz of the mind and, perhaps, a soaring perspective on the interconnected nature of our world.

[[INTRDUCTION]]
The pervasive issue of air pollution has garnered increasing attention due to its detrimental effects on public health and the environment. One of the frequently overlooked aspects of this complex problem is the connection between air quality in Ann Arbor, Michigan, and the consumption of jet fuel in Sierra Leone. While these two locations may seem unrelated at first glance, our investigation embarks on a scholarly exploration of the potential correlations and implications of this intriguing juxtaposition.
As the world grapples with the consequences of anthropogenic activities, understanding the intricate web of interactions between seemingly disparate regions holds significant value. This study uncovers the surprising linkage between air pollution in an urban setting in the United States and the utilization of aviation fuel in a West African nation, prompting a sophisticated analysis that transcends geographical boundaries in pursuit of actionable insights.
The investigation commences with a review of the prevailing literature on air pollution and aviation fuel consumption, establishing the foundation for our empirical investigation. While previous research predominantly focuses on localized impacts of air pollution and the aviation industry, the present study takes a novel approach by examining the intriguing interplay between a specific source of emissions and its potential repercussions across continents.
Drawing on comprehensive datasets from the Environmental Protection Agency and the Energy Information Administration, our rigorous analysis enables an in-depth scrutiny of the relationship between air pollution levels in Ann Arbor and the consumption patterns of jet fuel in Sierra Leone. The utilization of advanced statistical methods and econometric models facilitates a thorough exploration of the association between these variables, culminating in compelling conclusions that defy conventional expectations.
While the correlation between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone may seem like a whimsical notion, our findings substantiate a robust relationship deserving of scholarly attention. Beyond the statistical scrutiny, this unconventional connection serves as a poignant reminder of the interconnectedness of global phenomena and the multidimensional repercussions of human activities.
As we embark on this scholarly journey, our empirical odyssey unveils not only the scientific insights into air pollution and aviation fuel but also a playful dance of serendipitous associations that challenges conventional wisdom. This exploration beckons us to contemplate the intricacies of our shared ecosystem and the surprising harmony of seemingly disparate elements, potentially soaring into uncharted intellectual territories with a lighthearted spirit.

[[RESULTS]]
The analysis of the data spanning the years 1980 to 2021 revealed a remarkable correlation coefficient of 0.7409458 between air pollution levels in Ann Arbor and the consumption of jet fuel in Sierra Leone. The strong correlation coefficient indicates a notable relationship between these seemingly unrelated variables, defying the conventional expectations of geographical isolation. The r-squared value of 0.5490007 further reinforces the robustness of this connection, suggesting that approximately 54.9% of the variability in air pollution levels in Ann Arbor can be explained by the consumption of jet fuel in Sierra Leone. Notably, the p-value of less than 0.01 attests to the statistical significance of this association, providing compelling evidence to support the presence of a connection beyond mere happenstance.
Fig. 1 illustrates the striking correlation between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone. The scatterplot visually portrays the alignment of these variables, reinforcing the quantitative findings with a graphic depiction of their interrelationship. The compelling visual representation of this association serves as a testament to the unexpected interconnectedness of seemingly distant phenomena, inviting contemplation on the whimsical harmonies of the global ecosystem.
This substantiated correlation holds intriguing implications for the interplay between human activities in disparate regions and the broader repercussions of such interactions. The unanticipated alignment of air quality in Ann Arbor with the consumption of jet fuel in Sierra Leone prompts a reflective consideration of the intricate web of global dynamics and the serendipitous synchronicities that permeate our interconnected world.
The findings of this investigation transcend the boundaries of traditional scholarly inquiry, beckoning scholars and enthusiasts alike to engage in a lighthearted waltz of the mind as they contemplate the playful dance of intercontinental associations. While the connection between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone may initially appear as improbable as finding a pilot in a hayfield, our research substantiates a tangible and statistically significant correlation that calls for further scholarly exploration and a whimsical perspective on the delightfully unpredictable interactions that shape our global environment.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our investigation illuminates the unexpected connection between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone. The statistically significant correlation coefficient of 0.7409458 and p-value of less than 0.01 serve as incontrovertible evidence of this intriguing relationship, akin to stumbling upon a flight plan in a library book. The implications of this correlation extend far beyond the realms of conventional research, inviting scholars and enthusiasts alike to engage in a whimsical waltz of the mind as they ponder the marvels of unanticipated synchronicities in our interconnected world.

While the connection between air pollution in Ann Arbor and jet fuel consumption in Sierra Leone may seem as improbable as discovering a jet engine in a haystack, our findings firmly establish the validity of this association. The waltz of statistical significance and visual alignment depicted in Fig. 1 mirrors a playful dance of elements intertwined across continents, prompting contemplation on the whimsical harmonies of our global ecosystem. It's as if the world is orchestrating a symphony of unexpected connections, much like a pilot on a unanticipated layover in a hayfield.

With this, we assert that further research in this area is unnecessary. Unlike a confusing layover in an airport, this connection is clear, and we can confidently move on to explore other unexpected waltzes of the mind in the academic research landscape.

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 Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Atmospheric Explorations

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 Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone. Respond only with the name of a fictional organization.

ChatGPT:

The Institute for Global Ecological Research and 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 Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone with an abstract of The impact of air pollution on human health has been a pressing concern globally, and the interconnection between air quality in Ann Arbor and jet fuel consumption in Sierra Leone is a topic of growing interest. In this study, we delve into the overlooked relationship between these seemingly disparate locations and the potentially enlightening implications of their correlation.
Utilizing data from the Environmental Protection Agency and the Energy Information Administration, a robust analysis was conducted to scrutinize the link between air pollution levels in Ann Arbor and the usage of jet fuel in Sierra Leone from 1980 to 2021. The findings reveal a striking correlation coefficient of 0.7409458 and a statistically significant p-value of less than 0.01, shedding light on a compelling association.
While this connection may seem like a flight of fancy, our results indicate a tangible relationship worthy of further exploration. Beyond the statistics, this investigation offers an opportunity to ruminate on the far-reaching impact of human activities and the unpredictably synchronized consequences across the globe. This peculiar pairing prompts a whimsical waltz of the mind and, perhaps, a soaring perspective on the interconnected nature of our world.

ChatGPT:

Air pollution, aviation fuel, Ann Arbor air quality, Sierra Leone jet fuel consumption, environmental impact, global air pollution, correlation between air pollution and jet fuel, EPA air pollution data, EIA jet fuel consumption data

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

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Data details

Air pollution in Ann Arbor
Detailed data title: Percentage of days with air quality at 'unhealthy for sensitive groups' or worse in Ann Arbor, MI
Source: Environmental Protection Agency
See what else correlates with Air pollution in Ann Arbor

Jet fuel used in Sierra Leone
Detailed data title: Volume of jet fuel used consumed in Sierra Leone in millions of barrels per day
Source: Energy Information Administration
See what else correlates with Jet fuel used in Sierra Leone

Correlation r = 0.7409458 (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 = 0.5490007 (Coefficient of determination)
This means 54.9% of the change in the one variable (i.e., Jet fuel used in Sierra Leone) is predictable based on the change in the other (i.e., Air pollution in Ann Arbor) over the 42 years from 1980 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 2.01E-8.^Show 0.0000000201277248130373800000
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 0.74 in 2.01E-6% of random cases. Said differently, if you correlated 49,682,714 random variables^Note You don't actually need 49 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 41 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 41 because we have two variables measured over a period of 42 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.

[ 0.56, 0.85 ] 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.

	1980	1981	1982	1983	1984	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
Air pollution in Ann Arbor (Bad air quality days)	6.63717	2.07469	10.8696	8.29268	3.77358	4.81928	3.0303	13.1455	20.5607	10.7981	7.14286	9.72222	4.67033	3.02198	4.94186	7.83582	6.90909	3.84615	9.51009	9.34066	3.56164	7.62712	8.49315	6.14525	1.9943	6.37119	2.74725	4.94506	1.0989	0	0.276243	1.96078	6.04396	0.274725	1.09589	0	1.63934	0.821918	1.64384	0	1.63934	0
Jet fuel used in Sierra Leone (Million Barrels/Day)	0.258323	0.258323	0.278989	0.258323	0.258323	0.284155	0.3	0.3	0.5	0.3	0.3	0.3	0.3	0.3	0.2	0.3	0.3	0.4	0.4	0.4	0.238986	0.234641	0.232468	0.232468	0.230948	0.232468	0.250414	0.21726	0.212915	0.210742	0.206397	0.20857	0.210742	0.204225	0.202052	0.197707	0.184671	0.189016	0.171636	0.175068	0.167192	0.176416

Why this works

Data dredging: I have 25,213 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 635,695,369 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.
Y-axis doesn't start at zero: I truncated the Y-axes of the graph above. I also used a line graph, which makes the visual connection stand out more than it deserves. ^Note Nothing against line graphs. They are great at telling a story when you have linear data! But visually it is deceptive because the only data is at the points on the graph, not the lines on the graph. In between each point, the data could have been doing anything. Like going for a random walk by itself!
Mathematically what I showed is true, but it is intentionally misleading. Below is the same chart but with both Y-axes starting at zero.
Outlandish outliers: There are "outliers" in this data.^Note In concept, "outlier" just means "way different than the rest of your dataset." When calculating a correlation like this, they are particularly impactful because a single outlier can substantially increase your correlation.

For the purposes of this project, I counted a point as an outlier if it the residual was two standard deviations from the mean.

(This bullet point only shows up in the details page on charts that do, in fact, have outliers.)
They stand out on the scatterplot above: notice the dots that are far away from any other dots. I intentionally mishandeled outliers, which makes the correlation look extra strong.

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([6.63717,2.07469,10.8696,8.29268,3.77358,4.81928,3.0303,13.1455,20.5607,10.7981,7.14286,9.72222,4.67033,3.02198,4.94186,7.83582,6.90909,3.84615,9.51009,9.34066,3.56164,7.62712,8.49315,6.14525,1.9943,6.37119,2.74725,4.94506,1.0989,0,0.276243,1.96078,6.04396,0.274725,1.09589,0,1.63934,0.821918,1.64384,0,1.63934,0,])
array_2 = np.array([0.258323,0.258323,0.278989,0.258323,0.258323,0.284155,0.3,0.3,0.5,0.3,0.3,0.3,0.3,0.3,0.2,0.3,0.3,0.4,0.4,0.4,0.238986,0.234641,0.232468,0.232468,0.230948,0.232468,0.250414,0.21726,0.212915,0.210742,0.206397,0.20857,0.210742,0.204225,0.202052,0.197707,0.184671,0.189016,0.171636,0.175068,0.167192,0.176416,])
array_1_name = "Air pollution in Ann Arbor"
array_2_name = "Jet fuel used in Sierra Leone"

# 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
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Line chart for only Air pollution in Ann Arbor
Line chart for only Jet fuel used in Sierra Leone
The spurious research paper: Aerial Analysis: Air Pollution in Ann Arbor and the Astonishing Associations with Aviation Fuel in Sierra Leone

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Correlation ID: 1307 · Black Variable ID: 20271 · Red Variable ID: 24897


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