Spurious correlation #3,893 · 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 St. Louis and the second variable is Petroluem consumption in Denmark. The chart goes from 1980 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 St. Louis and the second variable is Petroluem consumption in Denmark. The chart goes from 1980 to 2022, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As air pollution in St. Louis decreased, it created a ripple effect in the atmosphere. This led to a series of high-pressure systems that ultimately influenced the wind patterns over the North Sea, inadvertently impacting Denmark's petroleum consumption. You see, the cleaner air acted as a catalyst for a chain of events that culminated in Danes spontaneously carpooling on energized unicorns, thereby reducing their reliance on petroleum. Who would have thought that the road to sustainable energy could be paved with the whimsical hoofbeats of eco-friendly unicorns, all thanks to St. Louis' cleaner air?

^{Show image generation prompt} Model: dalle-3
Prompt: [ Air pollution in St. Louis: Low poly ] In a low-polygon style, create an image of a hazy skyline of St. Louis. A heavy smog looms over the city, with stylized cars emitting thick plumes of exhaust. In the outskirts, depict a group of unicorns with shimmering coats grazing peacefully in a lush green field in Denmark. These unicorns consume petroleum spills from old barrels, which are now abundant due to a decrease in petroleum consumption. 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: Air pollution in St. Louis and Petroluem consumption in Denmark. 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: Oragami a funny image you would see on reddit 3D Pixar Style Cute 2D animation Low poly
ChatGPT: Air pollution in St. Louis: Low poly

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 Air pollution in St. Louis and Petroluem consumption in Denmark, in the following situation: The decrease in air pollution in St. Louis disrupted the delicate balance of cosmic energy, causing a chain reaction that led to a surplus of petroleum-eating unicorns in Denmark, thus decreasing petroleum consumption.. Keep the description simple.
ChatGPT: In a hazy skyline of St. Louis, a heavy smog looms over the city, with cars emitting thick plumes of exhaust. On the outskirts of the city, a group of unicorns with shimmering coats graze peacefully in a lush green field in Denmark. The unicorns consume petroleum spills from old barrels, which are now abundant due to a decrease in petroleum consumption.

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: [ Air pollution in St. Louis: Low poly ] and depicting this scene: In a hazy skyline of St. Louis, a heavy smog looms over the city, with cars emitting thick plumes of exhaust. On the outskirts of the city, a group of unicorns with shimmering coats graze peacefully in a lush green field in Denmark. The unicorns consume petroleum spills from old barrels, which are now abundant due to a decrease in petroleum consumption. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: [ Air pollution in St. Louis: Low poly ] In a low-polygon style, create an image of a hazy skyline of St. Louis. A heavy smog looms over the city, with stylized cars emitting thick plumes of exhaust. In the outskirts, depict a group of unicorns with shimmering coats grazing peacefully in a lush green field in Denmark. These unicorns consume petroleum spills from old barrels, which are now abundant due to a decrease in petroleum consumption.

*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 St. Louis caused Petroluem consumption in Denmark to decrease.\Make it sound serious until the end.

AI academic paper

(Because p < 0.01)

Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand

The Journal of Ecological Economics and Environmental Management

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 St. Louis and Petroluem consumption in Denmark. Make lots of 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. Perhaps you also got inspiration from some board games that are vaugely related.

Here is the title and abstract of the paper:
[[TITLE]]
Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand

[[ABSTRACT]]
In this study, we delved into the curious conundrum of the relationship between air pollution in St. Louis and petroleum consumption in Denmark. Amidst the fog of environmental concerns, we sought to unearth whether there exists a connection between these seemingly disparate entities. Utilizing data from the Environmental Protection Agency and the Energy Information Administration, our team embarked on a quest to shed light on this enigmatic coupling.

After rigorous analysis, we discovered a notable correlation coefficient of 0.7456287 and a statistically significant p-value of less than 0.01 for the timeframe spanning from 1980 to 2022. Our findings unveil a surprising interplay between St. Louis' air quality woes and the demand for petroleum in the Danish market, illuminating the unexpected entanglement of ecological concerns across geographical boundaries. Through our work, we hope to spark a wider dialogue on the interconnectedness of environmental issues and the unexpected ways in which they manifest.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Introduction
In the grand theater of environmental research, where the curtains rise on the stage of data and statistics, we find ourselves captivated by the peculiar pas de deux of air pollution in St. Louis and petroleum consumption in Denmark. As researchers, we often find ourselves treading the treacherous waters of correlation, causation, and a whole lot of caffeination. Nevertheless, armed with our trusty statistical tools and an unhealthy obsession with spreadsheets, we ventured into this scholarly tango to uncover the hidden connections and untangle the enigmatic web of variables.
The notion of St. Louis and Denmark forming an ecological odd couple might seem as improbable as a lab-coated stand-up comedian, but as the saying goes, "the data never lies, but it often tries to confuse us." Our quest led us to the labyrinthine pathways of environmental databases, where we sifted through numbers with the fervor of a detective solving a particularly perplexing case. The quixotic nature of our undertaking was met with both excitement and caffeine-induced jitters, as we sought to shed light on this curious conundrum, armed with nothing but curiosity and an excessive amount of post-it notes.
The rampant complexities of air pollution and petroleum consumption provided an exhilarating challenge, not unlike trying to calculate the number of molecules in a drop of water using only a toothpick and a pair of safety goggles. As we traversed the landscape of environmental data, we found ourselves muttering incantations to the statistical deities, fervently hoping for a glimpse of that elusive correlation coefficient, that magical number which would validate all our efforts and grant us entry into the hallowed halls of scientific significance.
With bated breath and unwavering determination, we endeavored to unearth the hidden truths lurking beneath the surface of sprawling datasets. And lo and behold, after a dance with the devil that is statistical analysis, we emerged victorious, armed with a correlation coefficient of 0.7456287, a result so tantalizing it could make even the most stoic statistician break into an impromptu statistical jig.
In this paper, we aim to cast a spotlight on the unexpected intertwining of St. Louis' air pollution woes and the siren call of petroleum consumption in Denmark. Through our findings, we hope to invite fellow researchers and environmental enthusiasts to indulge in the delightful paradoxes of our interconnected world and ponder over the whimsical ways in which ecological concerns transcend geographical boundaries. So, dear reader, fasten your seatbelts and prepare to embark on a whimsical journey through the eccentric corridors of statistical analysis and environmental eccentricities.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The study of environmental connections between seemingly unrelated geographical locations has attracted significant scholarly attention in recent decades. Researchers have sought to unravel the intricate tapestry of ecological interdependencies, akin to detectives pursuing clues in a sprawling whodunit mystery. In the pursuit of understanding the perplexing link between St. Louis air pollution and Danish petroleum consumption, scholars have ventured into the labyrinth of interdisciplinary literature, navigating through dense forests of academic papers and journal articles.

Smith et al. (2010) provide an insightful analysis of the impact of air pollution on urban environments, shedding light on the complex dynamics of particulate matter and gaseous emissions. Meanwhile, Doe and Jones (2015) present a comprehensive overview of petroleum consumption trends in European nations, offering a panoramic view of the myriad factors influencing fuel demands in the continent. These studies serve as pillars in the edifice of environmental literature, laying the groundwork for our exploration of the unexpected correlation between two disparate locales.

Diving deeper into the literature, "The Environmental Impact of Industrialization" (Brown, 2008) presents a comprehensive examination of the historical relationship between industrial development and air pollution, offering valuable insights into the long-term ramifications of human activities on environmental sustainability. In a similarly illuminating vein, "Energy Economics: Theory and Applications" (Miller, 2019) delves into the intricate web of energy markets and consumption patterns, providing a holistic perspective on the multifaceted drivers of global fuel demands.

Venturing into more unconventional literature, Orwell's "1984" whispers enigmatic allusions to the pervading influence of governmental policies on environmental degradation, offering a dystopian reflection on the consequences of unchecked power. On a lighter note, "The Lorax" by Dr. Seuss stands as a playful parable, reminding readers of the whimsical ways in which environmental concerns can shape our collective consciousness. One cannot dismiss the potential influence of literary works on our understanding of ecological connections, for as the adage goes, truth often hides in the unlikeliest of tales.

In a surprising twist, our exploration of board games revealed striking parallels to our research endeavor. The intricate resource management of "Terraforming Mars" and the strategic decision-making embedded in "Power Grid" resonate with the complexities of environmental dynamics and energy consumption, infusing our academic pursuits with a touch of ludic inspiration.

As we meander through this cornucopia of literature, it becomes evident that the intersection of air pollution in St. Louis and petroleum consumption in Denmark transcends the conventional boundaries of scholarly inquiry. Our path, dear reader, is strewn not only with data points and regression analyses but also with the colorful tapestry of literary musings and ludic reflections. So, let us march forth, with a twinkle in our eyes and a smattering of whimsy, as we navigate the sea of knowledge in pursuit of enlightenment and perhaps a dash of merriment.

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 St. Louis and Petroluem consumption in Denmark. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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 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]]
Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand

[[ABSTRACT]]
In this study, we delved into the curious conundrum of the relationship between air pollution in St. Louis and petroleum consumption in Denmark. Amidst the fog of environmental concerns, we sought to unearth whether there exists a connection between these seemingly disparate entities. Utilizing data from the Environmental Protection Agency and the Energy Information Administration, our team embarked on a quest to shed light on this enigmatic coupling.

After rigorous analysis, we discovered a notable correlation coefficient of 0.7456287 and a statistically significant p-value of less than 0.01 for the timeframe spanning from 1980 to 2022. Our findings unveil a surprising interplay between St. Louis' air quality woes and the demand for petroleum in the Danish market, illuminating the unexpected entanglement of ecological concerns across geographical boundaries. Through our work, we hope to spark a wider dialogue on the interconnectedness of environmental issues and the unexpected ways in which they manifest.

[[INTRODUCTION]]
Introduction
In the grand theater of environmental research, where the curtains rise on the stage of data and statistics, we find ourselves captivated by the peculiar pas de deux of air pollution in St. Louis and petroleum consumption in Denmark. As researchers, we often find ourselves treading the treacherous waters of correlation, causation, and a whole lot of caffeination. Nevertheless, armed with our trusty statistical tools and an unhealthy obsession with spreadsheets, we ventured into this scholarly tango to uncover the hidden connections and untangle the enigmatic web of variables.
The notion of St. Louis and Denmark forming an ecological odd couple might seem as improbable as a lab-coated stand-up comedian, but as the saying goes, "the data never lies, but it often tries to confuse us." Our quest led us to the labyrinthine pathways of environmental databases, where we sifted through numbers with the fervor of a detective solving a particularly perplexing case. The quixotic nature of our undertaking was met with both excitement and caffeine-induced jitters, as we sought to shed light on this curious conundrum, armed with nothing but curiosity and an excessive amount of post-it notes.
The rampant complexities of air pollution and petroleum consumption provided an exhilarating challenge, not unlike trying to calculate the number of molecules in a drop of water using only a toothpick and a pair of safety goggles. As we traversed the landscape of environmental data, we found ourselves muttering incantations to the statistical deities, fervently hoping for a glimpse of that elusive correlation coefficient, that magical number which would validate all our efforts and grant us entry into the hallowed halls of scientific significance.
With bated breath and unwavering determination, we endeavored to unearth the hidden truths lurking beneath the surface of sprawling datasets. And lo and behold, after a dance with the devil that is statistical analysis, we emerged victorious, armed with a correlation coefficient of 0.7456287, a result so tantalizing it could make even the most stoic statistician break into an impromptu statistical jig.
In this paper, we aim to cast a spotlight on the unexpected intertwining of St. Louis' air pollution woes and the siren call of petroleum consumption in Denmark. Through our findings, we hope to invite fellow researchers and environmental enthusiasts to indulge in the delightful paradoxes of our interconnected world and ponder over the whimsical ways in which ecological concerns transcend geographical boundaries. So, dear reader, fasten your seatbelts and prepare to embark on a whimsical journey through the eccentric corridors of statistical analysis and environmental eccentricities.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

Research Design:
To take on the fantastical conundrum of air pollution in St. Louis and petroleum consumption in Denmark, our research team employed a methodological concoction that would make even the most seasoned statistician raise an eyebrow. We opted for a blend of retrospective data analysis and trend examination, akin to unraveling the plot twists of a scientific whodunit. Armed with an arsenal of spreadsheets and a borderline unhealthy obsession with data visualization, we delved into the labyrinthine archives of the Environmental Protection Agency and the Energy Information Administration, like intrepid explorers seeking buried treasure, albeit in the form of statistical correlations.

Data Collection:
Our data spelunking expedition covered the time span from 1980 to 2022, where we traversed the digital landscapes of esoteric databases with the fervor of treasure hunters seeking the fabled correlations X marks the spot. The primary sources of our data were the aforementioned Environmental Protection Agency and the Energy Information Administration, although we must confess that a significant portion of our research involved navigating through the perilous jungles of the internet, where misinformation lurks like scientific quicksand. However, with our trusty compass of critical analysis and a healthy dose of skepticism, we managed to salvage the most reliable data nuggets.

Variables:
In a rousing display of statistical acrobatics, we juggled an assortment of variables that could rival a circus act for its complexity. For St. Louis air pollution, we honed in on key pollutant levels, including but not limited to ozone, particulate matter, and nitrogen dioxide, treating them as the eccentric protagonists of our ecological saga. On the other side of the ring, we scrutinized petroleum consumption in Denmark, dissecting the intricacies of diesel demand and gasoline guzzling with the precision of a scientific scalpel.

Statistical Analysis:
In our attempt to wrangle the empirical beasts within the data, we engaged in an exuberant tango with statistical software, unleashing a whirlwind of hypothesis testing, correlation coefficients, and regression models that would make even a mathematical virtuoso raise an eyebrow. Our analysis involved computing the ever-elusive correlation coefficient, the magical number that would grant us entry into the hallowed halls of scientific significance. With the fervor of a scientist in a caffeine-induced frenzy, we dabbled in time series analysis and t-tests, hoping to distinguish the signal from the noise with the precision of a sonic screwdriver untangling the mysteries of the universe.

Ethical Considerations:
As fervent advocates of scientific integrity, we adhered to the ethical guidelines of data collection and analysis, ensuring that our research practices upheld the noble principles of transparency and accuracy. With a nod to the statistical deities, we pledged to present our findings with the unwavering honesty of a courtroom witness and the enthusiasm of a scientist discovering a new species.

In summary, our methodology resembled a madcap scientific expedition through the wildest terrains of statistical analysis and data interpretation, where every twist and turn led us closer to unraveling the eccentric connection between air pollution in St. Louis and petroleum consumption in Denmark. And after navigating through the convoluted pathways of research design and data mining, we emerged triumphant, armed with a treasure trove of statistical peculiarities and quirky correlations that lend an air of whimsy to the oftentimes staid world of scientific inquiry.

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 St. Louis and Petroluem consumption in Denmark. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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 2022, you found a correlation 0.7456287, r-squared of 0.5559621, 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]]
Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand

[[ABSTRACT]]
In this study, we delved into the curious conundrum of the relationship between air pollution in St. Louis and petroleum consumption in Denmark. Amidst the fog of environmental concerns, we sought to unearth whether there exists a connection between these seemingly disparate entities. Utilizing data from the Environmental Protection Agency and the Energy Information Administration, our team embarked on a quest to shed light on this enigmatic coupling.

After rigorous analysis, we discovered a notable correlation coefficient of 0.7456287 and a statistically significant p-value of less than 0.01 for the timeframe spanning from 1980 to 2022. Our findings unveil a surprising interplay between St. Louis' air quality woes and the demand for petroleum in the Danish market, illuminating the unexpected entanglement of ecological concerns across geographical boundaries. Through our work, we hope to spark a wider dialogue on the interconnectedness of environmental issues and the unexpected ways in which they manifest.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
Introduction
In the grand theater of environmental research, where the curtains rise on the stage of data and statistics, we find ourselves captivated by the peculiar pas de deux of air pollution in St. Louis and petroleum consumption in Denmark. As researchers, we often find ourselves treading the treacherous waters of correlation, causation, and a whole lot of caffeination. Nevertheless, armed with our trusty statistical tools and an unhealthy obsession with spreadsheets, we ventured into this scholarly tango to uncover the hidden connections and untangle the enigmatic web of variables.
The notion of St. Louis and Denmark forming an ecological odd couple might seem as improbable as a lab-coated stand-up comedian, but as the saying goes, "the data never lies, but it often tries to confuse us." Our quest led us to the labyrinthine pathways of environmental databases, where we sifted through numbers with the fervor of a detective solving a particularly perplexing case. The quixotic nature of our undertaking was met with both excitement and caffeine-induced jitters, as we sought to shed light on this curious conundrum, armed with nothing but curiosity and an excessive amount of post-it notes.
The rampant complexities of air pollution and petroleum consumption provided an exhilarating challenge, not unlike trying to calculate the number of molecules in a drop of water using only a toothpick and a pair of safety goggles. As we traversed the landscape of environmental data, we found ourselves muttering incantations to the statistical deities, fervently hoping for a glimpse of that elusive correlation coefficient, that magical number which would validate all our efforts and grant us entry into the hallowed halls of scientific significance.
With bated breath and unwavering determination, we endeavored to unearth the hidden truths lurking beneath the surface of sprawling datasets. And lo and behold, after a dance with the devil that is statistical analysis, we emerged victorious, armed with a correlation coefficient of 0.7456287, a result so tantalizing it could make even the most stoic statistician break into an impromptu statistical jig.
In this paper, we aim to cast a spotlight on the unexpected intertwining of St. Louis' air pollution woes and the siren call of petroleum consumption in Denmark. Through our findings, we hope to invite fellow researchers and environmental enthusiasts to indulge in the delightful paradoxes of our interconnected world and ponder over the whimsical ways in which ecological concerns transcend geographical boundaries. So, dear reader, fasten your seatbelts and prepare to embark on a whimsical journey through the eccentric corridors of statistical analysis and environmental eccentricities.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

In our quest to unravel the mysterious connection between St. Louis air pollution and Danish petroleum consumption, we were met with a statistical waltz that seemed straight out of a quirky science fiction novel. After sifting through a copious amount of data, we stumbled upon a correlation coefficient of 0.7456287, an r-squared of 0.5559621, and a p-value of less than 0.01 for the time period ranging from 1980 to 2022. It's like stumbling upon a rare Pokémon in a sea of common statistics!

The strength of the correlation coefficient indicates a robust relationship between these seemingly dissimilar variables, akin to finding out that SpongeBob and Squidward are distant cousins once removed. Our scatterplot (Fig. 1) beautifully illustrates this strong connection, painting a vivid picture of the interwoven dance between air pollution in St. Louis and the demand for petroleum in Denmark. It's as if the data itself wanted to waltz its way into our hearts and minds!

This eyebrow-raising discovery serves as a gentle reminder that in the world of environmental research, the most unexpected partnerships can emerge, much like an odd couple finding love in the unlikeliest of places. It's a bit like witnessing a scientific rom-com unfold in the realm of statistical analysis!

Our findings unveil a captivating tapestry of ecological interplay that transcends geographical boundaries, inviting us to marvel at the whimsical twists and turns of our interconnected world. Who would have thought that St. Louis and Denmark could be entangled in such an ecological pas de deux? It's as surprising as finding out that your pet goldfish has secretly been pen pals with a sea turtle all these years.

Through this enlightening journey into the mysterious realms of statistical analysis, we yearn to spark discussions and contemplations on the intricate and often comical relationships that underpin our environmental conundrums. After all, in the words of Albert Einstein, "The most beautiful thing we can experience is the mysterious. It's the source of all true art and science." And in our case, it's also the source of some seriously entertaining data analysis!

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 St. Louis and Petroluem consumption in Denmark. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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]]
Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand

[[ABSTRACT]]
In this study, we delved into the curious conundrum of the relationship between air pollution in St. Louis and petroleum consumption in Denmark. Amidst the fog of environmental concerns, we sought to unearth whether there exists a connection between these seemingly disparate entities. Utilizing data from the Environmental Protection Agency and the Energy Information Administration, our team embarked on a quest to shed light on this enigmatic coupling.

After rigorous analysis, we discovered a notable correlation coefficient of 0.7456287 and a statistically significant p-value of less than 0.01 for the timeframe spanning from 1980 to 2022. Our findings unveil a surprising interplay between St. Louis' air quality woes and the demand for petroleum in the Danish market, illuminating the unexpected entanglement of ecological concerns across geographical boundaries. Through our work, we hope to spark a wider dialogue on the interconnectedness of environmental issues and the unexpected ways in which they manifest.

[[LITERATURE REVIEW]]
The study of environmental connections between seemingly unrelated geographical locations has attracted significant scholarly attention in recent decades. Researchers have sought to unravel the intricate tapestry of ecological interdependencies, akin to detectives pursuing clues in a sprawling whodunit mystery. In the pursuit of understanding the perplexing link between St. Louis air pollution and Danish petroleum consumption, scholars have ventured into the labyrinth of interdisciplinary literature, navigating through dense forests of academic papers and journal articles.
Smith et al. (2010) provide an insightful analysis of the impact of air pollution on urban environments, shedding light on the complex dynamics of particulate matter and gaseous emissions. Meanwhile, Doe and Jones (2015) present a comprehensive overview of petroleum consumption trends in European nations, offering a panoramic view of the myriad factors influencing fuel demands in the continent. These studies serve as pillars in the edifice of environmental literature, laying the groundwork for our exploration of the unexpected correlation between two disparate locales.
Diving deeper into the literature, "The Environmental Impact of Industrialization" (Brown, 2008) presents a comprehensive examination of the historical relationship between industrial development and air pollution, offering valuable insights into the long-term ramifications of human activities on environmental sustainability. In a similarly illuminating vein, "Energy Economics: Theory and Applications" (Miller, 2019) delves into the intricate web of energy markets and consumption patterns, providing a holistic perspective on the multifaceted drivers of global fuel demands.
Venturing into more unconventional literature, Orwell's "1984" whispers enigmatic allusions to the pervading influence of governmental policies on environmental degradation, offering a dystopian reflection on the consequences of unchecked power. On a lighter note, "The Lorax" by Dr. Seuss stands as a playful parable, reminding readers of the whimsical ways in which environmental concerns can shape our collective consciousness. One cannot dismiss the potential influence of literary works on our understanding of ecological connections, for as the adage goes, truth often hides in the unlikeliest of tales.
In a surprising twist, our exploration of board games revealed striking parallels to our research endeavor. The intricate resource management of "Terraforming Mars" and the strategic decision-making embedded in "Power Grid" resonate with the complexities of environmental dynamics and energy consumption, infusing our academic pursuits with a touch of ludic inspiration.
As we meander through this cornucopia of literature, it becomes evident that the intersection of air pollution in St. Louis and petroleum consumption in Denmark transcends the conventional boundaries of scholarly inquiry. Our path, dear reader, is strewn not only with data points and regression analyses but also with the colorful tapestry of literary musings and ludic reflections. So, let us march forth, with a twinkle in our eyes and a smattering of whimsy, as we navigate the sea of knowledge in pursuit of enlightenment and perhaps a dash of merriment.

[[RESULTS]]
In our quest to unravel the mysterious connection between St. Louis air pollution and Danish petroleum consumption, we were met with a statistical waltz that seemed straight out of a quirky science fiction novel. After sifting through a copious amount of data, we stumbled upon a correlation coefficient of 0.7456287, an r-squared of 0.5559621, and a p-value of less than 0.01 for the time period ranging from 1980 to 2022. It's like stumbling upon a rare Pokémon in a sea of common statistics!
The strength of the correlation coefficient indicates a robust relationship between these seemingly dissimilar variables, akin to finding out that SpongeBob and Squidward are distant cousins once removed. Our scatterplot (Fig. 1) beautifully illustrates this strong connection, painting a vivid picture of the interwoven dance between air pollution in St. Louis and the demand for petroleum in Denmark. It's as if the data itself wanted to waltz its way into our hearts and minds!
This eyebrow-raising discovery serves as a gentle reminder that in the world of environmental research, the most unexpected partnerships can emerge, much like an odd couple finding love in the unlikeliest of places. It's a bit like witnessing a scientific rom-com unfold in the realm of statistical analysis!
Our findings unveil a captivating tapestry of ecological interplay that transcends geographical boundaries, inviting us to marvel at the whimsical twists and turns of our interconnected world. Who would have thought that St. Louis and Denmark could be entangled in such an ecological pas de deux? It's as surprising as finding out that your pet goldfish has secretly been pen pals with a sea turtle all these years.
Through this enlightening journey into the mysterious realms of statistical analysis, we yearn to spark discussions and contemplations on the intricate and often comical relationships that underpin our environmental conundrums. After all, in the words of Albert Einstein, "The most beautiful thing we can experience is the mysterious. It's the source of all true art and science." And in our case, it's also the source of some seriously entertaining data analysis!

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

Our findings affirm and expand upon the prior research that has teased us with hints of the intricate dance between St. Louis air pollution and Danish petroleum consumption. Like the culmination of a thrilling mystery novel, our study has shed light on the unexpected connection between these two seemingly disparate entities. It's almost as if Sherlock Holmes himself would have marveled at the revelation, exclaiming, "Elementary, my dear data points!"

The significant correlation coefficient we uncovered mirrors the persistent themes in the works of prior scholars, akin to uncovering hidden Easter eggs in a complex video game. Smith et al. (2010) and Doe and Jones (2015) laid the groundwork for our exploration by spotlighting the nuances of air pollution and petroleum consumption, akin to providing us with a treasure map in the dense jungle of environmental literature. The unlikely connections we found are akin to discovering buried treasure at the X marked by our academic predecessors.

The surprising revelations from our statistical analyses reflect the whimsical twists and turns of our interconnected world, reminiscent of a rollercoaster ride in an amusement park of scholarly inquiry. Just when we thought we had our feet on solid ground, the data swept us away into the whirlwind of ecological interplay, much like a surprise plot twist in a riveting novel. As we traverse the uncharted territory of interdisciplinary studies, we must not forget the playful and unorthodox influences that subtly shape our research journey, much like a mischievous imp casting its whimsical spells on our path to enlightenment.

In the grand tapestry of scientific inquiry, our study serves as a colorful thread woven into the fabric of environmental research, adding a touch of levity and unexpected charm to the complex ecosystem of scholarly discourse. Our findings beckon us to embrace the delightful unpredictability of our scientific pursuits, much like embarking on a whimsical quest with the wit of Monty Python and the precision of a keen-eyed researcher. So, let us marvel at the quirks and curiosities unveiled in our statistical odyssey and embrace the playful spirit that infuses our pursuit of knowledge. After all, in the words of Isaac Newton, "Nature is pleased with simplicity. And nature is no dummy. She's a jester, a prankster, and a clever trickster, always ready to dazzle us with her riddles."

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 St. Louis and Petroluem consumption in Denmark. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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]]
Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand

[[ABSTRACT]]
In this study, we delved into the curious conundrum of the relationship between air pollution in St. Louis and petroleum consumption in Denmark. Amidst the fog of environmental concerns, we sought to unearth whether there exists a connection between these seemingly disparate entities. Utilizing data from the Environmental Protection Agency and the Energy Information Administration, our team embarked on a quest to shed light on this enigmatic coupling.

After rigorous analysis, we discovered a notable correlation coefficient of 0.7456287 and a statistically significant p-value of less than 0.01 for the timeframe spanning from 1980 to 2022. Our findings unveil a surprising interplay between St. Louis' air quality woes and the demand for petroleum in the Danish market, illuminating the unexpected entanglement of ecological concerns across geographical boundaries. Through our work, we hope to spark a wider dialogue on the interconnectedness of environmental issues and the unexpected ways in which they manifest.

[[INTRDUCTION]]
Introduction
In the grand theater of environmental research, where the curtains rise on the stage of data and statistics, we find ourselves captivated by the peculiar pas de deux of air pollution in St. Louis and petroleum consumption in Denmark. As researchers, we often find ourselves treading the treacherous waters of correlation, causation, and a whole lot of caffeination. Nevertheless, armed with our trusty statistical tools and an unhealthy obsession with spreadsheets, we ventured into this scholarly tango to uncover the hidden connections and untangle the enigmatic web of variables.
The notion of St. Louis and Denmark forming an ecological odd couple might seem as improbable as a lab-coated stand-up comedian, but as the saying goes, "the data never lies, but it often tries to confuse us." Our quest led us to the labyrinthine pathways of environmental databases, where we sifted through numbers with the fervor of a detective solving a particularly perplexing case. The quixotic nature of our undertaking was met with both excitement and caffeine-induced jitters, as we sought to shed light on this curious conundrum, armed with nothing but curiosity and an excessive amount of post-it notes.
The rampant complexities of air pollution and petroleum consumption provided an exhilarating challenge, not unlike trying to calculate the number of molecules in a drop of water using only a toothpick and a pair of safety goggles. As we traversed the landscape of environmental data, we found ourselves muttering incantations to the statistical deities, fervently hoping for a glimpse of that elusive correlation coefficient, that magical number which would validate all our efforts and grant us entry into the hallowed halls of scientific significance.
With bated breath and unwavering determination, we endeavored to unearth the hidden truths lurking beneath the surface of sprawling datasets. And lo and behold, after a dance with the devil that is statistical analysis, we emerged victorious, armed with a correlation coefficient of 0.7456287, a result so tantalizing it could make even the most stoic statistician break into an impromptu statistical jig.
In this paper, we aim to cast a spotlight on the unexpected intertwining of St. Louis' air pollution woes and the siren call of petroleum consumption in Denmark. Through our findings, we hope to invite fellow researchers and environmental enthusiasts to indulge in the delightful paradoxes of our interconnected world and ponder over the whimsical ways in which ecological concerns transcend geographical boundaries. So, dear reader, fasten your seatbelts and prepare to embark on a whimsical journey through the eccentric corridors of statistical analysis and environmental eccentricities.

[[RESULTS]]
In our quest to unravel the mysterious connection between St. Louis air pollution and Danish petroleum consumption, we were met with a statistical waltz that seemed straight out of a quirky science fiction novel. After sifting through a copious amount of data, we stumbled upon a correlation coefficient of 0.7456287, an r-squared of 0.5559621, and a p-value of less than 0.01 for the time period ranging from 1980 to 2022. It's like stumbling upon a rare Pokémon in a sea of common statistics!
The strength of the correlation coefficient indicates a robust relationship between these seemingly dissimilar variables, akin to finding out that SpongeBob and Squidward are distant cousins once removed. Our scatterplot (Fig. 1) beautifully illustrates this strong connection, painting a vivid picture of the interwoven dance between air pollution in St. Louis and the demand for petroleum in Denmark. It's as if the data itself wanted to waltz its way into our hearts and minds!
This eyebrow-raising discovery serves as a gentle reminder that in the world of environmental research, the most unexpected partnerships can emerge, much like an odd couple finding love in the unlikeliest of places. It's a bit like witnessing a scientific rom-com unfold in the realm of statistical analysis!
Our findings unveil a captivating tapestry of ecological interplay that transcends geographical boundaries, inviting us to marvel at the whimsical twists and turns of our interconnected world. Who would have thought that St. Louis and Denmark could be entangled in such an ecological pas de deux? It's as surprising as finding out that your pet goldfish has secretly been pen pals with a sea turtle all these years.
Through this enlightening journey into the mysterious realms of statistical analysis, we yearn to spark discussions and contemplations on the intricate and often comical relationships that underpin our environmental conundrums. After all, in the words of Albert Einstein, "The most beautiful thing we can experience is the mysterious. It's the source of all true art and science." And in our case, it's also the source of some seriously entertaining data analysis!

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our expedition into the whimsical realm of St. Louis air pollution and Danish petroleum consumption has left us feeling as exhilarated as a scientist discovering a new element. The prodigious correlation coefficient of 0.7456287 and statistically significant p-value of less than 0.01 have illuminated a connection so undeniable, it's like finding out that Batman and Bruce Wayne are indeed the same person!

Our foray into the statistical labyrinth has uncovered a captivating dance between these seemingly incongruous variables, much like witnessing a cosmic tango between two celestial bodies. The strength of this unearthed relationship is as solid as a well-constructed hypothesis, and it urges us to reconsider the interconnectedness of environmental phenomena with the reverence usually reserved for groundbreaking scientific theories. It's like stumbling upon a unicorn in a field of ordinary statistical analyses!

Through this research, we aspire to not only entertain the scientific community with our statistical exploits but also to ignite a blazing inferno of curiosity about the peculiar ways in which our world intertwines. It's as if Mother Nature herself has deigned to throw us a curveball, leaving us to marvel at the serendipitous discoveries that await those who dare to venture into the boundless realm of data analysis.

With our findings in hand, we confidently declare that no further research is needed in this area. The connection between St. Louis air pollution and Danish petroleum consumption has been unraveled, much like a magician unveiling a dazzling trick. It's time to celebrate this discovery, kick back, and bask in the glory of our engaging statistical odyssey. As the great Carl Sagan once said, "Somewhere, something incredible is waiting to be known," and lo and behold, we've found our incredible something in the unlikeliest of places. It's a reminder that in the world of research, sometimes the most unexpected connections can lead to the most delightful discoveries.

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 Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Ecological Economics and Environmental Management

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 Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand. Respond only with the name of a fictional organization.

ChatGPT:

Institute for Sustainable Energy Solutions

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 Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand with an abstract of In this study, we delved into the curious conundrum of the relationship between air pollution in St. Louis and petroleum consumption in Denmark. Amidst the fog of environmental concerns, we sought to unearth whether there exists a connection between these seemingly disparate entities. Utilizing data from the Environmental Protection Agency and the Energy Information Administration, our team embarked on a quest to shed light on this enigmatic coupling.
After rigorous analysis, we discovered a notable correlation coefficient of 0.7456287 and a statistically significant p-value of less than 0.01 for the timeframe spanning from 1980 to 2022. Our findings unveil a surprising interplay between St. Louis' air quality woes and the demand for petroleum in the Danish market, illuminating the unexpected entanglement of ecological concerns across geographical boundaries. Through our work, we hope to spark a wider dialogue on the interconnectedness of environmental issues and the unexpected ways in which they manifest.

ChatGPT:

St. Louis air pollution, Denmark diesel demand, petroleum consumption, environmental concerns, correlation coefficient, statistical significance, data analysis, EPA, Energy Information Administration, ecological entanglement, geographical boundaries, environmental issues interconnectedness, petroleum demand, air quality woes, environmental dialogue

*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 St. Louis
Detailed data title: Percentage of days 'unhealthy' or worse air quality in St. Louis, MO-IL
Source: Environmental Protection Agency
See what else correlates with Air pollution in St. Louis

Petroluem consumption in Denmark
Detailed data title: Volume of petroluem consumption consumed in Denmark in millions of barrels per day
Source: Energy Information Administration
See what else correlates with Petroluem consumption in Denmark

Correlation r = 0.7456287 (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 = 0.5559621 (Coefficient of determination)
This means 55.6% of the change in the one variable (i.e., Petroluem consumption in Denmark) is predictable based on the change in the other (i.e., Air pollution in St. Louis) over the 43 years from 1980 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 9.7E-9.^Show 0.0000000096549508168835180000
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 0.75 in 9.7E-7% of random cases. Said differently, if you correlated 103,573,806 random variables^Note You don't actually need 103 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 42 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 42 because we have two variables measured over a period of 43 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.

[ 0.57, 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	2022
Air pollution in St. Louis (Bad air quality days)	18.0328	5.47945	4.38356	14.5205	9.83607	6.0274	6.84932	9.86301	13.9344	6.30137	6.84932	8.49315	3.55191	2.19178	8.76712	11.2329	6.01093	3.56164	6.57534	7.94521	4.64481	4.10959	8.49315	3.0137	0.546448	7.67123	4.65753	6.30137	0.273224	0.273973	1.91781	3.0137	5.46448	0.547945	0	0.547945	0.546448	0.273973	0.547945	0.547945	0.273224	0.547945	0
Petroluem consumption in Denmark (Million Barrels/Day)	290.3	243	230	219	215.585	222.704	219.548	213.696	204.016	195.608	192.449	194.365	192.582	198.967	211.407	222.715	234.954	226.616	222.847	220.252	210	213.411	197.164	188.271	185.333	183.463	189.858	190.326	181.055	166.512	167.468	163.367	155.492	154.762	153.622	154.479	158.202	158.537	161.236	165.392	136.934	140.501	148.482

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.
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.

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([18.0328,5.47945,4.38356,14.5205,9.83607,6.0274,6.84932,9.86301,13.9344,6.30137,6.84932,8.49315,3.55191,2.19178,8.76712,11.2329,6.01093,3.56164,6.57534,7.94521,4.64481,4.10959,8.49315,3.0137,0.546448,7.67123,4.65753,6.30137,0.273224,0.273973,1.91781,3.0137,5.46448,0.547945,0,0.547945,0.546448,0.273973,0.547945,0.547945,0.273224,0.547945,0,])
array_2 = np.array([290.3,243,230,219,215.585,222.704,219.548,213.696,204.016,195.608,192.449,194.365,192.582,198.967,211.407,222.715,234.954,226.616,222.847,220.252,210,213.411,197.164,188.271,185.333,183.463,189.858,190.326,181.055,166.512,167.468,163.367,155.492,154.762,153.622,154.479,158.202,158.537,161.236,165.392,136.934,140.501,148.482,])
array_1_name = "Air pollution in St. Louis"
array_2_name = "Petroluem consumption in Denmark"

# 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 St. Louis
Line chart for only Petroluem consumption in Denmark
AI-generated correlation image
The spurious research paper: Pondering Petroleum Pinpointed: St. Louis Air Pollution and Danish Diesel Demand

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Correlation ID: 3893 · Black Variable ID: 21309 · Red Variable ID: 24348


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