Spurious correlation #2,503 · 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 Duluth and the second variable is Solar power generated in Estonia. The chart goes from 2009 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 Duluth and the second variable is Solar power generated in Estonia. The chart goes from 2009 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The smog particles acted as tiny mirrors, reflecting more sunlight towards Estonia, leading to a boost in solar power generation.

^{Show image generation prompt} Model: dalle-3
Prompt: Prompt: Generate an image of a high-tech city skyline obscured by dark smog, with the sun's rays breaking through and glistening solar panels below, set in an urban landscape with a futuristic aesthetic. The smog and sunlight should interact to create a striking visual contrast, showcasing the dual impact of pollution and clean energy technology on the environment. 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 Duluth and Solar power generated in Estonia. 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: A comic-book-style illustration with muted colors and a dotted halftone pattern from the 1960s Voxel art High-tech Hyper-realistic Cutsy art illustration
ChatGPT: High-tech

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 Duluth and Solar power generated in Estonia, in the following situation: The smog particles acted like tiny mirrors, reflecting more sunlight towards Estonia's solar panels. As a result, the solar power output soared, proving that even pollution can have a silver lining... or rather, a solar lining!. Keep the description simple.
ChatGPT: In Duluth, dark clouds of smog hung heavily over the city, veiling the skyline in a hazy shroud. Despite the pollution, the sun's rays peeked through the thick layer, casting scattered light. Meanwhile, in Estonia, the solar panels gleamed brightly, harnessing the intensified sunlight and generating an impressive surge of solar power. The smog particles acted as a surprising ally, reflecting the sun's rays towards the solar panels, amplifying their energy output.

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: [ High-tech ] and depicting this scene: In Duluth, dark clouds of smog hung heavily over the city, veiling the skyline in a hazy shroud. Despite the pollution, the sun's rays peeked through the thick layer, casting scattered light. Meanwhile, in Estonia, the solar panels gleamed brightly, harnessing the intensified sunlight and generating an impressive surge of solar power. The smog particles acted as a surprising ally, reflecting the sun's rays towards the solar panels, amplifying their energy output. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Prompt: Generate an image of a high-tech city skyline obscured by dark smog, with the sun's rays breaking through and glistening solar panels below, set in an urban landscape with a futuristic aesthetic. The smog and sunlight should interact to create a striking visual contrast, showcasing the dual impact of pollution and clean energy technology on the environment.

*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 an increase in Air pollution in Duluth caused Solar power generated in Estonia to increase.

AI academic paper

(Because p < 0.01)

Breezy Business: The Sky's the Limit for Duluth's Air Pollution and Estonia's Solar Power

The Journal of Environmental Dynamics and Renewable Energy

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 dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.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 Duluth and Solar power generated in Estonia. 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. Then name a few real TV shows that sound like they might be relevant to the topic that you watched as research.

Here is the title and abstract of the paper:
[[TITLE]]
Breezy Business: The Sky's the Limit for Duluth's Air Pollution and Estonia's Solar Power

[[ABSTRACT]]
This paper delves into the breezy business of air pollution and solar power, exploring the unexpected connection between the industrial hub of Duluth and the solar energy haven of Estonia. Utilizing data from the Environmental Protection Agency and Energy Information Administration, our research team uncovered a surprising correlation between air pollution levels in Duluth and the solar power generated in Estonia, with a robust correlation coefficient of 0.8878797 and p < 0.01 from 2009 to 2021. The findings suggest a link between the two seemingly unrelated phenomena, prompting further investigation into the atmospheric dynamics that tie together the Midwestern air and Baltic sunshine. The interplay of pollution and solar power unveils a nuanced relationship that reaches across continents, demonstrating that even the most distant places can be connected by the invisible threads of environmental impact.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
As we all know, the study of environmental impact can be a breath of fresh air, especially when it leads us down unexpected pathways. In the ever-expanding realm of environmental research, the connection between air pollution and solar power may seem like a match made in the stratosphere! After all, what could the gritty industrial city of Duluth and the sun-drenched land of Estonia possibly have in common, besides perhaps an affinity for interesting vowel placement in their names?
Despite the initial appearance of these two phenomena being poles apart, our research has revealed a compelling correlation between the air pollution levels in Duluth and the solar power generated in Estonia. It's a bit like discovering that a dusty old attic fan in Duluth is somehow influencing the array of solar panels in Estonia. This seemingly whimsical linkage has set us on a quest to untangle the atmospheric yarn that binds these distant locales together, and in doing so, we have found ourselves in the midst of a curious pursuit – a pursuit that dances among the data, statistics, and the sweet serendipity of science.
In this paper, we will delve into the data from the Environmental Protection Agency and the Energy Information Administration, where we've uncovered a strong and statistically significant correlation coefficient of 0.8878797, with a p-value less than 0.01 from 2009 to 2021. This tantalizing tidbit of statistical evidence has raised eyebrows and left even the most seasoned researchers scratching their heads, pondering the enigmatic dance of pollutants and photons across continents.
And so, with a gleam of curiosity and a touch of statistical skepticism, we invite you to join us on this intellectual adventure through the realms of air pollution and solar power, where the skies above Duluth and Estonia hold secrets that are as complex as they are captivating.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

Previous studies have unearthed substantive findings concerning air pollution and its impact on various environmental and public health indicators. Smith et al. (2018) conducted a comprehensive analysis of air pollution in urban areas, shedding light on the nuanced dynamics at play within these densely populated regions. Additionally, Doe and Jones (2015) examined the correlation between industrial emissions and atmospheric conditions, providing valuable insights into the far-reaching consequences of pollution.

Turning to the realm of renewable energy, Book (2020) delves into the intricacies of solar power generation, offering a comprehensive overview of photovoltaic systems and their potential to revolutionize energy production. Similarly, Book (2017) explores the environmental implications of transitioning to solar energy, capturing the essence of the solar power movement and its intersection with ecological concerns.

On a different note, the fictional works of Ray Solaris and E. Sunstein, such as "Solar Flares at Midnight" and "The Light of Estonia," offer a whimsical yet surprisingly informative perspective on the relationship between celestial bodies and human endeavors. These imaginative narratives serve as a playful yet intriguing backdrop to the more formal research on solar power and its connection to environmental factors.

The authors also delved into popular culture to draw inspiration from unrelated fields that might provide unexpected insights. For instance, "Solar Power Wars" and "Duluth Nights: Pollution Patrol" - both captivating TV shows - provided an entertaining lens through which to view the interplay of pollution and solar power. While these sources may not align directly with scholarly research, they nonetheless inform the exploratory nature of our investigation and inject a sense of levity into an otherwise weighty subject matter.

The eclectic mix of academic literature, fictional narratives, and pop culture representations paves the way for a multidimensional examination of the connection between air pollution in Duluth and solar power generated in Estonia. With this diverse array of sources as our guide, we set out to unravel the enigmatic relationship that traverses continents and defies conventional expectations.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.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 Duluth and Solar power generated in Estonia. 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 2009 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]]
Breezy Business: The Sky's the Limit for Duluth's Air Pollution and Estonia's Solar Power

[[ABSTRACT]]
This paper delves into the breezy business of air pollution and solar power, exploring the unexpected connection between the industrial hub of Duluth and the solar energy haven of Estonia. Utilizing data from the Environmental Protection Agency and Energy Information Administration, our research team uncovered a surprising correlation between air pollution levels in Duluth and the solar power generated in Estonia, with a robust correlation coefficient of 0.8878797 and p < 0.01 from 2009 to 2021. The findings suggest a link between the two seemingly unrelated phenomena, prompting further investigation into the atmospheric dynamics that tie together the Midwestern air and Baltic sunshine. The interplay of pollution and solar power unveils a nuanced relationship that reaches across continents, demonstrating that even the most distant places can be connected by the invisible threads of environmental impact.

[[INTRODUCTION]]
As we all know, the study of environmental impact can be a breath of fresh air, especially when it leads us down unexpected pathways. In the ever-expanding realm of environmental research, the connection between air pollution and solar power may seem like a match made in the stratosphere! After all, what could the gritty industrial city of Duluth and the sun-drenched land of Estonia possibly have in common, besides perhaps an affinity for interesting vowel placement in their names?
Despite the initial appearance of these two phenomena being poles apart, our research has revealed a compelling correlation between the air pollution levels in Duluth and the solar power generated in Estonia. It's a bit like discovering that a dusty old attic fan in Duluth is somehow influencing the array of solar panels in Estonia. This seemingly whimsical linkage has set us on a quest to untangle the atmospheric yarn that binds these distant locales together, and in doing so, we have found ourselves in the midst of a curious pursuit – a pursuit that dances among the data, statistics, and the sweet serendipity of science.
In this paper, we will delve into the data from the Environmental Protection Agency and the Energy Information Administration, where we've uncovered a strong and statistically significant correlation coefficient of 0.8878797, with a p-value less than 0.01 from 2009 to 2021. This tantalizing tidbit of statistical evidence has raised eyebrows and left even the most seasoned researchers scratching their heads, pondering the enigmatic dance of pollutants and photons across continents.
And so, with a gleam of curiosity and a touch of statistical skepticism, we invite you to join us on this intellectual adventure through the realms of air pollution and solar power, where the skies above Duluth and Estonia hold secrets that are as complex as they are captivating.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

The methodology employed in this research endeavor involves the collection and analysis of data from the Environmental Protection Agency (EPA) and the Energy Information Administration (EIA). The research team utilized a combination of archival data and contemporary statistics to investigate the relationship between air pollution in Duluth and solar power generation in Estonia from 2009 to 2021.

Data Collection:
To gather data on air pollution levels in Duluth, the research team scoured through the EPA's databases, meticulously sifting through an atmospheric maze of particulate matter, volatile organic compounds, nitrogen dioxide, and sulfur dioxide levels. The pursuit of this data was akin to navigating a labyrinth of environmental esoterica, where the researchers donned their statistical armor and ventured forth into the realm of pollutant concentrations.

In parallel, the team combed through the EIA's treasure trove of solar power generation statistics for Estonia, basking in the glow of kilowatt-hour metrics and photovoltaic panel yields. They navigated through the streams of data like intrepid sailors steering through a sea of solar irradiance and energy production figures, always mindful of the currents of statistical fluctuation and the winds of methodological uncertainty.

Data Analysis:
The collected data were subjected to a robust process of statistical analysis, which included exploratory data visualization, correlation analysis, and regression modeling. With the aid of statistical software, the researchers donned their metaphorical lab coats and embarked on a journey through the landscape of statistical methods, armed with scatter plots, correlation matrices, and regression diagnostics as their trusty companions.

The correlation analysis sought to unveil the degree of association between air pollution levels in Duluth and solar power generation in Estonia, unveiling a relationship that was as unexpected as it was statistically significant. The examination of this relationship allowed the researchers to chart a course through the nebulous territory of environmental impact, where the pollutants and photons seemed to engage in an intricate dance across time and space.

Significance Testing:
In evaluating the significance of the observed relationship, the research team applied conventional inferential statistics, invoking the mighty p-value to ascertain the strength of evidence against the null hypothesis. The p-value, like a discerning arbiter of statistical truth, rendered its verdict, signaling that the observed association between air pollution in Duluth and solar power generation in Estonia was not a mere chance occurrence but a statistically noteworthy phenomenon.

Limitations:
While the methodology adopted in this research endeavor provided substantial insights into the linkage between air pollution and solar power, it is essential to acknowledge the inherent limitations of secondary data analysis. The reliance on archival and publicly available data sources necessitated careful validation and consideration of potential confounding variables, akin to navigating a maze of statistical caveats while searching for the proverbial light at the end of the methodological tunnel.

Overall, the methodology employed in this study combined meticulous data collection, rigorous statistical analysis, and a dash of scientific fortuity to unravel the unexpected ties between atmospheric pollutants in Duluth and solar energy in Estonia. This methodological odyssey was marked by the pursuit of statistical enlightenment and the exploration of environmental entanglements, guiding the research team through the intricacies of data-driven discovery and the mysteries of methodological adventure.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.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 Duluth and Solar power generated in Estonia. 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]]
Breezy Business: The Sky's the Limit for Duluth's Air Pollution and Estonia's Solar Power

[[ABSTRACT]]
This paper delves into the breezy business of air pollution and solar power, exploring the unexpected connection between the industrial hub of Duluth and the solar energy haven of Estonia. Utilizing data from the Environmental Protection Agency and Energy Information Administration, our research team uncovered a surprising correlation between air pollution levels in Duluth and the solar power generated in Estonia, with a robust correlation coefficient of 0.8878797 and p < 0.01 from 2009 to 2021. The findings suggest a link between the two seemingly unrelated phenomena, prompting further investigation into the atmospheric dynamics that tie together the Midwestern air and Baltic sunshine. The interplay of pollution and solar power unveils a nuanced relationship that reaches across continents, demonstrating that even the most distant places can be connected by the invisible threads of environmental impact.

[[LITERATURE REVIEW]]
Previous studies have unearthed substantive findings concerning air pollution and its impact on various environmental and public health indicators. Smith et al. (2018) conducted a comprehensive analysis of air pollution in urban areas, shedding light on the nuanced dynamics at play within these densely populated regions. Additionally, Doe and Jones (2015) examined the correlation between industrial emissions and atmospheric conditions, providing valuable insights into the far-reaching consequences of pollution.
Turning to the realm of renewable energy, Book (2020) delves into the intricacies of solar power generation, offering a comprehensive overview of photovoltaic systems and their potential to revolutionize energy production. Similarly, Book (2017) explores the environmental implications of transitioning to solar energy, capturing the essence of the solar power movement and its intersection with ecological concerns.
On a different note, the fictional works of Ray Solaris and E. Sunstein, such as "Solar Flares at Midnight" and "The Light of Estonia," offer a whimsical yet surprisingly informative perspective on the relationship between celestial bodies and human endeavors. These imaginative narratives serve as a playful yet intriguing backdrop to the more formal research on solar power and its connection to environmental factors.
The authors also delved into popular culture to draw inspiration from unrelated fields that might provide unexpected insights. For instance, "Solar Power Wars" and "Duluth Nights: Pollution Patrol" - both captivating TV shows - provided an entertaining lens through which to view the interplay of pollution and solar power. While these sources may not align directly with scholarly research, they nonetheless inform the exploratory nature of our investigation and inject a sense of levity into an otherwise weighty subject matter.
The eclectic mix of academic literature, fictional narratives, and pop culture representations paves the way for a multidimensional examination of the connection between air pollution in Duluth and solar power generated in Estonia. With this diverse array of sources as our guide, we set out to unravel the enigmatic relationship that traverses continents and defies conventional expectations.

[[RESULTS]]
The analysis of the data obtained from the Environmental Protection Agency and the Energy Information Administration unveiled an intriguing connection between air pollution in Duluth and solar power generated in Estonia. This unexpected correlation of 0.8878797 has raised eyebrows and piqued the interest of researchers, akin to stumbling upon a hidden recipe for solar-powered smog reduction.
The calculated r-squared value of 0.7883304 further indicates that a substantial portion of the variability in solar power generation in Estonia can be explained by the fluctuations in air pollution levels in Duluth. It's as if the emissive tendencies of Duluth's industrial endeavors have found a way to moonlight as meteorological maestros, conducting an atmospheric symphony that resonates with solar panels on the distant shores of Estonia.
Moreover, with a p-value of less than 0.01, the statistical analysis reinforces the robustness of the correlation, leaving naysayers with little room for skepticism. One might imagine the statistical significance marching triumphantly through the data, waving a flag emboldened with the insignia of solar-powered solidarity.
The scatterplot (Fig. 1) depicts a striking visual representation of this relationship, where the data points seem to frolic across the Cartesian plane like mischievous particles caught in the whimsical waltz of environmental interconnectedness. It's almost as if the scatterplot is winking at us, silently daring us to unravel the secrets hidden within its colorful embrace.
These results underscore the intricate dance of atmospheric interplay, emphasizing that the impact of air pollution can transcend borders and influence solar power generation in unsuspecting lands. The findings beckon further exploration into the atmospheric alchemy that weaves together the gusts of industrial emissions and the radiance of solar energy, inviting researchers to delve deeper into the cross-continental currents of environmental influence.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The findings of this study indeed reflect the unexpected but intriguing relationship between air pollution in Duluth and solar power generated in Estonia. The results have surpassed our initial expectations, akin to uncovering a fusion of science and serendipity.

The substantial correlation coefficient and statistical significance not only validate our primary hypothesis but also serve as a testament to the whimsical nature of scientific inquiry. While the connection between industrial emissions in Duluth and solar power in Estonia might seem as disparate as a physicist at a poetry reading, our results reveal an intricate interplay that defies conventional boundaries.

The literature review provided a crucial foundation for our research, incorporating insights from scholarly studies and even light-hearted fictional works. The fictional narratives of Ray Solaris and E. Sunstein, though non-scientific in nature, imparted a sense of imaginative wonder that parallels the unexpected patterns we uncovered in our analysis. The playful references to "Solar Power Wars" and "Duluth Nights: Pollution Patrol" now take on a surreal significance, as if the lines between scientific investigation and entertainment have become delightfully blurred.

The scatterplot, with its whimsical depiction of the relationship between pollution levels and solar power generation, seems to mimic the capricious nature of the cosmic ballet. Much like celestial bodies performing an intricate dance, the data points pirouette across the plot, embodying the harmonious yet unpredictable dynamics of environmental impact. One could almost imagine the scatterplot whispering secrets of atmospheric intrigue, inviting researchers to join its merry revelry.

The robustness of the correlation and the substantial portion of variability explained by our model echo the sentiment that as researchers, we must allow ourselves to be guided not only by hard data but also by the unassuming spirit of curiosity. Our study underscores the interconnectedness of global environmental phenomena, demonstrating that the effects of industrial emissions in one corner of the world can manifest in unexpected ways across oceans and continents.

In conclusion, our findings carry significant implications for policymakers, environmental advocates, and renewable energy enthusiasts alike. The revelation of this peculiar link between distant locales compels a reevaluation of our understanding of environmental interconnectedness. It reinforces the notion that environmental impact transcends geographic boundaries and beckons further investigation into the cosmic choreography of industrial emissions and solar radiance. As we embark on this scholarly voyage of discovery, we are reminded that amidst the empirical rigor and statistical scrutiny, there exists a wondrous, enigmatic tapestry waiting to be unraveled.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.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 Duluth and Solar power generated in Estonia. 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]]
Breezy Business: The Sky's the Limit for Duluth's Air Pollution and Estonia's Solar Power

[[ABSTRACT]]
This paper delves into the breezy business of air pollution and solar power, exploring the unexpected connection between the industrial hub of Duluth and the solar energy haven of Estonia. Utilizing data from the Environmental Protection Agency and Energy Information Administration, our research team uncovered a surprising correlation between air pollution levels in Duluth and the solar power generated in Estonia, with a robust correlation coefficient of 0.8878797 and p < 0.01 from 2009 to 2021. The findings suggest a link between the two seemingly unrelated phenomena, prompting further investigation into the atmospheric dynamics that tie together the Midwestern air and Baltic sunshine. The interplay of pollution and solar power unveils a nuanced relationship that reaches across continents, demonstrating that even the most distant places can be connected by the invisible threads of environmental impact.

[[INTRDUCTION]]
As we all know, the study of environmental impact can be a breath of fresh air, especially when it leads us down unexpected pathways. In the ever-expanding realm of environmental research, the connection between air pollution and solar power may seem like a match made in the stratosphere! After all, what could the gritty industrial city of Duluth and the sun-drenched land of Estonia possibly have in common, besides perhaps an affinity for interesting vowel placement in their names?
Despite the initial appearance of these two phenomena being poles apart, our research has revealed a compelling correlation between the air pollution levels in Duluth and the solar power generated in Estonia. It's a bit like discovering that a dusty old attic fan in Duluth is somehow influencing the array of solar panels in Estonia. This seemingly whimsical linkage has set us on a quest to untangle the atmospheric yarn that binds these distant locales together, and in doing so, we have found ourselves in the midst of a curious pursuit – a pursuit that dances among the data, statistics, and the sweet serendipity of science.
In this paper, we will delve into the data from the Environmental Protection Agency and the Energy Information Administration, where we've uncovered a strong and statistically significant correlation coefficient of 0.8878797, with a p-value less than 0.01 from 2009 to 2021. This tantalizing tidbit of statistical evidence has raised eyebrows and left even the most seasoned researchers scratching their heads, pondering the enigmatic dance of pollutants and photons across continents.
And so, with a gleam of curiosity and a touch of statistical skepticism, we invite you to join us on this intellectual adventure through the realms of air pollution and solar power, where the skies above Duluth and Estonia hold secrets that are as complex as they are captivating.

[[RESULTS]]
The analysis of the data obtained from the Environmental Protection Agency and the Energy Information Administration unveiled an intriguing connection between air pollution in Duluth and solar power generated in Estonia. This unexpected correlation of 0.8878797 has raised eyebrows and piqued the interest of researchers, akin to stumbling upon a hidden recipe for solar-powered smog reduction.
The calculated r-squared value of 0.7883304 further indicates that a substantial portion of the variability in solar power generation in Estonia can be explained by the fluctuations in air pollution levels in Duluth. It's as if the emissive tendencies of Duluth's industrial endeavors have found a way to moonlight as meteorological maestros, conducting an atmospheric symphony that resonates with solar panels on the distant shores of Estonia.
Moreover, with a p-value of less than 0.01, the statistical analysis reinforces the robustness of the correlation, leaving naysayers with little room for skepticism. One might imagine the statistical significance marching triumphantly through the data, waving a flag emboldened with the insignia of solar-powered solidarity.
The scatterplot (Fig. 1) depicts a striking visual representation of this relationship, where the data points seem to frolic across the Cartesian plane like mischievous particles caught in the whimsical waltz of environmental interconnectedness. It's almost as if the scatterplot is winking at us, silently daring us to unravel the secrets hidden within its colorful embrace.
These results underscore the intricate dance of atmospheric interplay, emphasizing that the impact of air pollution can transcend borders and influence solar power generation in unsuspecting lands. The findings beckon further exploration into the atmospheric alchemy that weaves together the gusts of industrial emissions and the radiance of solar energy, inviting researchers to delve deeper into the cross-continental currents of environmental influence.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our study has unveiled a whimsical and unexpected correlation between the air pollution in Duluth and the solar power generated in Estonia, resembling a peculiar pas de deux between gritty particles and gleaming photons across continents. The robust correlation coefficient of 0.8878797 and r-squared value of 0.7883304, akin to a statistical tango, have left even the staunchest skeptics marveling at the harmonious interplay of these seemingly disparate environmental factors.

The striking visual representation of our findings in the scatterplot (Fig. 1) feels like a mischievous wink from the data, goading us to uncover the hidden secrets of this atmospheric affair – a truly captivating dance of pollution and solar power that transcends geographical boundaries. It's as if the scatterplot itself has donned a masquerade mask, teasing us with its colorful charm and enigmatic allure.

While our investigation has shed light on this enthralling connection, it also raises the question: What other unseen threads of environmental influence are waiting to be unraveled? The atmospheric dynamics that link Duluth's pollution and Estonia's solar power beckon further exploration, dangling before us an intellectual carrot that is as tantalizing as it is perplexing.

Based on the compelling statistical evidence and the captivating nature of this phenomenon, it is clear that no additional research is needed in this area. After all, why delve deeper into this atmospheric intrigue when there are so many other quirky quizical conundrums awaiting our scientific scrutiny?

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 Breezy Business: The Sky's the Limit for Duluth's Air Pollution and Estonia's Solar Power. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental Dynamics and Renewable Energy

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 Breezy Business: The Sky's the Limit for Duluth's Air Pollution and Estonia's Solar Power. Respond only with the name of a fictional organization.

ChatGPT:

The Institute for Eco-Sustainable Air Quality and Renewable Energy Integration (IESAQREI)

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 Breezy Business: The Sky's the Limit for Duluth's Air Pollution and Estonia's Solar Power with an abstract of This paper delves into the breezy business of air pollution and solar power, exploring the unexpected connection between the industrial hub of Duluth and the solar energy haven of Estonia. Utilizing data from the Environmental Protection Agency and Energy Information Administration, our research team uncovered a surprising correlation between air pollution levels in Duluth and the solar power generated in Estonia, with a robust correlation coefficient of 0.8878797 and p < 0.01 from 2009 to 2021. The findings suggest a link between the two seemingly unrelated phenomena, prompting further investigation into the atmospheric dynamics that tie together the Midwestern air and Baltic sunshine. The interplay of pollution and solar power unveils a nuanced relationship that reaches across continents, demonstrating that even the most distant places can be connected by the invisible threads of environmental impact.

ChatGPT:

air pollution, solar power, Duluth, Estonia, environmental impact, correlation coefficient, atmospheric dynamics, industrial hub, solar energy, Environmental Protection Agency, Energy Information Administration, pollution levels, solar power generation

*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 Duluth
Detailed data title: Percentage of days with air quality at 'unhealthy for sensitive groups' or worse in Duluth, MN-WI
Source: Environmental Protection Agency
See what else correlates with Air pollution in Duluth

Solar power generated in Estonia
Detailed data title: Total solar power generated in Estonia in billion kWh
Source: Energy Information Administration
See what else correlates with Solar power generated in Estonia

Correlation r = 0.8878797 (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 = 0.7883304 (Coefficient of determination)
This means 78.8% of the change in the one variable (i.e., Solar power generated in Estonia) is predictable based on the change in the other (i.e., Air pollution in Duluth) over the 13 years from 2009 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 5.08E-5.^Show 0.0000507629616049417700000000
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 0.89 in 0.00508% of random cases. Said differently, if you correlated 19,699 random variables^Note Which I absolutely did.
with the same 12 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 12 because we have two variables measured over a period of 13 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.

[ 0.66, 0.97 ] 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.

	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021
Air pollution in Duluth (Bad air quality days)	0	0.547945	0.273973	0.273224	0	0	0.547945	0.273224	0	0.547945	0.273973	0.273224	3.0137
Solar power generated in Estonia (Billion kWh)	0.0001	0.0001	0.0002	0.0003	0.001	0.003	0.006	0.009677	0.014491	0.030802	0.0735	0.123	0.305

Why this works

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

Try it yourself

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

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([0,0.547945,0.273973,0.273224,0,0,0.547945,0.273224,0,0.547945,0.273973,0.273224,3.0137,])
array_2 = np.array([0.0001,0.0001,0.0002,0.0003,0.001,0.003,0.006,0.009677,0.014491,0.030802,0.0735,0.123,0.305,])
array_1_name = "Air pollution in Duluth"
array_2_name = "Solar power generated in Estonia"

# 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 Duluth
Line chart for only Solar power generated in Estonia
AI-generated correlation image
The spurious research paper: Breezy Business: The Sky's the Limit for Duluth's Air Pollution and Estonia's Solar Power

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Correlation ID: 2503 · Black Variable ID: 20566 · Red Variable ID: 23656


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