Spurious correlation #4,653 · 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 Billings, Montana and the second variable is Google searches for '3Blue1Brown'. The chart goes from 2007 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 Billings, Montana and the second variable is Google searches for '3Blue1Brown'. The chart goes from 2007 to 2022, and the two variables track closely in value over that time.

Download png, svg

AI explanation

Perhaps the locals mistook the smog for a new type of colorful mathematical visualization, prompting them to delve into the world of 3Blue1Brown in a quest for cleaner, clearer perspectives.

^{Show image generation prompt} Model: dalle-3
Prompt: Prompt: Create a hyper-realistic visual of the streets of Billings, Montana blanketed in a thick layer of smog. In the distance, the city skyline is barely visible through the haze. Amongst the pollution, depict locals frantically typing "3Blue1Brown" into their smartphones, with their faces illuminated by the glow of the screens, as they seek out a world of mathematical visualization. The scene should evoke a sense of urgency and longing for clarity amidst the obscured cityscape. 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 Billings, Montana and Google searches for '3Blue1Brown'. 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: Cubism Data cyber art Voxel art Macabre Hyper-realistic
ChatGPT: Hyper-realistic

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 Billings, Montana and Google searches for '3Blue1Brown', in the following situation: Perhaps the locals mistook the smog for a new type of colorful mathematical visualization, prompting them to delve into the world of 3Blue1Brown in a quest for cleaner, clearer perspectives.. Keep the description simple.
ChatGPT: The streets of Billings, Montana are shrouded in a thick haze of smog, with the city skyline barely visible in the distance. Amidst the pollution, locals are seen frantically typing "3Blue1Brown" into their smartphones, their faces illuminated by the glow of their screens as they seek out a clearer, brighter world of mathematical visualization.

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: [ Hyper-realistic ] and depicting this scene: The streets of Billings, Montana are shrouded in a thick haze of smog, with the city skyline barely visible in the distance. Amidst the pollution, locals are seen frantically typing "3Blue1Brown" into their smartphones, their faces illuminated by the glow of their screens as they seek out a clearer, brighter world of mathematical visualization. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Prompt: Create a hyper-realistic visual of the streets of Billings, Montana blanketed in a thick layer of smog. In the distance, the city skyline is barely visible through the haze. Amongst the pollution, depict locals frantically typing "3Blue1Brown" into their smartphones, with their faces illuminated by the glow of the screens, as they seek out a world of mathematical visualization. The scene should evoke a sense of urgency and longing for clarity amidst the obscured cityscape.

*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 Billings, Montana caused 3Blue1Brown (Google searches for '3Blue1Brown') to increase.

AI academic paper

(Because p < 0.01)

Clearing the Air: Exploring the '3Blue1Brown' Connection to Air Pollution in Billings, Montana

The Journal of Ecological Mathematics and Environmental Studies

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 Billings, Montana and Google searches for '3Blue1Brown'. 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]]
"Clearing the Air: Exploring the '3Blue1Brown' Connection to Air Pollution in Billings, Montana"

[[ABSTRACT]]
In this study, we embark on a lighthearted journey to uncover the peculiar relationship between air pollution in Billings, Montana, and Google searches for the beloved educational YouTube channel '3Blue1Brown.' Leveraging data from the Environmental Protection Agency and Google Trends, we sought to answer the pressing question: is there a correlation between air quality and the brainy inquiries of '3Blue1Brown' enthusiasts? To our surprise, we stumbled upon a correlation coefficient of 0.9363108, which left us feeling more astonished than a mathematician discovering a hidden pattern in a complex equation. With p < 0.01, our findings suggest a robust statistical relationship between air pollution levels and the quest for math enlightenment through online resources. So, join us as we unravel this whimsical mystery and breathe in the unexpected links between environmental factors and digital curiosity.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
INTRODUCTION
The quest for knowledge often leads us down unexpected paths. In this study, we venture into the realm of peculiar correlations to unravel the mysterious connection between air pollution in Billings, Montana, and the digital inquiries of '3Blue1Brown' enthusiasts. While this research may seem as whimsical as a unicorn sighting in a statistics textbook, we assure you that our approach is as rigorous as a marathon runner's training regimen.
Air pollution, a persistent environmental concern, has been the subject of numerous studies due to its impact on public health and the environment. From automobile emissions to industrial activities, the sources of air pollution are as diverse as the flavors in a Ben & Jerry's ice cream parlor. Similarly, '3Blue1Brown,' an educational YouTube channel dedicated to the art of math and visual explanations, has garnered a devoted following of math aficionados, who are as enthusiastic about calculus as any sports fan during the Super Bowl.
Our curiosity piqued by this unlikely pairing, we set out to investigate whether there exists a meaningful relationship between the two seemingly disparate entities. Leveraging data from the Environmental Protection Agency and Google Trends, we embarked on a lighthearted yet scholarly endeavor to shed light on this intriguing connection. Our aspiration was to unravel a connection as captivating as a mystery novel and as enlightening as a eureka moment in a research laboratory.
While our investigation may seem like searching for a needle in a haystack, we were determined to uncover any correlations between air pollution levels and the intellectual musings of '3Blue1Brown' enthusiasts. Our findings, as we shall soon reveal, surprised us more than a magician pulling a rabbit out of a hat at a statistics convention.
So, fasten your seatbelts as we embark on this exhilarating research journey, where the ordinary becomes extraordinary, and the unexpected connections make us feel like detectives unraveling a mathematical whodunit. Let's clear the air and delve into the seemingly improbable, for sometimes, in the realm of scientific inquiry, truth is indeed stranger than fiction.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The existing literature on air pollution and its effects on human behavior has delved into a wide array of topics, from its impact on physical health to its influence on cognitive functions. Smith et al. (2015) conducted a comprehensive analysis of air pollution in urban areas, highlighting its detrimental effects on respiratory health and overall well-being. Doe and Jones (2018) explored the association between air quality and mental acuity, revealing a surprising link between pollution levels and cognitive performance.

Moving beyond the traditional scope of air pollution research, our investigation seeks to illuminate a rather unconventional relationship— the connection between the air quality in Billings, Montana, and the phenomenon of Google searches for '3Blue1Brown.' As we delve into this uncharted territory, we must not overlook the work of notable figures in the field of environmental psychology and digital trends.

Turning our attention to related non-fiction literature, it is imperative to consider the insights offered by "The Sixth Extinction: An Unnatural History" by Elizabeth Kolbert and "This Changes Everything: Capitalism vs. The Climate" by Naomi Klein. While these works may not seem immediately relevant to our peculiar investigation, they serve as reminders of the interconnectedness of environmental factors and human activities, including digital pursuits.

In the realm of fiction, the writings of Michael Crichton, particularly "State of Fear," offer a thrilling portrayal of environmental issues intertwined with technological advancements. Meanwhile, the thought-provoking narrative of "The Air You Breathe" by Frances de Pontes Peebles prompts contemplation on the significance of air quality and its potential impact on intellectual curiosity.

Taking a more lighthearted approach to gathering insights, we expanded our exploration to include popular television shows that might provide unexpected parallels to our research endeavors. As diligent researchers, we found ourselves embarking on "Breaking Bad" and "Stranger Things" marathons, eagerly seeking any subtle references to air quality and mathematical inquiries. While these shows may not directly contribute to scholarly discourse on our topic, the search for unconventional inspiration led us to uncover unforeseen connections between seemingly unrelated phenomena—much like our quest to understand the '3Blue1Brown' and air pollution correlation.

In the pursuit of scientific inquiry, it is essential to approach the subject matter from diverse and unexpected angles. Thus, our foray into the literary and media landscape has enriched our perspective, reminding us that insight often arises from the most surprising sources. As we prepare to unveil the fascinating results of our investigation, we encourage readers to approach our findings with an open mind and a playful spirit, for in the world of research, unexpected discoveries often prove to be the most enlightening.

Stay tuned for our next section, where we will illuminate the methods and data analysis employed to uncover the captivating connection between air pollution in Billings, Montana, and the virtual quest for mathematical enlightenment through '3Blue1Brown.'

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 Billings, Montana and Google searches for '3Blue1Brown'. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Google Trends . You used data from 2007 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]]
"Clearing the Air: Exploring the '3Blue1Brown' Connection to Air Pollution in Billings, Montana"

[[ABSTRACT]]
In this study, we embark on a lighthearted journey to uncover the peculiar relationship between air pollution in Billings, Montana, and Google searches for the beloved educational YouTube channel '3Blue1Brown.' Leveraging data from the Environmental Protection Agency and Google Trends, we sought to answer the pressing question: is there a correlation between air quality and the brainy inquiries of '3Blue1Brown' enthusiasts? To our surprise, we stumbled upon a correlation coefficient of 0.9363108, which left us feeling more astonished than a mathematician discovering a hidden pattern in a complex equation. With p < 0.01, our findings suggest a robust statistical relationship between air pollution levels and the quest for math enlightenment through online resources. So, join us as we unravel this whimsical mystery and breathe in the unexpected links between environmental factors and digital curiosity.

[[INTRODUCTION]]
INTRODUCTION
The quest for knowledge often leads us down unexpected paths. In this study, we venture into the realm of peculiar correlations to unravel the mysterious connection between air pollution in Billings, Montana, and the digital inquiries of '3Blue1Brown' enthusiasts. While this research may seem as whimsical as a unicorn sighting in a statistics textbook, we assure you that our approach is as rigorous as a marathon runner's training regimen.
Air pollution, a persistent environmental concern, has been the subject of numerous studies due to its impact on public health and the environment. From automobile emissions to industrial activities, the sources of air pollution are as diverse as the flavors in a Ben & Jerry's ice cream parlor. Similarly, '3Blue1Brown,' an educational YouTube channel dedicated to the art of math and visual explanations, has garnered a devoted following of math aficionados, who are as enthusiastic about calculus as any sports fan during the Super Bowl.
Our curiosity piqued by this unlikely pairing, we set out to investigate whether there exists a meaningful relationship between the two seemingly disparate entities. Leveraging data from the Environmental Protection Agency and Google Trends, we embarked on a lighthearted yet scholarly endeavor to shed light on this intriguing connection. Our aspiration was to unravel a connection as captivating as a mystery novel and as enlightening as a eureka moment in a research laboratory.
While our investigation may seem like searching for a needle in a haystack, we were determined to uncover any correlations between air pollution levels and the intellectual musings of '3Blue1Brown' enthusiasts. Our findings, as we shall soon reveal, surprised us more than a magician pulling a rabbit out of a hat at a statistics convention.
So, fasten your seatbelts as we embark on this exhilarating research journey, where the ordinary becomes extraordinary, and the unexpected connections make us feel like detectives unraveling a mathematical whodunit. Let's clear the air and delve into the seemingly improbable, for sometimes, in the realm of scientific inquiry, truth is indeed stranger than fiction.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

To venture into the whimsical world of unraveling the connection between air pollution in Billings, Montana, and the digital queries regarding '3Blue1Brown,' we employed a dance of data collection, statistical analysis, and a touch of whimsy. Our fascination with this peculiar correlation fueled our drive to craft a methodological approach as rigorous as a crossword puzzle enthusiast tackling a Sunday edition.

1. Data Collection:
To quantify the levels of air pollution in Billings, Montana, from 2007 to 2022, we turned to the Environmental Protection Agency's repository of air quality data like a treasure hunter seeks valuable artifacts. Embracing the digital era, we utilized Google Trends to capture the search interest for '3Blue1Brown' over the same time period, akin to an anthropologist observing the digital habits of contemporary netizens.

2. Statistical Analysis:
Armed with our arsenal of air quality data and Google search patterns, we eagerly dove into the depths of statistical analysis. We calculated aggregate air pollution levels, employing metrics such as concentrations of particulate matter (PM2.5 and PM10) and ozone, treating each datum point with the care of a gardener tending to delicate orchids. Then, we harmonized these with Google search interest data, performing a correlation analysis with the precision of a maestro conducting a symphony orchestra, and in doing so, unveiled the hidden melody between air quality and digital investigations.

3. Control Variables:
Acknowledging the importance of controlling for extraneous influences, we considered various demographic, seasonal, and socioeconomic factors that could potentially sway the search activities for '3Blue1Brown.' We navigated through these confounding variables like intrepid explorers in uncharted territory, ensuring that our analysis remained as robust as a sturdy bridge in a mathematical landscape.

4. Sensitivity Analysis:
To reaffirm the resilience of our findings, we conducted sensitivity analyses with the meticulousness of a jeweler examining the facets of a precious gemstone. We evaluated the robustness of the correlation under different model specifications and scenarios, ensuring that our results remained as steadfast as the laws of arithmetic.

5. Ethical Considerations:
Throughout our research journey, we adhered to the ethical principles of data usage and privacy protection, treating each piece of information with the respect and confidentiality of a librarian safeguarding literary treasures within the hallowed walls of a library.

In summary, our methodological approach combined meticulous data collection, rigorous statistical scrutiny, and a splash of whimsy to unravel the enigmatic bond between air pollution in Billings, Montana, and the cerebral quests for '3Blue1Brown.' Like intrepid investigators in the world of numbers and inquiries, we approached this study with fervor and scholarly rigor, seeking to illuminate the unexpected connections that weave through the fabric of our digital and environmental landscapes.

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 Billings, Montana and Google searches for '3Blue1Brown'. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Limit your response to 500 tokens.

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

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

[[TITLE]]
"Clearing the Air: Exploring the '3Blue1Brown' Connection to Air Pollution in Billings, Montana"

[[ABSTRACT]]
In this study, we embark on a lighthearted journey to uncover the peculiar relationship between air pollution in Billings, Montana, and Google searches for the beloved educational YouTube channel '3Blue1Brown.' Leveraging data from the Environmental Protection Agency and Google Trends, we sought to answer the pressing question: is there a correlation between air quality and the brainy inquiries of '3Blue1Brown' enthusiasts? To our surprise, we stumbled upon a correlation coefficient of 0.9363108, which left us feeling more astonished than a mathematician discovering a hidden pattern in a complex equation. With p < 0.01, our findings suggest a robust statistical relationship between air pollution levels and the quest for math enlightenment through online resources. So, join us as we unravel this whimsical mystery and breathe in the unexpected links between environmental factors and digital curiosity.

[[LITERATURE REVIEW]]
The existing literature on air pollution and its effects on human behavior has delved into a wide array of topics, from its impact on physical health to its influence on cognitive functions. Smith et al. (2015) conducted a comprehensive analysis of air pollution in urban areas, highlighting its detrimental effects on respiratory health and overall well-being. Doe and Jones (2018) explored the association between air quality and mental acuity, revealing a surprising link between pollution levels and cognitive performance.
Moving beyond the traditional scope of air pollution research, our investigation seeks to illuminate a rather unconventional relationship— the connection between the air quality in Billings, Montana, and the phenomenon of Google searches for '3Blue1Brown.' As we delve into this uncharted territory, we must not overlook the work of notable figures in the field of environmental psychology and digital trends.
Turning our attention to related non-fiction literature, it is imperative to consider the insights offered by "The Sixth Extinction: An Unnatural History" by Elizabeth Kolbert and "This Changes Everything: Capitalism vs. The Climate" by Naomi Klein. While these works may not seem immediately relevant to our peculiar investigation, they serve as reminders of the interconnectedness of environmental factors and human activities, including digital pursuits.
In the realm of fiction, the writings of Michael Crichton, particularly "State of Fear," offer a thrilling portrayal of environmental issues intertwined with technological advancements. Meanwhile, the thought-provoking narrative of "The Air You Breathe" by Frances de Pontes Peebles prompts contemplation on the significance of air quality and its potential impact on intellectual curiosity.
Taking a more lighthearted approach to gathering insights, we expanded our exploration to include popular television shows that might provide unexpected parallels to our research endeavors. As diligent researchers, we found ourselves embarking on "Breaking Bad" and "Stranger Things" marathons, eagerly seeking any subtle references to air quality and mathematical inquiries. While these shows may not directly contribute to scholarly discourse on our topic, the search for unconventional inspiration led us to uncover unforeseen connections between seemingly unrelated phenomena—much like our quest to understand the '3Blue1Brown' and air pollution correlation.
In the pursuit of scientific inquiry, it is essential to approach the subject matter from diverse and unexpected angles. Thus, our foray into the literary and media landscape has enriched our perspective, reminding us that insight often arises from the most surprising sources. As we prepare to unveil the fascinating results of our investigation, we encourage readers to approach our findings with an open mind and a playful spirit, for in the world of research, unexpected discoveries often prove to be the most enlightening.
Stay tuned for our next section, where we will illuminate the methods and data analysis employed to uncover the captivating connection between air pollution in Billings, Montana, and the virtual quest for mathematical enlightenment through '3Blue1Brown.'

[[RESULTS]]
The statistical analysis of the data collected revealed a striking correlation between air pollution levels in Billings, Montana, and Google searches for '3Blue1Brown.' The correlation coefficient of 0.9363108 indicates a strong positive relationship between these two seemingly unrelated phenomena. This finding left us more puzzled than a mathematician trying to solve a non-linear differential equation with no initial conditions.
Furthermore, the r-squared value of 0.8766779 suggests that approximately 87.67% of the variability in '3Blue1Brown' searches can be explained by variations in air pollution levels. That's a stronger relationship than peanut butter and jelly, or even salt and pepper - a mathematical harmony that surprised us more than finding a unicorn in a statistics textbook.
The p-value of less than 0.01 provides compelling evidence to reject the null hypothesis, indicating that the observed correlation is unlikely to be a chance occurrence. This level of statistical significance made us feel more confident in our findings than a scientist who has finally discovered the missing piece of a scientific puzzle.
Fig. 1 presents a scatterplot illustrating the robust correlation between air pollution levels and Google searches for '3Blue1Brown.' The tightly clustered data points resemble a cohesive mathematical proof, painting a picture that is as clear as the air after a thunderstorm.
In summary, our results reveal a surprising and statistically significant relationship between air pollution in Billings, Montana, and the digital quest for mathematical enlightenment. This unexpected connection between environmental factors and online education left us feeling as curious as a cat who has stumbled upon a particularly perplexing algebra problem.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The findings of our study provide compelling evidence for the existence of a robust relationship between air pollution levels in Billings, Montana, and Google searches for '3Blue1Brown.' Our results not only support prior research on the correlation between air quality and human behavior but also shed light on the unanticipated intersection between environmental factors and online mathematical exploration. This peculiar connection underscores the intricate web of influences that shape digital curiosity and information-seeking behavior.

As we reflect on the literary inspirations that permeated our literature review, we cannot dismiss the unexpected relevance of Michael Crichton's "State of Fear." While the novel may belong to the realm of fiction, its portrayal of environmental issues intertwined with technological advancements serves as a poignant reflection of the real-world interplay between air quality and digital pursuits. Likewise, the thought-provoking narrative of "The Air You Breathe" by Frances de Pontes Peebles nudges us to contemplate the significance of air quality and its potential impact on intellectual curiosity. As we ponder these fictional explorations, our empirical findings resonate with the underlying themes of interconnectedness and influence, demonstrating that truth can indeed be stranger than fiction.

Our results also align with the broader body of literature on air pollution and its effects on human behavior. Smith et al.'s (2015) comprehensive analysis of air pollution in urban areas, emphasizing its detrimental effects on respiratory health, echoes the relevance of our findings in uncovering a distinct association between air quality and online information-seeking behavior. Furthermore, the surprising link between pollution levels and cognitive performance reported by Doe and Jones (2018) finds resonance in our discovery of a substantial relationship between air pollution and the pursuit of mathematical knowledge through digital platforms. The convergence of these findings bolsters the notion that air quality exerts a multifaceted influence on human activities, spanning from physical health to cognitive engagement in virtual spaces.

Moreover, our study extends beyond the traditional scope of environmental psychology by illuminating the unlikely correlation between air pollution levels and online educational pursuits. Just as our investigation ventured into unexpected territories, the discovery of this intricate relationship underscores the dynamic interplay between environmental contexts and the digital landscape. While our research may seem whimsical on the surface, the serious implications of our findings invite a reevaluation of the nuanced ways in which environmental factors can shape cognitive endeavors in the virtual sphere.

In conclusion, our study unravels a captivating link between air pollution in Billings, Montana, and the digital quest for mathematical enlightenment, offering a lighthearted yet substantive contribution to the understanding of environmental influences on digital information-seeking behavior. As we further contemplate the implications of this correlation, we remain mindful of the delightful surprises that await in the intersection of science, humor, and statistical 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 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 Billings, Montana and Google searches for '3Blue1Brown'. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
"Clearing the Air: Exploring the '3Blue1Brown' Connection to Air Pollution in Billings, Montana"

[[ABSTRACT]]
In this study, we embark on a lighthearted journey to uncover the peculiar relationship between air pollution in Billings, Montana, and Google searches for the beloved educational YouTube channel '3Blue1Brown.' Leveraging data from the Environmental Protection Agency and Google Trends, we sought to answer the pressing question: is there a correlation between air quality and the brainy inquiries of '3Blue1Brown' enthusiasts? To our surprise, we stumbled upon a correlation coefficient of 0.9363108, which left us feeling more astonished than a mathematician discovering a hidden pattern in a complex equation. With p < 0.01, our findings suggest a robust statistical relationship between air pollution levels and the quest for math enlightenment through online resources. So, join us as we unravel this whimsical mystery and breathe in the unexpected links between environmental factors and digital curiosity.

[[INTRDUCTION]]
INTRODUCTION
The quest for knowledge often leads us down unexpected paths. In this study, we venture into the realm of peculiar correlations to unravel the mysterious connection between air pollution in Billings, Montana, and the digital inquiries of '3Blue1Brown' enthusiasts. While this research may seem as whimsical as a unicorn sighting in a statistics textbook, we assure you that our approach is as rigorous as a marathon runner's training regimen.
Air pollution, a persistent environmental concern, has been the subject of numerous studies due to its impact on public health and the environment. From automobile emissions to industrial activities, the sources of air pollution are as diverse as the flavors in a Ben & Jerry's ice cream parlor. Similarly, '3Blue1Brown,' an educational YouTube channel dedicated to the art of math and visual explanations, has garnered a devoted following of math aficionados, who are as enthusiastic about calculus as any sports fan during the Super Bowl.
Our curiosity piqued by this unlikely pairing, we set out to investigate whether there exists a meaningful relationship between the two seemingly disparate entities. Leveraging data from the Environmental Protection Agency and Google Trends, we embarked on a lighthearted yet scholarly endeavor to shed light on this intriguing connection. Our aspiration was to unravel a connection as captivating as a mystery novel and as enlightening as a eureka moment in a research laboratory.
While our investigation may seem like searching for a needle in a haystack, we were determined to uncover any correlations between air pollution levels and the intellectual musings of '3Blue1Brown' enthusiasts. Our findings, as we shall soon reveal, surprised us more than a magician pulling a rabbit out of a hat at a statistics convention.
So, fasten your seatbelts as we embark on this exhilarating research journey, where the ordinary becomes extraordinary, and the unexpected connections make us feel like detectives unraveling a mathematical whodunit. Let's clear the air and delve into the seemingly improbable, for sometimes, in the realm of scientific inquiry, truth is indeed stranger than fiction.

[[RESULTS]]
The statistical analysis of the data collected revealed a striking correlation between air pollution levels in Billings, Montana, and Google searches for '3Blue1Brown.' The correlation coefficient of 0.9363108 indicates a strong positive relationship between these two seemingly unrelated phenomena. This finding left us more puzzled than a mathematician trying to solve a non-linear differential equation with no initial conditions.
Furthermore, the r-squared value of 0.8766779 suggests that approximately 87.67% of the variability in '3Blue1Brown' searches can be explained by variations in air pollution levels. That's a stronger relationship than peanut butter and jelly, or even salt and pepper - a mathematical harmony that surprised us more than finding a unicorn in a statistics textbook.
The p-value of less than 0.01 provides compelling evidence to reject the null hypothesis, indicating that the observed correlation is unlikely to be a chance occurrence. This level of statistical significance made us feel more confident in our findings than a scientist who has finally discovered the missing piece of a scientific puzzle.
Fig. 1 presents a scatterplot illustrating the robust correlation between air pollution levels and Google searches for '3Blue1Brown.' The tightly clustered data points resemble a cohesive mathematical proof, painting a picture that is as clear as the air after a thunderstorm.
In summary, our results reveal a surprising and statistically significant relationship between air pollution in Billings, Montana, and the digital quest for mathematical enlightenment. This unexpected connection between environmental factors and online education left us feeling as curious as a cat who has stumbled upon a particularly perplexing algebra problem.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our research has uncovered a correlation as strong as the force pulling mathematicians towards '3Blue1Brown.' We've established a connection between air pollution in Billings, Montana, and the yearning for mathematical enlightenment, perhaps proving that clean air leads to clearer mathematical ponderings. This relationship is more intriguing than a mystery novel featuring Sherlock Holmes solving differential equations, leaving us as baffled as a pig in a calculus class.

Despite the whimsical nature of our investigation, the robust statistical significance and the strong correlation coefficient have lent credence to our findings, akin to discovering a hidden mathematical pattern in an algebraic equation. We are more confident in this connection than a statistician armed with a solid sample size and a strong cup of coffee.

With these results, we are inclined to assert the hypothesis that there is indeed a meaningful link between air pollution levels and the quest for mathematical knowledge, akin to discovering the missing variable in an equation.

We believe that our findings shed light on an unexpected intersection between environmental factors and digital curiosity, and we are as satisfied with this conclusion as a mathematician solving a particularly vexing problem.

It is our fervent hope that this study paves the way for further research in unlikely correlations and amuses academics and enthusiasts alike. However, based on our findings, we declare that no more research is needed in this area, as we have surely reached the pinnacle of peculiar yet fascinating connections.

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 Clearing the Air: Exploring the '3Blue1Brown' Connection to Air Pollution in Billings, Montana. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Ecological Mathematics and Environmental Studies

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 Clearing the Air: Exploring the '3Blue1Brown' Connection to Air Pollution in Billings, Montana. Respond only with the name of a fictional organization.

ChatGPT:

The Institute for Comedic Environmental Research

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 Clearing the Air: Exploring the '3Blue1Brown' Connection to Air Pollution in Billings, Montana with an abstract of In this study, we embark on a lighthearted journey to uncover the peculiar relationship between air pollution in Billings, Montana, and Google searches for the beloved educational YouTube channel '3Blue1Brown.' Leveraging data from the Environmental Protection Agency and Google Trends, we sought to answer the pressing question: is there a correlation between air quality and the brainy inquiries of '3Blue1Brown' enthusiasts? To our surprise, we stumbled upon a correlation coefficient of 0.9363108, which left us feeling more astonished than a mathematician discovering a hidden pattern in a complex equation. With p < 0.01, our findings suggest a robust statistical relationship between air pollution levels and the quest for math enlightenment through online resources. So, join us as we unravel this whimsical mystery and breathe in the unexpected links between environmental factors and digital curiosity.

ChatGPT:

air pollution, Billings, Montana, 3Blue1Brown, correlation, EPA data, Google Trends, correlation coefficient, statistical relationship, environmental factors, digital curiosity, online resources

*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 Billings, Montana
Detailed data title: Percentage of days 'unhealthy' or worse air quality in Billings, MT
Source: Environmental Protection Agency
See what else correlates with Air pollution in Billings, Montana

Google searches for '3Blue1Brown'
Detailed data title: Relative volume of Google searches for '3Blue1Brown' (Worldwide, without quotes)
Source: Google Trends
Additional Info: ^{See full details} Relative search volume (not absolute numbers)

See what else correlates with Google searches for '3Blue1Brown'

Correlation r = 0.9363108 (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 = 0.8766779 (Coefficient of determination)
This means 87.7% of the change in the one variable (i.e., Google searches for '3Blue1Brown') is predictable based on the change in the other (i.e., Air pollution in Billings, Montana) over the 16 years from 2007 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 9.6E-8.^Show 0.0000000962157792066782000000
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 0.94 in 9.6E-6% of random cases. Said differently, if you correlated 10,393,306 random variables^Note You don't actually need 10 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 15 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 15 because we have two variables measured over a period of 16 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.

[ 0.82, 0.98 ] 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.

	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
Air pollution in Billings, Montana (Bad air quality days)	0	0	0	0	0	0	0	0	0	0	0	0.289855	0.342466	0.274725	0.294118	0.273973
Google searches for '3Blue1Brown' (Rel. search volume)	2.33333	2.5	1.5	0.416667	0.416667	0.333333	0	0.333333	0.5	2.66667	21.5833	39.0833	47.4167	57.3333	33.3333	48.6667

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([0,0,0,0,0,0,0,0,0,0,0,0.289855,0.342466,0.274725,0.294118,0.273973,])
array_2 = np.array([2.33333,2.5,1.5,0.416667,0.416667,0.333333,0,0.333333,0.5,2.66667,21.5833,39.0833,47.4167,57.3333,33.3333,48.6667,])
array_1_name = "Air pollution in Billings, Montana"
array_2_name = "Google searches for '3Blue1Brown'"

# 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 Billings, Montana
Line chart for only Google searches for '3Blue1Brown'
AI-generated correlation image
The spurious research paper: Clearing the Air: Exploring the '3Blue1Brown' Connection to Air Pollution in Billings, Montana

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Correlation ID: 4653 · Black Variable ID: 20344 · Red Variable ID: 1454


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