Spurious correlation #2,703 · 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 Buffalo and the second variable is Kerosene used in Peru. The chart goes from 1980 to 2021, and the two variables track closely in value over that time.

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Buffalo and the second variable is Kerosene used in Peru. The chart goes from 1980 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The cleaner air in Buffalo led to an influx of eco-conscious Canadian geese who migrated to Peru and started a grassroots movement against kerosene usage. These geese, known for their honk-and-activism approach, were able to convince the locals to switch to cleaner energy sources like solar power and alpaca-approved wind turbines. This unexpected avian intervention sparked a feather-ruffling debate in the Peruvian government, ultimately leading to a ban on kerosene for anything other than emergency condor lanterns. The Buffalo Effect, as it's now known, has proven that when it comes to environmental change, every birdie counts!

^{Show image generation prompt} Model: dalle-3
Prompt: In a stunning display of unity and progress, vividly-hued hot air balloons rise against the backdrop of a clear Buffalo sky. The balloons gracefully float above the city, mirroring the residents' enthusiasm for this surreal experience. Meanwhile, in Peru, the scarcity of kerosene has led to a stark contrast; depict people relying on alternative methods for everyday tasks. The contrasting images convey a compelling narrative of environmental joy and hardship, merging them into a visually captivating cyber art composition. 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 Buffalo and Kerosene used in Peru. 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: Data cyber art A scene from Skyrim Whimsical illustration Psychedelic Minimalism
ChatGPT: Data cyber art

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 Buffalo and Kerosene used in Peru, in the following situation: Because the decrease in air pollution in Buffalo led to cleaner air, it caused Buffalo residents to start taking more hot air balloon rides for recreational purposes. This sudden surge in hot air balloon popularity led to a shortage of kerosene, which is a key component for hot air balloons, and consequently decreased the amount of kerosene available for use in Peru.. Keep the description simple.
ChatGPT: In Buffalo, clear blue skies are filled with colorful hot air balloons, floating gracefully over the city. The residents are gathering to take off on these whimsical rides, enjoying the cleaner air. Meanwhile, in Peru, people are facing a shortage of kerosene, impacting their ability to use it for various daily needs.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ Data cyber art ] and depicting this scene: In Buffalo, clear blue skies are filled with colorful hot air balloons, floating gracefully over the city. The residents are gathering to take off on these whimsical rides, enjoying the cleaner air. Meanwhile, in Peru, people are facing a shortage of kerosene, impacting their ability to use it for various daily needs. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: In a stunning display of unity and progress, vividly-hued hot air balloons rise against the backdrop of a clear Buffalo sky. The balloons gracefully float above the city, mirroring the residents' enthusiasm for this surreal experience. Meanwhile, in Peru, the scarcity of kerosene has led to a stark contrast; depict people relying on alternative methods for everyday tasks. The contrasting images convey a compelling narrative of environmental joy and hardship, merging them into a visually captivating cyber art composition.

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

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

AI academic paper

(Because p < 0.01)

Burning Bridges: The Fumes of Buffalo and the Glow of Peru

The Journal of Quirky Atmospheric Phenomena

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 Buffalo and Kerosene used in Peru. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then devolve ever further, and mention something completely ridiculous, like you conducted literature review by reading CVS receipts.

Here is the title and abstract of the paper:
[[TITLE]]
Burning Bridges: The Fumes of Buffalo and the Glow of Peru

[[ABSTRACT]]
In this paper, we delve into the surprising correlation between air pollution in Buffalo, New York, and the use of kerosene as a source of energy in Peru. While the connection may initially seem as improbable as finding a polar bear in the Sahara, our research uncovers a statistical relationship that is as strong as the aroma of freshly brewed coffee on a Monday morning. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, our findings reveal a notable correlation coefficient of 0.7872489 and p < 0.01 spanning the years 1980 to 2021.

Through our analysis, we aim to shed light on the often overlooked dynamics of air pollution and energy consumption on a global scale. While the link between Buffalo and Peru may seem tenuous, we argue that understanding these patterns can provide valuable insights into the interconnectedness of environmental factors across distant regions. By marrying rigorous statistical analysis with a sprinkle of whimsy, we hope to pave the way for further exploration of unforeseen connections in the realm of environmental research.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The quest for uncovering surprising connections in the world of science has often been likened to searching for a needle in a haystack, or perhaps more aptly, hunting for a statistically significant correlation in a sea of data. In this pursuit of scientific serendipity, our study sets its sights on the enigmatic relationship between air pollution in Buffalo, New York, and the utilization of kerosene as a primary energy source in the picturesque landscapes of Peru. While this coupling might seem as unlikely as stumbling upon a unicorn in a petting zoo, our investigation has unearthed a captivating correlation that rivals the drama of a reality TV show finale.
As we embark on this scholarly odyssey, it is essential to acknowledge that the amalgamation of seemingly disparate variables, much like trying to mix oil and water, often leads to skepticism among the scientific community. However, armed with a robust dataset from the Environmental Protection Agency and the Energy Information Administration, we aimed to tackle this conundrum head-on, with all the gusto of a caffeine-deprived researcher stumbling upon a bottomless pot of coffee.
The underlying motivation for this inquiry stems from the desire to parse through the intricate tapestry of global environmental interconnectedness. Just as the flutter of a butterfly's wings can trigger a typhoon on the other side of the world, we postulate that the interplay between air quality in upstate New York and the flickering glow of kerosene lamps in the villages of Peru may harbor profound implications for our understanding of cross-continental environmental dynamics.
With a nod to the gods of statistical significance, our analysis has unveiled a correlation coefficient of 0.7872489, a figure as robust as a sumo wrestler in an arm-wrestling contest, with a p-value of less than 0.01. This compelling statistic not only caught our attention like a magnet drawn to a particularly attractive refrigerator door but also fuelled our enthusiasm to delve deeper into the underlying mechanisms that underpin this unexpected relationship.
As we wade into the murky waters of empirical analysis, our commitment to blending rigorous methodology with a dash of levity mirrors the delicate balance of a scientist infusing statistical rigor with a sprinkle of humor – much like a carefully concocted laboratory experiment mixed with a pinch of spontaneous laughter. Accordingly, our study paves the way for an exploration of peculiar connections that may just unravel the mysteries of environmental interactions in novel and unforeseen ways.
In the subsequent sections of this paper, we will unravel the strands of this intriguing tapestry, unpacking the intricacies of air pollution in Buffalo and the utilization of kerosene in Peru, with the hope that this investigation will spark curiosity and perhaps a chuckle or two amidst the rigorous pursuit of scientific inquiry.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

Smith et al. (2018) conducted a comprehensive analysis of air pollution in urban settings, emphasizing the impact of industrial emissions and vehicular traffic on ambient air quality. Their findings underscore the intricate web of factors contributing to urban air pollution, which serves as a fundamental backdrop to our investigation. The relevance of their work is as undeniable as the appeal of a freshly baked batch of chocolate chip cookies – a universally recognized truth.

Moving beyond the realm of environmental science, Doe and Jones (2016) delved into the socioeconomic implications of energy usage in developing nations, shedding light on the reliance on traditional fuels such as kerosene in remote communities. Their insights provide a valuable framework for understanding the cultural and economic dimensions at play in our exploration of kerosene usage in Peru. The applicability of their research is as clear as a glass of pristine mountain spring water.

In a groundbreaking monograph, "The Air We Breathe: A Global Perspective" (Johnson, 2019), the author offers a panoramic view of air quality challenges across continents, from bustling metropolises to remote rural areas. While the book may not hold the key to eternal happiness, its comprehensive survey of air pollution dynamics lays the groundwork for contextualizing our specific focus on Buffalo.

Similarly, "Luminescent Nights: A Cultural History of Kerosene" (Garcia, 2017) provides an illuminating (pun intended) examination of the historical and cultural significance of kerosene as a source of illumination. While the relevance of this work may not be immediately apparent, its exploration of the romanticized imagery associated with kerosene lamps in literature and art serves to enrich our understanding of the cultural dimensions surrounding our study.

Venturing into the realm of fiction, "Smoke and Mirrors: A Tale of Two Cities" (Wilde, 1999) emerges as an unexpected source of inspiration, weaving a narrative tapestry that entwines the smoky atmospheres of urban settings with the mystical allure of distant lands. While fiction may seem like an unconventional source for scholarly inquiry, the evocative imagery presented in this work sparks a creative spark that resonates with our endeavor to unravel the enigmatic connection between Buffalo and Peru.

In a departure from conventional scholarly sources, the authors opted to peruse a diverse array of resources, including but not limited to, "The Complete Works of Shakespeare," "The Diary of a Wimpy Kid," and a collection of grocery lists and CVS receipts. While these unconventional sources may raise a skeptical eyebrow or two, their eclectic nature mirrors the unpredictable and serendipitous nature of scientific exploration.

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 Buffalo and Kerosene used in Peru. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Energy Information Administration . You used data from 1980 to 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]]
Burning Bridges: The Fumes of Buffalo and the Glow of Peru

[[ABSTRACT]]
In this paper, we delve into the surprising correlation between air pollution in Buffalo, New York, and the use of kerosene as a source of energy in Peru. While the connection may initially seem as improbable as finding a polar bear in the Sahara, our research uncovers a statistical relationship that is as strong as the aroma of freshly brewed coffee on a Monday morning. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, our findings reveal a notable correlation coefficient of 0.7872489 and p < 0.01 spanning the years 1980 to 2021.

Through our analysis, we aim to shed light on the often overlooked dynamics of air pollution and energy consumption on a global scale. While the link between Buffalo and Peru may seem tenuous, we argue that understanding these patterns can provide valuable insights into the interconnectedness of environmental factors across distant regions. By marrying rigorous statistical analysis with a sprinkle of whimsy, we hope to pave the way for further exploration of unforeseen connections in the realm of environmental research.

[[INTRODUCTION]]
The quest for uncovering surprising connections in the world of science has often been likened to searching for a needle in a haystack, or perhaps more aptly, hunting for a statistically significant correlation in a sea of data. In this pursuit of scientific serendipity, our study sets its sights on the enigmatic relationship between air pollution in Buffalo, New York, and the utilization of kerosene as a primary energy source in the picturesque landscapes of Peru. While this coupling might seem as unlikely as stumbling upon a unicorn in a petting zoo, our investigation has unearthed a captivating correlation that rivals the drama of a reality TV show finale.
As we embark on this scholarly odyssey, it is essential to acknowledge that the amalgamation of seemingly disparate variables, much like trying to mix oil and water, often leads to skepticism among the scientific community. However, armed with a robust dataset from the Environmental Protection Agency and the Energy Information Administration, we aimed to tackle this conundrum head-on, with all the gusto of a caffeine-deprived researcher stumbling upon a bottomless pot of coffee.
The underlying motivation for this inquiry stems from the desire to parse through the intricate tapestry of global environmental interconnectedness. Just as the flutter of a butterfly's wings can trigger a typhoon on the other side of the world, we postulate that the interplay between air quality in upstate New York and the flickering glow of kerosene lamps in the villages of Peru may harbor profound implications for our understanding of cross-continental environmental dynamics.
With a nod to the gods of statistical significance, our analysis has unveiled a correlation coefficient of 0.7872489, a figure as robust as a sumo wrestler in an arm-wrestling contest, with a p-value of less than 0.01. This compelling statistic not only caught our attention like a magnet drawn to a particularly attractive refrigerator door but also fuelled our enthusiasm to delve deeper into the underlying mechanisms that underpin this unexpected relationship.
As we wade into the murky waters of empirical analysis, our commitment to blending rigorous methodology with a dash of levity mirrors the delicate balance of a scientist infusing statistical rigor with a sprinkle of humor – much like a carefully concocted laboratory experiment mixed with a pinch of spontaneous laughter. Accordingly, our study paves the way for an exploration of peculiar connections that may just unravel the mysteries of environmental interactions in novel and unforeseen ways.
In the subsequent sections of this paper, we will unravel the strands of this intriguing tapestry, unpacking the intricacies of air pollution in Buffalo and the utilization of kerosene in Peru, with the hope that this investigation will spark curiosity and perhaps a chuckle or two amidst the rigorous pursuit of scientific inquiry.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

Our methodology was as carefully crafted as a delicate soufflé, incorporating a blend of rigorous statistical techniques and a touch of whimsy to illuminate the connection between air pollution in Buffalo and the utilization of kerosene in Peru. We embarked on this scholarly escapade armed with data spanning over four decades, meticulously collected from the Environmental Protection Agency and the Energy Information Administration, resembling digital treasure hunters scouring the depths of the internet.

To kickstart our analysis, we employed a robust time-series approach akin to a CSI investigator meticulously piecing together evidence, examining air pollution levels in Buffalo and kerosene usage in the Peruvian regions. Our dedicated team of researchers performed a proverbial scientific tango with the dataset, executing deft maneuvers to unravel the dance of these seemingly disparate variables.

A key component of our methodology involved the application of advanced statistical techniques, including but not limited to multivariate regression analysis and time-series modeling. Like master mixologists concocting the perfect cocktail, we skillfully blended these methods to discern the intricate relationship between air pollution in Buffalo and the use of kerosene in Peru. Through this analytical alchemy, we endeavored to extract meaningful insights, distilling the essence of these interconnected environmental factors.

Furthermore, we sought to mitigate potential confounding variables with the meticulousness of a cat groomer carefully untangling a feline's fur, ensuring that our analysis encapsulated the nuanced interplay between air pollution and kerosene use, akin to unraveling a complex detective novel where every clue is vital.

In addition to quantitative analyses, we also delved into qualitative research, conducting interviews with individuals from both locales to gain deeper insights into the cultural and societal factors influencing energy usage patterns. This qualitative foray allowed us to humanize the data, painting a vivid portrait of the individuals impacted by these environmental dynamics and injecting a dose of empathy into our analytical framework.

Finally, to ensure the robustness of our findings, we employed rigorous sensitivity analyses, akin to stress-testing a bridge to confirm its structural integrity. This meticulous scrutiny provided an added layer of confidence in the veracity of our results, offering a sturdy foundation upon which to build our case for the unexpected correlation between the fumes of Buffalo and the glow of Peru.

In the subsequent sections of this paper, we will unfurl the tapestry woven through our methodological approach, presenting the intricate steps taken to unearth the compelling connection between air pollution in Buffalo and the utilization of kerosene in Peru. With the precision of a virtuoso and the curiosity of an explorer, we invite readers to join us on this scholarly adventure, as we shed light on the surprising interplay of environmental factors across continents.

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

Please make up the results section of an academic research paper presenting the findings of the connection between Air pollution in Buffalo and Kerosene used in Peru. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Energy Information Administration .

For the time period 1980 to 2021, you found a correlation 0.7872489, r-squared of 0.6197608, and p < 0.01.

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

Here is the title and abstract of the paper:
[[TITLE]]
Burning Bridges: The Fumes of Buffalo and the Glow of Peru

[[ABSTRACT]]
In this paper, we delve into the surprising correlation between air pollution in Buffalo, New York, and the use of kerosene as a source of energy in Peru. While the connection may initially seem as improbable as finding a polar bear in the Sahara, our research uncovers a statistical relationship that is as strong as the aroma of freshly brewed coffee on a Monday morning. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, our findings reveal a notable correlation coefficient of 0.7872489 and p < 0.01 spanning the years 1980 to 2021.

Through our analysis, we aim to shed light on the often overlooked dynamics of air pollution and energy consumption on a global scale. While the link between Buffalo and Peru may seem tenuous, we argue that understanding these patterns can provide valuable insights into the interconnectedness of environmental factors across distant regions. By marrying rigorous statistical analysis with a sprinkle of whimsy, we hope to pave the way for further exploration of unforeseen connections in the realm of environmental research.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The quest for uncovering surprising connections in the world of science has often been likened to searching for a needle in a haystack, or perhaps more aptly, hunting for a statistically significant correlation in a sea of data. In this pursuit of scientific serendipity, our study sets its sights on the enigmatic relationship between air pollution in Buffalo, New York, and the utilization of kerosene as a primary energy source in the picturesque landscapes of Peru. While this coupling might seem as unlikely as stumbling upon a unicorn in a petting zoo, our investigation has unearthed a captivating correlation that rivals the drama of a reality TV show finale.
As we embark on this scholarly odyssey, it is essential to acknowledge that the amalgamation of seemingly disparate variables, much like trying to mix oil and water, often leads to skepticism among the scientific community. However, armed with a robust dataset from the Environmental Protection Agency and the Energy Information Administration, we aimed to tackle this conundrum head-on, with all the gusto of a caffeine-deprived researcher stumbling upon a bottomless pot of coffee.
The underlying motivation for this inquiry stems from the desire to parse through the intricate tapestry of global environmental interconnectedness. Just as the flutter of a butterfly's wings can trigger a typhoon on the other side of the world, we postulate that the interplay between air quality in upstate New York and the flickering glow of kerosene lamps in the villages of Peru may harbor profound implications for our understanding of cross-continental environmental dynamics.
With a nod to the gods of statistical significance, our analysis has unveiled a correlation coefficient of 0.7872489, a figure as robust as a sumo wrestler in an arm-wrestling contest, with a p-value of less than 0.01. This compelling statistic not only caught our attention like a magnet drawn to a particularly attractive refrigerator door but also fuelled our enthusiasm to delve deeper into the underlying mechanisms that underpin this unexpected relationship.
As we wade into the murky waters of empirical analysis, our commitment to blending rigorous methodology with a dash of levity mirrors the delicate balance of a scientist infusing statistical rigor with a sprinkle of humor – much like a carefully concocted laboratory experiment mixed with a pinch of spontaneous laughter. Accordingly, our study paves the way for an exploration of peculiar connections that may just unravel the mysteries of environmental interactions in novel and unforeseen ways.
In the subsequent sections of this paper, we will unravel the strands of this intriguing tapestry, unpacking the intricacies of air pollution in Buffalo and the utilization of kerosene in Peru, with the hope that this investigation will spark curiosity and perhaps a chuckle or two amidst the rigorous pursuit of scientific inquiry.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

Upon uncovering the statistical relationship between air pollution in Buffalo, New York, and the usage of kerosene in Peru, our research team was both intrigued and bemused by the strength of the correlation. The correlation coefficient of 0.7872489 suggests a robust association between the two variables, akin to finding a perfectly ripe avocado at the grocery store – a rare and delightful occurrence. The r-squared value of 0.6197608 further corroborates the substantial proportion of variance in air pollution in Buffalo that can be explained by the use of kerosene in Peru, as clear as a sunny day after a week of rain in Seattle.

Given the p-value of less than 0.01, we can confidently reject the null hypothesis and assert that the observed correlation is not just a fluke, but a genuine connection worthy of further investigation. This outcome is as significant as a groundbreaking new scientific discovery or securing the last slice of pizza at a crowded party – a triumph in the realm of statistical analysis.

In Figure 1, the scatterplot vividly illustrates the strong correlation between air pollution in Buffalo and kerosene usage in Peru. The data points seem to dance together in a harmonious choreography, reminiscent of a finely orchestrated ballet performance, showcasing the interconnectedness of environmental factors across geographical boundaries. It's as if the variables themselves are engaging in a lively tango, demonstrating the captivating nature of their relationship.

The remarkable strength of this correlation prompts us to ponder the potential mechanisms underlying this unexpected connection. Could the smog in Buffalo be sending secret smoke signals across continents, influencing the energy choices of households in the Peruvian highlands? Or perhaps it's merely a case of statistical whimsy, with the numbers aligning like stars in a serendipitous celestial display.

In any case, these findings add a colorful thread to the tapestry of environmental research, emphasizing the intricate and often surprising linkages among disparate elements in our global ecosystem. As we continue to unravel the mysteries of this correlation, we eagerly anticipate the insights and revelations that await, much like a scientist eagerly awaiting the results of an experiment, or a child eagerly anticipating the next punchline of a well-crafted joke.

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 Buffalo and Kerosene used in Peru. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, 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]]
Burning Bridges: The Fumes of Buffalo and the Glow of Peru

[[ABSTRACT]]
In this paper, we delve into the surprising correlation between air pollution in Buffalo, New York, and the use of kerosene as a source of energy in Peru. While the connection may initially seem as improbable as finding a polar bear in the Sahara, our research uncovers a statistical relationship that is as strong as the aroma of freshly brewed coffee on a Monday morning. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, our findings reveal a notable correlation coefficient of 0.7872489 and p < 0.01 spanning the years 1980 to 2021.

Through our analysis, we aim to shed light on the often overlooked dynamics of air pollution and energy consumption on a global scale. While the link between Buffalo and Peru may seem tenuous, we argue that understanding these patterns can provide valuable insights into the interconnectedness of environmental factors across distant regions. By marrying rigorous statistical analysis with a sprinkle of whimsy, we hope to pave the way for further exploration of unforeseen connections in the realm of environmental research.

[[LITERATURE REVIEW]]
Smith et al. (2018) conducted a comprehensive analysis of air pollution in urban settings, emphasizing the impact of industrial emissions and vehicular traffic on ambient air quality. Their findings underscore the intricate web of factors contributing to urban air pollution, which serves as a fundamental backdrop to our investigation. The relevance of their work is as undeniable as the appeal of a freshly baked batch of chocolate chip cookies – a universally recognized truth.
Moving beyond the realm of environmental science, Doe and Jones (2016) delved into the socioeconomic implications of energy usage in developing nations, shedding light on the reliance on traditional fuels such as kerosene in remote communities. Their insights provide a valuable framework for understanding the cultural and economic dimensions at play in our exploration of kerosene usage in Peru. The applicability of their research is as clear as a glass of pristine mountain spring water.
In a groundbreaking monograph, "The Air We Breathe: A Global Perspective" (Johnson, 2019), the author offers a panoramic view of air quality challenges across continents, from bustling metropolises to remote rural areas. While the book may not hold the key to eternal happiness, its comprehensive survey of air pollution dynamics lays the groundwork for contextualizing our specific focus on Buffalo.
Similarly, "Luminescent Nights: A Cultural History of Kerosene" (Garcia, 2017) provides an illuminating (pun intended) examination of the historical and cultural significance of kerosene as a source of illumination. While the relevance of this work may not be immediately apparent, its exploration of the romanticized imagery associated with kerosene lamps in literature and art serves to enrich our understanding of the cultural dimensions surrounding our study.
Venturing into the realm of fiction, "Smoke and Mirrors: A Tale of Two Cities" (Wilde, 1999) emerges as an unexpected source of inspiration, weaving a narrative tapestry that entwines the smoky atmospheres of urban settings with the mystical allure of distant lands. While fiction may seem like an unconventional source for scholarly inquiry, the evocative imagery presented in this work sparks a creative spark that resonates with our endeavor to unravel the enigmatic connection between Buffalo and Peru.
In a departure from conventional scholarly sources, the authors opted to peruse a diverse array of resources, including but not limited to, "The Complete Works of Shakespeare," "The Diary of a Wimpy Kid," and a collection of grocery lists and CVS receipts. While these unconventional sources may raise a skeptical eyebrow or two, their eclectic nature mirrors the unpredictable and serendipitous nature of scientific exploration.

[[RESULTS]]
Upon uncovering the statistical relationship between air pollution in Buffalo, New York, and the usage of kerosene in Peru, our research team was both intrigued and bemused by the strength of the correlation. The correlation coefficient of 0.7872489 suggests a robust association between the two variables, akin to finding a perfectly ripe avocado at the grocery store – a rare and delightful occurrence. The r-squared value of 0.6197608 further corroborates the substantial proportion of variance in air pollution in Buffalo that can be explained by the use of kerosene in Peru, as clear as a sunny day after a week of rain in Seattle.
Given the p-value of less than 0.01, we can confidently reject the null hypothesis and assert that the observed correlation is not just a fluke, but a genuine connection worthy of further investigation. This outcome is as significant as a groundbreaking new scientific discovery or securing the last slice of pizza at a crowded party – a triumph in the realm of statistical analysis.
In Figure 1, the scatterplot vividly illustrates the strong correlation between air pollution in Buffalo and kerosene usage in Peru. The data points seem to dance together in a harmonious choreography, reminiscent of a finely orchestrated ballet performance, showcasing the interconnectedness of environmental factors across geographical boundaries. It's as if the variables themselves are engaging in a lively tango, demonstrating the captivating nature of their relationship.
The remarkable strength of this correlation prompts us to ponder the potential mechanisms underlying this unexpected connection. Could the smog in Buffalo be sending secret smoke signals across continents, influencing the energy choices of households in the Peruvian highlands? Or perhaps it's merely a case of statistical whimsy, with the numbers aligning like stars in a serendipitous celestial display.
In any case, these findings add a colorful thread to the tapestry of environmental research, emphasizing the intricate and often surprising linkages among disparate elements in our global ecosystem. As we continue to unravel the mysteries of this correlation, we eagerly anticipate the insights and revelations that await, much like a scientist eagerly awaiting the results of an experiment, or a child eagerly anticipating the next punchline of a well-crafted joke.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The relationship between air pollution in Buffalo and kerosene usage in Peru has sparked both fascination and amusement among our research team. While the initial connection between these seemingly disparate variables might raise eyebrows, our findings support and even amplify the peculiar insights gleaned from previous literature. The correlation coefficient of 0.7872489, akin to discovering a hidden treasure trove of data, provides robust evidence for a substantial association that echoes the sentiments expressed in the works of Smith et al. (2018) and Doe and Jones (2016).

The strength of this correlation, as vividly portrayed in the scatterplot, speaks volumes about the interconnectedness of environmental factors – a realization that may have eluded even the most astute observers. This unexpected kinship between air pollution in Buffalo and kerosene usage in Peru has implications as far-reaching as the tendrils of a vine, intertwining and binding these variables in a dance as mesmerizing as it is confounding.

Furthermore, the p-value of less than 0.01 allows us to confidently dismiss chance as the orchestrator of this intricate relationship. This statistical triumph echoes the sentiment expressed in "The Diary of a Wimpy Kid" – sometimes, mysteries unfold in the most unexpected places. Just as the enigmatic nature of the relationship seemed to permeate even our whimsical sources of inquiry, the statistical significance of the observed correlation leaves no room for doubt.

As we grapple with the dizzying implications of the Buffalo-Peru nexus, we are reminded of the unpredictability and serendipity that often underpin scientific inquiry. Much like characters in a Shakespearian play, our variables have embarked on a dramatic, albeit unconventional, journey of discovery. The fusion of statistical rigor and unexpected whimsy exemplifies the remarkable potential of interdisciplinary inquiry – a union as harmonious as Beethoven's Symphony No. 9.

In light of these revelatory findings, we are left with a tantalizing quandary: what cosmic forces may have conspired to align the trajectories of air pollution in Buffalo and kerosene usage in Peru? While we resist the urge to indulge in flights of fancy, the captivating allure of this correlation invites speculation worthy of a detective novel. As we tread further into the uncharted territories of this confounding relationship, we eagerly anticipate the unfolding of new chapters in this environmental enigma – a narrative as captivating as it is unexpected.

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 Buffalo and Kerosene used in Peru. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, 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]]
Burning Bridges: The Fumes of Buffalo and the Glow of Peru

[[ABSTRACT]]
In this paper, we delve into the surprising correlation between air pollution in Buffalo, New York, and the use of kerosene as a source of energy in Peru. While the connection may initially seem as improbable as finding a polar bear in the Sahara, our research uncovers a statistical relationship that is as strong as the aroma of freshly brewed coffee on a Monday morning. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, our findings reveal a notable correlation coefficient of 0.7872489 and p < 0.01 spanning the years 1980 to 2021.

Through our analysis, we aim to shed light on the often overlooked dynamics of air pollution and energy consumption on a global scale. While the link between Buffalo and Peru may seem tenuous, we argue that understanding these patterns can provide valuable insights into the interconnectedness of environmental factors across distant regions. By marrying rigorous statistical analysis with a sprinkle of whimsy, we hope to pave the way for further exploration of unforeseen connections in the realm of environmental research.

[[INTRDUCTION]]
The quest for uncovering surprising connections in the world of science has often been likened to searching for a needle in a haystack, or perhaps more aptly, hunting for a statistically significant correlation in a sea of data. In this pursuit of scientific serendipity, our study sets its sights on the enigmatic relationship between air pollution in Buffalo, New York, and the utilization of kerosene as a primary energy source in the picturesque landscapes of Peru. While this coupling might seem as unlikely as stumbling upon a unicorn in a petting zoo, our investigation has unearthed a captivating correlation that rivals the drama of a reality TV show finale.
As we embark on this scholarly odyssey, it is essential to acknowledge that the amalgamation of seemingly disparate variables, much like trying to mix oil and water, often leads to skepticism among the scientific community. However, armed with a robust dataset from the Environmental Protection Agency and the Energy Information Administration, we aimed to tackle this conundrum head-on, with all the gusto of a caffeine-deprived researcher stumbling upon a bottomless pot of coffee.
The underlying motivation for this inquiry stems from the desire to parse through the intricate tapestry of global environmental interconnectedness. Just as the flutter of a butterfly's wings can trigger a typhoon on the other side of the world, we postulate that the interplay between air quality in upstate New York and the flickering glow of kerosene lamps in the villages of Peru may harbor profound implications for our understanding of cross-continental environmental dynamics.
With a nod to the gods of statistical significance, our analysis has unveiled a correlation coefficient of 0.7872489, a figure as robust as a sumo wrestler in an arm-wrestling contest, with a p-value of less than 0.01. This compelling statistic not only caught our attention like a magnet drawn to a particularly attractive refrigerator door but also fuelled our enthusiasm to delve deeper into the underlying mechanisms that underpin this unexpected relationship.
As we wade into the murky waters of empirical analysis, our commitment to blending rigorous methodology with a dash of levity mirrors the delicate balance of a scientist infusing statistical rigor with a sprinkle of humor – much like a carefully concocted laboratory experiment mixed with a pinch of spontaneous laughter. Accordingly, our study paves the way for an exploration of peculiar connections that may just unravel the mysteries of environmental interactions in novel and unforeseen ways.
In the subsequent sections of this paper, we will unravel the strands of this intriguing tapestry, unpacking the intricacies of air pollution in Buffalo and the utilization of kerosene in Peru, with the hope that this investigation will spark curiosity and perhaps a chuckle or two amidst the rigorous pursuit of scientific inquiry.

[[RESULTS]]
Upon uncovering the statistical relationship between air pollution in Buffalo, New York, and the usage of kerosene in Peru, our research team was both intrigued and bemused by the strength of the correlation. The correlation coefficient of 0.7872489 suggests a robust association between the two variables, akin to finding a perfectly ripe avocado at the grocery store – a rare and delightful occurrence. The r-squared value of 0.6197608 further corroborates the substantial proportion of variance in air pollution in Buffalo that can be explained by the use of kerosene in Peru, as clear as a sunny day after a week of rain in Seattle.
Given the p-value of less than 0.01, we can confidently reject the null hypothesis and assert that the observed correlation is not just a fluke, but a genuine connection worthy of further investigation. This outcome is as significant as a groundbreaking new scientific discovery or securing the last slice of pizza at a crowded party – a triumph in the realm of statistical analysis.
In Figure 1, the scatterplot vividly illustrates the strong correlation between air pollution in Buffalo and kerosene usage in Peru. The data points seem to dance together in a harmonious choreography, reminiscent of a finely orchestrated ballet performance, showcasing the interconnectedness of environmental factors across geographical boundaries. It's as if the variables themselves are engaging in a lively tango, demonstrating the captivating nature of their relationship.
The remarkable strength of this correlation prompts us to ponder the potential mechanisms underlying this unexpected connection. Could the smog in Buffalo be sending secret smoke signals across continents, influencing the energy choices of households in the Peruvian highlands? Or perhaps it's merely a case of statistical whimsy, with the numbers aligning like stars in a serendipitous celestial display.
In any case, these findings add a colorful thread to the tapestry of environmental research, emphasizing the intricate and often surprising linkages among disparate elements in our global ecosystem. As we continue to unravel the mysteries of this correlation, we eagerly anticipate the insights and revelations that await, much like a scientist eagerly awaiting the results of an experiment, or a child eagerly anticipating the next punchline of a well-crafted joke.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our investigation has unraveled a compelling correlation between air pollution in Buffalo and kerosene usage in Peru, painting a picture as vivid and intriguing as a Jackson Pollock masterpiece. The robust correlation coefficient and r-squared value have illuminated this unexpected relationship, akin to stumbling upon a hidden treasure chest in a research expedition.

As we reflect on the whimsical dance of variables in our statistical tango, it is clear that this unexpected connection between distant locales holds significant implications for understanding global environmental dynamics. This correlation, stronger than the gravitational pull of a black hole, underscores the interconnectedness of environmental factors in geographically distant regions and prompts contemplation of the unseen forces at play.

The scatterplot, akin to a visual symphony, has visually encapsulated the intertwined nature of air pollution in Buffalo and kerosene usage in Peru, leaving us pondering the potential mechanisms at work with a sense of scientific whimsy. These findings, as captivating as a magician's sleight of hand, add a delightful twist to the fabric of environmental research, offering a window into the unexpected interconnectedness of seemingly unrelated variables.

In consideration of these compelling results, we assert with a tongue-in-cheek confidence that further research in this realm would be akin to reinventing the wheel - unnecessary and potentially more whimsical than substantive. Our study serves as a lighthearted yet rigorous exploration of the unexpected correlations that permeate the scientific landscape, leaving us with a newfound appreciation for the whimsy of statistical analysis and the unforeseen connections that await discovery in the vast world of environmental research. It is time to let this amusing correlation rest in peace, much like a well-executed pun that should not be overexplained.

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 Burning Bridges: The Fumes of Buffalo and the Glow of Peru. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Quirky Atmospheric Phenomena

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 Burning Bridges: The Fumes of Buffalo and the Glow of Peru. Respond only with the name of a fictional organization.

ChatGPT:

The International Society for Comparative Pyrotechnics and Atmospheric Phenomena

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 Burning Bridges: The Fumes of Buffalo and the Glow of Peru with an abstract of In this paper, we delve into the surprising correlation between air pollution in Buffalo, New York, and the use of kerosene as a source of energy in Peru. While the connection may initially seem as improbable as finding a polar bear in the Sahara, our research uncovers a statistical relationship that is as strong as the aroma of freshly brewed coffee on a Monday morning. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, our findings reveal a notable correlation coefficient of 0.7872489 and p < 0.01 spanning the years 1980 to 2021.
Through our analysis, we aim to shed light on the often overlooked dynamics of air pollution and energy consumption on a global scale. While the link between Buffalo and Peru may seem tenuous, we argue that understanding these patterns can provide valuable insights into the interconnectedness of environmental factors across distant regions. By marrying rigorous statistical analysis with a sprinkle of whimsy, we hope to pave the way for further exploration of unforeseen connections in the realm of environmental research.

ChatGPT:

air pollution, Buffalo New York, kerosene energy, Peru, correlation, statistical relationship, Environmental Protection Agency, Energy Information Administration, correlation coefficient, global air pollution, energy consumption, environmental factors, statistical analysis

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

Kerosene used in Peru
Detailed data title: Volume of kerosene used consumed in Peru in millions of barrels per day
Source: Energy Information Administration
See what else correlates with Kerosene used in Peru

Correlation r = 0.7872489 (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 = 0.6197608 (Coefficient of determination)
This means 62% of the change in the one variable (i.e., Kerosene used in Peru) is predictable based on the change in the other (i.e., Air pollution in Buffalo) over the 42 years from 1980 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 6.3E-10.^Show 0.0000000006267356533750374000
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 0.79 in 6.3E-8% of random cases. Said differently, if you correlated 1,595,569,032 random variables^Note You don't actually need 1 billion variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

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

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

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 41 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 41 because we have two variables measured over a period of 42 years. It's just the number of years minus ( the number of variables minus one ), which in this case simplifies to the number of years minus one.
you would randomly expect to find a correlation as strong as this one.

[ 0.64, 0.88 ] 95% correlation confidence interval (using the Fisher z-transformation)
^{Read more about the confidence interval} The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

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

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

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

	1980	1981	1982	1983	1984	1985	1986	1987	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021
Air pollution in Buffalo (Bad air quality days)	10.929	10.411	8.76712	10.411	8.74317	9.31507	9.31507	12.3288	12.8415	7.94521	6.30137	8.49315	3.27869	4.10959	6.0274	4.93151	3.55191	2.73973	9.86301	10.411	3.00546	8.76712	11.5068	5.20548	4.91803	10.411	4.10959	9.31507	2.73224	0.821918	2.46575	1.91781	3.82514	1.09589	0.273973	1.09589	1.63934	0.273973	0.821918	0	0.546448	0.547945
Kerosene used in Peru (Million Barrels/Day)	18.6082	19.1679	19.028	17.349	17.7688	17.489	19	22	22	18	16	15	6.9	15	13	14	14	14	14	14	14.0449	14.8882	14.9517	10.8008	6.84295	4.42622	1.77896	1.16479	0.97153	1.52482	1.41893	1.39775	1.03489	1.14362	1.24951	1	1	0.782137	0.412795	0.0651781	0.0434521	0.0434521

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([10.929,10.411,8.76712,10.411,8.74317,9.31507,9.31507,12.3288,12.8415,7.94521,6.30137,8.49315,3.27869,4.10959,6.0274,4.93151,3.55191,2.73973,9.86301,10.411,3.00546,8.76712,11.5068,5.20548,4.91803,10.411,4.10959,9.31507,2.73224,0.821918,2.46575,1.91781,3.82514,1.09589,0.273973,1.09589,1.63934,0.273973,0.821918,0,0.546448,0.547945,])
array_2 = np.array([18.6082,19.1679,19.028,17.349,17.7688,17.489,19,22,22,18,16,15,6.9,15,13,14,14,14,14,14,14.0449,14.8882,14.9517,10.8008,6.84295,4.42622,1.77896,1.16479,0.97153,1.52482,1.41893,1.39775,1.03489,1.14362,1.24951,1,1,0.782137,0.412795,0.0651781,0.0434521,0.0434521,])
array_1_name = "Air pollution in Buffalo"
array_2_name = "Kerosene used in Peru"

# 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 Buffalo
Line chart for only Kerosene used in Peru
AI-generated correlation image
The spurious research paper: Burning Bridges: The Fumes of Buffalo and the Glow of Peru

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Correlation ID: 2703 · Black Variable ID: 20391 · Red Variable ID: 24811


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