Spurious correlation #1,979 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air quality in Phoenix and the second variable is Kerosene used in Cuba. 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 quality in Phoenix and the second variable is Kerosene used in Cuba. The chart goes from 1980 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As the air quality in Phoenix decreased, it led to an updraft of sorts, which inadvertently carried away some of the kerosene molecules destined for Cuba. This caused a shortage, leaving the Cubans feeling a bit burned out. It's a case of pollution leading to a defuelopment in another country! But don't worry, they'll just have to wait for the winds of change to bring in a fresher supply.

^{Show image generation prompt} Model: dalle-3
Prompt: Create an image of a scene where the vibrant blue sky of Phoenix merges with the warm evening in Cuba. Show the contrast between the clear, crisp atmosphere of Phoenix with the cozy, intimate ambiance of the Cuban gathering. Bring out the angular and fragmented forms in the Cubist style, reflecting the two distinct environments coming together in a harmonious composition. Capture the pine trees and the kerosene lamp as central elements, emphasizing their individual characteristics while blending them into a single cohesive image. 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: Good air quality in Phoenix and Kerosene used in Cuba. 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: inspired by bauhaus Cubism Data cyber art Low poly Oragami
ChatGPT: Cubism

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 Good air quality in Phoenix and Kerosene used in Cuba together. Keep the description simple.
ChatGPT: In Phoenix, the sky is a clear, vibrant blue, and the air is filled with the crisp scent of pine trees. Meanwhile, in Cuba, people gather around a small kerosene lamp, its light illuminating their smiling faces as they relax on a warm evening.

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: [ Cubism ] and depicting this scene: In Phoenix, the sky is a clear, vibrant blue, and the air is filled with the crisp scent of pine trees. Meanwhile, in Cuba, people gather around a small kerosene lamp, its light illuminating their smiling faces as they relax on a warm evening. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Create an image of a scene where the vibrant blue sky of Phoenix merges with the warm evening in Cuba. Show the contrast between the clear, crisp atmosphere of Phoenix with the cozy, intimate ambiance of the Cuban gathering. Bring out the angular and fragmented forms in the Cubist style, reflecting the two distinct environments coming together in a harmonious composition. Capture the pine trees and the kerosene lamp as central elements, emphasizing their individual characteristics while blending them into a single cohesive image.

*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 quality in Phoenix caused Kerosene used in Cuba to decrease. Include one good pun.

AI academic paper

(Because p < 0.01)

Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba

The Journal of Atmospheric Dynamics and International Energy Markets

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 quality in Phoenix and Kerosene used in Cuba. 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 the backs of shampoo bottles.

Here is the title and abstract of the paper:
[[TITLE]]
Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba

[[ABSTRACT]]
In this study, we analyze the curious relationship between air quality in Phoenix, Arizona, and kerosene consumption in Cuba. While the connection between these two seemingly disparate factors may appear as nebulous as smog on a hazy day, our findings unveil a striking correlation. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, we meticulously sifted through decades of records to unearth this unexpected association.

Employing robust statistical methods, our research team identified a correlation coefficient of 0.7582886 and a p-value less than 0.01 for the period spanning 1980 to 2021. These results cast a revealing light on the intertwining dynamics of air quality in Phoenix and kerosene usage in Cuba. Surprisingly, the data suggests that the winds of change may blow far beyond traditional boundaries, carrying the impact of kerosene consumption across the seas to the deserts of the American Southwest.

As we delve deeper into this enigmatic connection, we unravel the intricate interplay of atmospheric currents and energy consumption patterns, shedding light on a complex, global tapestry. Our findings urge policymakers to consider the far-reaching implications of seemingly distant phenomena and to "fuel" discussions about collaborative efforts for environmental stewardship.

So, let us embark on this illuminating journey, exploring the "combustible" relationship between air quality in Phoenix and kerosene use in Cuba, and unveiling the interconnectedness of our planet's environmental dynamics.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
INTRODUCTION
The pursuit of knowledge has long been an illuminating journey, much like trying to find the light switch in a dark room – sometimes enlightening, often stumbled upon, and occasionally leaving one feeling utterly bemused. In this vein, our exploration of the curious relationship between air quality in Phoenix and kerosene consumption in Cuba represents a blending of scientific inquiry and stumbling upon sparks of unexpected insights. The endeavor is akin to grasping at the wisps of a gentle breeze intermingled with the pungent aroma of a neighbor's barbecue, leaving us pondering the whiffs and whiffs of correlations that may betray something significant amidst the haze.
It is a classic tale of tackling the seemingly unrelated with the fervor of a detective hot on the trail, piecing together an investigative puzzle with the gusto of a physicist seeking to crack the code of the universe. On the surface, one might assume that air quality in Phoenix and kerosene consumption in Cuba are as connected as a fish is to a bicycle – an apocryphal, incongruous affair. Nonetheless, as our research unravels, we find ourselves standing at the crossroads of climatic intricacies and energy consumption quirkiness, pondering the intercontinental reach of environmental influences.
Our study stands as a testament to the marriage of disciplines – a rendezvous between the atmospheric sciences and the fine art of energy accounting, much like a delightful fusion dish concocted from the most unlikely of ingredients. In this endeavor, we invoke the spirits of statistical rigor and scientific curiosity, endeavoring to cast a light on the shadows of correlation and causation, as if we were to wave a scientific torch through the murk and mire of nebulous associations.
As we embark on this expedition into the realm of empirical observation and robust data analysis, we aim not only to decipher the twists and turns of this unexpected dance between air quality in Phoenix and kerosene usage in Cuba, but also to stir the pot of contemplation on the interconnectedness of our planet's environmental dynamics. So, join us in this enlightening pursuit, where we untangle the web of relationships with the fervor of a scientist on the cusp of a groundbreaking discovery, and reveal the intriguing ties that bind atmospheric currents and energy consumption patterns across oceans and continents.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The connection between air quality and various environmental and human activities provides a rich tapestry of research, combining the fields of atmospheric science, environmental economics, and international relations. At the crux of our investigation into the correlation between air quality in Phoenix and kerosene consumption in Cuba lies a web of diverse studies, shedding light on the complex interplay of climatic factors and energy usage patterns. Our review encompasses a range of scholarly works and authoritative sources, beginning with the seminal studies by Smith, Doe, and Jones, and extending into literary works that delve into the nuances of environmental influences and cross-continental dynamics.

In "Atmospheric Dynamics and Urban Air Quality," Smith et al. navigate the convoluted patterns of air pollutant dispersion in urban settings, drawing attention to the manifold factors that contribute to the concentration of pollutants in metropolitan areas. Their findings serve as an invaluable backdrop to our exploration of the atmospheric intricacies within the context of Phoenix, Arizona, where the intermingling of industrial emissions and vehicular activity paints a portrait of atmospheric flux.

Doe's comprehensive analysis in "Energy Consumption Patterns and Socioeconomic Drivers" delves into the intricacies of energy usage across diverse socioeconomic strata, offering a lens through which we examine the patterns of kerosene consumption in Cuba. The intercontinental reach of energy dynamics is brought to the forefront, as we navigate the potential ripples of kerosene usage in Cuba on the atmospheric conditions of the American Southwest.

In juxtaposition to these scholarly works, non-fiction literature such as "The Global Impact of Energy Consumption" by Environmental Economist Jane Smith and "Cuban Energy Quandary: From Past to Present" by Energy Policy Analyst John Doe provides a multidimensional perspective on the complex interactions between global energy dynamics and environmental repercussions.

Venturing into the realm of fiction, works such as "The Wind Whisperers" by A. B. Cloudsworth and "Kerosene Dreams" by Luminous Jones offer glimpses into the poetic interweaving of atmospheric currents and energy symbolism, beckoning us to consider the abstract connections between seemingly distant phenomena.

Diverging from the typical sources, our literature review encompasses an eclectic mix of findings that extend beyond traditional research boundaries. Brief yet insightful glances at the backs of household products such as shampoo bottles, which often tout environmentally friendly formulas, reveal the ubiquitous nature of environmental discourse, albeit in the most peculiar of places.

As we progress through this literary odyssey, we pivot towards the empirical milieu of our investigation, where we seek to illuminate the threads that tether air quality in Phoenix to the flickering flames of kerosene usage in Cuba, in all their intricate and unforeseen splendor.

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 quality in Phoenix and Kerosene used in Cuba. 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]]
Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba

[[ABSTRACT]]
In this study, we analyze the curious relationship between air quality in Phoenix, Arizona, and kerosene consumption in Cuba. While the connection between these two seemingly disparate factors may appear as nebulous as smog on a hazy day, our findings unveil a striking correlation. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, we meticulously sifted through decades of records to unearth this unexpected association.

Employing robust statistical methods, our research team identified a correlation coefficient of 0.7582886 and a p-value less than 0.01 for the period spanning 1980 to 2021. These results cast a revealing light on the intertwining dynamics of air quality in Phoenix and kerosene usage in Cuba. Surprisingly, the data suggests that the winds of change may blow far beyond traditional boundaries, carrying the impact of kerosene consumption across the seas to the deserts of the American Southwest.

As we delve deeper into this enigmatic connection, we unravel the intricate interplay of atmospheric currents and energy consumption patterns, shedding light on a complex, global tapestry. Our findings urge policymakers to consider the far-reaching implications of seemingly distant phenomena and to "fuel" discussions about collaborative efforts for environmental stewardship.

So, let us embark on this illuminating journey, exploring the "combustible" relationship between air quality in Phoenix and kerosene use in Cuba, and unveiling the interconnectedness of our planet's environmental dynamics.

[[INTRODUCTION]]
INTRODUCTION
The pursuit of knowledge has long been an illuminating journey, much like trying to find the light switch in a dark room – sometimes enlightening, often stumbled upon, and occasionally leaving one feeling utterly bemused. In this vein, our exploration of the curious relationship between air quality in Phoenix and kerosene consumption in Cuba represents a blending of scientific inquiry and stumbling upon sparks of unexpected insights. The endeavor is akin to grasping at the wisps of a gentle breeze intermingled with the pungent aroma of a neighbor's barbecue, leaving us pondering the whiffs and whiffs of correlations that may betray something significant amidst the haze.
It is a classic tale of tackling the seemingly unrelated with the fervor of a detective hot on the trail, piecing together an investigative puzzle with the gusto of a physicist seeking to crack the code of the universe. On the surface, one might assume that air quality in Phoenix and kerosene consumption in Cuba are as connected as a fish is to a bicycle – an apocryphal, incongruous affair. Nonetheless, as our research unravels, we find ourselves standing at the crossroads of climatic intricacies and energy consumption quirkiness, pondering the intercontinental reach of environmental influences.
Our study stands as a testament to the marriage of disciplines – a rendezvous between the atmospheric sciences and the fine art of energy accounting, much like a delightful fusion dish concocted from the most unlikely of ingredients. In this endeavor, we invoke the spirits of statistical rigor and scientific curiosity, endeavoring to cast a light on the shadows of correlation and causation, as if we were to wave a scientific torch through the murk and mire of nebulous associations.
As we embark on this expedition into the realm of empirical observation and robust data analysis, we aim not only to decipher the twists and turns of this unexpected dance between air quality in Phoenix and kerosene usage in Cuba, but also to stir the pot of contemplation on the interconnectedness of our planet's environmental dynamics. So, join us in this enlightening pursuit, where we untangle the web of relationships with the fervor of a scientist on the cusp of a groundbreaking discovery, and reveal the intriguing ties that bind atmospheric currents and energy consumption patterns across oceans and continents.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

Data Collection and Compilation:
The data collection process set sail on the tempestuous seas of the internet, navigating through the digital waves like a trusty ship in search of treasure. Our intrepid crew scoured the Environmental Protection Agency and the Energy Information Administration's databases, casting digital nets to haul in the abundant fish of environmental and energy consumption data. We feathered through the years from 1980 to 2021, like a flock of data-hungry seagulls, capturing every morsel of information related to air quality in Phoenix and kerosene consumption in Cuba.

Upon reeling in this digital bounty, we undertook the meticulous task of pruning and grooming the data, much like taming a wild, overgrown hedge into a well-manicured topiary. We removed any outliers that threatened to steer our ship into treacherous waters, ensuring that our dataset remained as sturdy and seaworthy as the most reliable vessel in a storm.

Quantitative Analysis:
Our stat-mongering wizardry involved a blend of classic correlation analysis and time series modeling, akin to casting ancient runes to interpret the cosmic dance of variables. We calculated correlation coefficients with the precision of a heart surgeon, teasing out the hidden connections between air quality in Phoenix and kerosene usage in Cuba. This process allowed our research team to measure the strength and direction of the relationship, akin to gauging the tension between two characters in a high-stakes drama.

To further deepen our understanding, we employed time series models, gazing into the crystal ball of statistical forecasting with a mixture of awe and skepticism. These models, like a pack of precocious fortune-tellers, projected the trends and patterns in air quality and kerosene consumption over time, unraveling the enigmatic dance of the variables with the flair of a clairvoyant at a Renaissance fair.

After donning our lab coats of inquiry and dusting off our trusty calculators, we conducted hypothesis tests to assess the significance of our findings, akin to launching a probe into the scientific unknown. The p-values and confidence intervals served as our treasure map, guiding us through the statistical labyrinth to ascertain the credibility and reliability of our discovered connections.

Control Variables and Sensitivity Analysis:
Like cautious gardeners carefully adjusting the levels of sunlight and water for delicate blooms, we considered the potential influence of external factors on our findings. Controlling for variables such as population density, economic activity, and meteorological conditions, we conducted sensitivity analyses to ensure the robustness of our results. This process safeguarded against potential confounding influences that could cast shade on the clarity of our findings, akin to shielding a fragile sapling from the gusts of a statistical storm.

In tandem, we harnessed the power of subgroup analyses to delve into the nuances of the relationship between air quality in Phoenix and kerosene consumption in Cuba across different time periods and demographic characteristics. This endeavor enabled us to unearth potential variations in the association, akin to examining the different flavors and aromas of a fine wine from various vintages.

Econometric Modeling:
To untangle the intricate web of relationships, we embarked on the high seas of econometric modeling, navigating the choppy waters of energy consumption and environmental impact with the precision of a seasoned navigator. We employed multivariate regression models, much like orchestrating a symphony of variables, to disentangle the nuanced melodies of air quality and kerosene consumption. Through this approach, we endeavored to parse out the individual contributions of various factors, akin to discerning the distinctive notes in a complex musical composition.

Our foray into the realms of econometrics also involved grapple with instrumental variable estimation, employing cunning strategies to address potential endogeneity and lurking sources of bias in our analyses. This meticulous dance with instrumental variables allowed us to navigate the treacherous shoals of statistical inference, positioning us to uncover the true nature of the relationship between air quality in Phoenix and kerosene usage in Cuba with the finesse of a forensic detective solving a cryptic case.

In summary, our methodology reflects the synthesis of scientific rigor and scientific curiosity, a journey into the heart of statistical inquiry and empirical observation. With the wind of statistical significance at our backs, we set sail on this scientific odyssey to unravel the webs of correlation and causation, shedding light on the intertwined dynamics of air quality in Phoenix and kerosene consumption in Cuba with the fervor of a treasure-hunting buccaneer.

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 quality in Phoenix and Kerosene used in Cuba. 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 0.7582886, r-squared of 0.5750015, 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]]
Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba

[[ABSTRACT]]
In this study, we analyze the curious relationship between air quality in Phoenix, Arizona, and kerosene consumption in Cuba. While the connection between these two seemingly disparate factors may appear as nebulous as smog on a hazy day, our findings unveil a striking correlation. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, we meticulously sifted through decades of records to unearth this unexpected association.

Employing robust statistical methods, our research team identified a correlation coefficient of 0.7582886 and a p-value less than 0.01 for the period spanning 1980 to 2021. These results cast a revealing light on the intertwining dynamics of air quality in Phoenix and kerosene usage in Cuba. Surprisingly, the data suggests that the winds of change may blow far beyond traditional boundaries, carrying the impact of kerosene consumption across the seas to the deserts of the American Southwest.

As we delve deeper into this enigmatic connection, we unravel the intricate interplay of atmospheric currents and energy consumption patterns, shedding light on a complex, global tapestry. Our findings urge policymakers to consider the far-reaching implications of seemingly distant phenomena and to "fuel" discussions about collaborative efforts for environmental stewardship.

So, let us embark on this illuminating journey, exploring the "combustible" relationship between air quality in Phoenix and kerosene use in Cuba, and unveiling the interconnectedness of our planet's environmental dynamics.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
INTRODUCTION
The pursuit of knowledge has long been an illuminating journey, much like trying to find the light switch in a dark room – sometimes enlightening, often stumbled upon, and occasionally leaving one feeling utterly bemused. In this vein, our exploration of the curious relationship between air quality in Phoenix and kerosene consumption in Cuba represents a blending of scientific inquiry and stumbling upon sparks of unexpected insights. The endeavor is akin to grasping at the wisps of a gentle breeze intermingled with the pungent aroma of a neighbor's barbecue, leaving us pondering the whiffs and whiffs of correlations that may betray something significant amidst the haze.
It is a classic tale of tackling the seemingly unrelated with the fervor of a detective hot on the trail, piecing together an investigative puzzle with the gusto of a physicist seeking to crack the code of the universe. On the surface, one might assume that air quality in Phoenix and kerosene consumption in Cuba are as connected as a fish is to a bicycle – an apocryphal, incongruous affair. Nonetheless, as our research unravels, we find ourselves standing at the crossroads of climatic intricacies and energy consumption quirkiness, pondering the intercontinental reach of environmental influences.
Our study stands as a testament to the marriage of disciplines – a rendezvous between the atmospheric sciences and the fine art of energy accounting, much like a delightful fusion dish concocted from the most unlikely of ingredients. In this endeavor, we invoke the spirits of statistical rigor and scientific curiosity, endeavoring to cast a light on the shadows of correlation and causation, as if we were to wave a scientific torch through the murk and mire of nebulous associations.
As we embark on this expedition into the realm of empirical observation and robust data analysis, we aim not only to decipher the twists and turns of this unexpected dance between air quality in Phoenix and kerosene usage in Cuba, but also to stir the pot of contemplation on the interconnectedness of our planet's environmental dynamics. So, join us in this enlightening pursuit, where we untangle the web of relationships with the fervor of a scientist on the cusp of a groundbreaking discovery, and reveal the intriguing ties that bind atmospheric currents and energy consumption patterns across oceans and continents.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The analysis of the data yielded intriguing results, unveiling a substantial correlation between air quality in Phoenix, Arizona, and kerosene consumption in Cuba. Quantitatively, our research uncovered a correlation coefficient of 0.7582886, indicating a strong positive relationship between the two variables. This coefficient signifies that as kerosene consumption in Cuba rose or fell, air quality in Phoenix exhibited a corresponding trend, much like a duo engaged in a synchronized dance, albeit one that spans thousands of miles and stratospheric heights.

The coefficient of determination, or R-squared value, stood at 0.5750015, signifying that approximately 57.5% of the variability in air quality in Phoenix can be explained by changes in kerosene consumption in Cuba. The remaining 42.5% of the variability, much like the elusive whispers of the wind, may be influenced by other factors, such as local emissions, meteorological phenomena, and the occasional dust devil throwing a whimsical twist into the mixture.

In conjunction with the correlation coefficient, the p-value of less than 0.01 presents a compelling argument for the significance of the observed relationship. This statistical gem signifies that the likelihood of the relationship occurring by mere happenstance is less than 1%, lending substantial weight to the idea that the connection between air quality in Phoenix and kerosene consumption in Cuba is not merely a coincidental gust, but a deliberate, albeit surprising, confluence of atmospheric and energy dynamics.

To visually encapsulate the robust correlation uncovered in our analysis, we present Figure 1, a scatterplot illustrating the covariation between air quality in Phoenix and kerosene consumption in Cuba. The scatterplot paints a vivid picture of the harmonious ebb and flow of these interconnected variables, akin to a celestial ballet choreographed by the hand of statistical fate.

These results shed a revealing light on the interconnectedness of our planet, suggesting that seemingly disparate phenomena can indeed dance in tandem across global landscapes. The winds of change, it seems, are not bound by traditional geographies and may carry the imprint of kerosene consumption from the shores of distant lands to the skies over the arid expanse of Phoenix. Our findings ignite contemplation on the pervasive effects of energy consumption, sprouting roots as far-reaching as the air quality of a southwestern desert city.

The contours of this correlation offer an invitation for policymakers and environmental stewards to take heed of the far-reaching implications of global energy patterns. As we move forward, embracing a holistic perspective on environmental dynamics, the unexpected dance between air quality in Phoenix and kerosene usage in Cuba beckons us to transcend conventional boundaries and indulge in conversations of international import, "fueling" discussions on sustainability and cooperation, all with a playful nod to the capricious nature of global relationships.

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 quality in Phoenix and Kerosene used in Cuba. 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]]
Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba

[[ABSTRACT]]
In this study, we analyze the curious relationship between air quality in Phoenix, Arizona, and kerosene consumption in Cuba. While the connection between these two seemingly disparate factors may appear as nebulous as smog on a hazy day, our findings unveil a striking correlation. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, we meticulously sifted through decades of records to unearth this unexpected association.

Employing robust statistical methods, our research team identified a correlation coefficient of 0.7582886 and a p-value less than 0.01 for the period spanning 1980 to 2021. These results cast a revealing light on the intertwining dynamics of air quality in Phoenix and kerosene usage in Cuba. Surprisingly, the data suggests that the winds of change may blow far beyond traditional boundaries, carrying the impact of kerosene consumption across the seas to the deserts of the American Southwest.

As we delve deeper into this enigmatic connection, we unravel the intricate interplay of atmospheric currents and energy consumption patterns, shedding light on a complex, global tapestry. Our findings urge policymakers to consider the far-reaching implications of seemingly distant phenomena and to "fuel" discussions about collaborative efforts for environmental stewardship.

So, let us embark on this illuminating journey, exploring the "combustible" relationship between air quality in Phoenix and kerosene use in Cuba, and unveiling the interconnectedness of our planet's environmental dynamics.

[[LITERATURE REVIEW]]
The connection between air quality and various environmental and human activities provides a rich tapestry of research, combining the fields of atmospheric science, environmental economics, and international relations. At the crux of our investigation into the correlation between air quality in Phoenix and kerosene consumption in Cuba lies a web of diverse studies, shedding light on the complex interplay of climatic factors and energy usage patterns. Our review encompasses a range of scholarly works and authoritative sources, beginning with the seminal studies by Smith, Doe, and Jones, and extending into literary works that delve into the nuances of environmental influences and cross-continental dynamics.
In "Atmospheric Dynamics and Urban Air Quality," Smith et al. navigate the convoluted patterns of air pollutant dispersion in urban settings, drawing attention to the manifold factors that contribute to the concentration of pollutants in metropolitan areas. Their findings serve as an invaluable backdrop to our exploration of the atmospheric intricacies within the context of Phoenix, Arizona, where the intermingling of industrial emissions and vehicular activity paints a portrait of atmospheric flux.
Doe's comprehensive analysis in "Energy Consumption Patterns and Socioeconomic Drivers" delves into the intricacies of energy usage across diverse socioeconomic strata, offering a lens through which we examine the patterns of kerosene consumption in Cuba. The intercontinental reach of energy dynamics is brought to the forefront, as we navigate the potential ripples of kerosene usage in Cuba on the atmospheric conditions of the American Southwest.
In juxtaposition to these scholarly works, non-fiction literature such as "The Global Impact of Energy Consumption" by Environmental Economist Jane Smith and "Cuban Energy Quandary: From Past to Present" by Energy Policy Analyst John Doe provides a multidimensional perspective on the complex interactions between global energy dynamics and environmental repercussions.
Venturing into the realm of fiction, works such as "The Wind Whisperers" by A. B. Cloudsworth and "Kerosene Dreams" by Luminous Jones offer glimpses into the poetic interweaving of atmospheric currents and energy symbolism, beckoning us to consider the abstract connections between seemingly distant phenomena.
Diverging from the typical sources, our literature review encompasses an eclectic mix of findings that extend beyond traditional research boundaries. Brief yet insightful glances at the backs of household products such as shampoo bottles, which often tout environmentally friendly formulas, reveal the ubiquitous nature of environmental discourse, albeit in the most peculiar of places.
As we progress through this literary odyssey, we pivot towards the empirical milieu of our investigation, where we seek to illuminate the threads that tether air quality in Phoenix to the flickering flames of kerosene usage in Cuba, in all their intricate and unforeseen splendor.

[[RESULTS]]
The analysis of the data yielded intriguing results, unveiling a substantial correlation between air quality in Phoenix, Arizona, and kerosene consumption in Cuba. Quantitatively, our research uncovered a correlation coefficient of 0.7582886, indicating a strong positive relationship between the two variables. This coefficient signifies that as kerosene consumption in Cuba rose or fell, air quality in Phoenix exhibited a corresponding trend, much like a duo engaged in a synchronized dance, albeit one that spans thousands of miles and stratospheric heights.
The coefficient of determination, or R-squared value, stood at 0.5750015, signifying that approximately 57.5% of the variability in air quality in Phoenix can be explained by changes in kerosene consumption in Cuba. The remaining 42.5% of the variability, much like the elusive whispers of the wind, may be influenced by other factors, such as local emissions, meteorological phenomena, and the occasional dust devil throwing a whimsical twist into the mixture.
In conjunction with the correlation coefficient, the p-value of less than 0.01 presents a compelling argument for the significance of the observed relationship. This statistical gem signifies that the likelihood of the relationship occurring by mere happenstance is less than 1%, lending substantial weight to the idea that the connection between air quality in Phoenix and kerosene consumption in Cuba is not merely a coincidental gust, but a deliberate, albeit surprising, confluence of atmospheric and energy dynamics.
To visually encapsulate the robust correlation uncovered in our analysis, we present Figure 1, a scatterplot illustrating the covariation between air quality in Phoenix and kerosene consumption in Cuba. The scatterplot paints a vivid picture of the harmonious ebb and flow of these interconnected variables, akin to a celestial ballet choreographed by the hand of statistical fate.
These results shed a revealing light on the interconnectedness of our planet, suggesting that seemingly disparate phenomena can indeed dance in tandem across global landscapes. The winds of change, it seems, are not bound by traditional geographies and may carry the imprint of kerosene consumption from the shores of distant lands to the skies over the arid expanse of Phoenix. Our findings ignite contemplation on the pervasive effects of energy consumption, sprouting roots as far-reaching as the air quality of a southwestern desert city.
The contours of this correlation offer an invitation for policymakers and environmental stewards to take heed of the far-reaching implications of global energy patterns. As we move forward, embracing a holistic perspective on environmental dynamics, the unexpected dance between air quality in Phoenix and kerosene usage in Cuba beckons us to transcend conventional boundaries and indulge in conversations of international import, "fueling" discussions on sustainability and cooperation, all with a playful nod to the capricious nature of global relationships.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

Our findings illuminate the intricate dance of interconnectedness between air quality in Phoenix and kerosene consumption in Cuba, proving that when it comes to atmospheric dynamics, it's not all hot air. Our results bolster previous studies that hinted at the ethereal connection between seemingly unrelated variables. So, let's dive into the data and unpack the tangled web of correlation, much like untangling a stubborn knot in a string of statistical confetti.

The correlation coefficient of 0.7582886 that emerged from our analysis pulsates with statistical significance, signaling a strong positive relationship, much like the harmonious unity of peanut butter and jelly – a pairing that just seems right, regardless of the geographical chasm that separates them. A like-minded duo, kerosene consumption in Cuba and air quality in Phoenix appear to move in sync, harmonizing across continents like a global symphony orchestrated by unseen hands.

Our R-squared value of 0.5750015 further solidifies this enchanting waltz of variables, capturing approximately 57.5% of the variations in air quality in Phoenix. The remaining 42.5%, not unlike a whisper lost in the wind, may be influenced by other capricious elements, from local emissions to the occasional tumbleweed conspiring with the breeze. Yet, within this cacophony of meteorological factors, the discernible melody of kerosene usage still resounds, lending credence to the significance of the observed correlation.

The obstinate p-value of less than 0.01 elegantly rebuffs any notion of this relationship being a mere fluke, resonating with the certainty of a clinking toast at a scientific gala. Our statistical analyses affirm that this coupling between kerosene consumption in Cuba and air quality in Phoenix is not a chance encounter, but a deliberate fusion of global scales and invisible currents.

Like celestial cartographers charting the alignment of stars, our scatterplot in Figure 1 illustrates the coalescence of air quality in Phoenix and kerosene consumption in Cuba, painting a vivid picture of their intertwined trajectory. The scintillating dance of these variables traverses borders and atmospheric layers, much like the gravitational pull of cosmic bodies locked in a celestial pirouette.

Our findings, much like a scientist with a magnifying glass discovering a hidden microcosm, urge us to consider the ripple effects of seemingly distant phenomena. Just as a butterfly flapping its wings in Brazil can trigger a tornado in Texas, the impact of kerosene usage in Cuba wafts across vast distances, leaving an indelible imprint on the air quality of Phoenix. These revelations summon policymakers and environmental stewards to eavesdrop on the planetary symphony, embracing a unified vision of cooperation and sustainability that transcends traditional boundaries.

In conclusion, our research invites us to peel back the layers of our global tapestry, aiming not only to understand the intricacies of our environment but also to celebrate the harmonious, if at times enigmatic, interplay between variables. As we "fuel" discussions on environmental stewardship, our findings beckon us to recognize the cosmic rhythms that underlie the delicate balance of our planet's interconnected systems.

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 quality in Phoenix and Kerosene used in Cuba. 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]]
Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba

[[ABSTRACT]]
In this study, we analyze the curious relationship between air quality in Phoenix, Arizona, and kerosene consumption in Cuba. While the connection between these two seemingly disparate factors may appear as nebulous as smog on a hazy day, our findings unveil a striking correlation. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, we meticulously sifted through decades of records to unearth this unexpected association.

Employing robust statistical methods, our research team identified a correlation coefficient of 0.7582886 and a p-value less than 0.01 for the period spanning 1980 to 2021. These results cast a revealing light on the intertwining dynamics of air quality in Phoenix and kerosene usage in Cuba. Surprisingly, the data suggests that the winds of change may blow far beyond traditional boundaries, carrying the impact of kerosene consumption across the seas to the deserts of the American Southwest.

As we delve deeper into this enigmatic connection, we unravel the intricate interplay of atmospheric currents and energy consumption patterns, shedding light on a complex, global tapestry. Our findings urge policymakers to consider the far-reaching implications of seemingly distant phenomena and to "fuel" discussions about collaborative efforts for environmental stewardship.

So, let us embark on this illuminating journey, exploring the "combustible" relationship between air quality in Phoenix and kerosene use in Cuba, and unveiling the interconnectedness of our planet's environmental dynamics.

[[INTRDUCTION]]
INTRODUCTION
The pursuit of knowledge has long been an illuminating journey, much like trying to find the light switch in a dark room – sometimes enlightening, often stumbled upon, and occasionally leaving one feeling utterly bemused. In this vein, our exploration of the curious relationship between air quality in Phoenix and kerosene consumption in Cuba represents a blending of scientific inquiry and stumbling upon sparks of unexpected insights. The endeavor is akin to grasping at the wisps of a gentle breeze intermingled with the pungent aroma of a neighbor's barbecue, leaving us pondering the whiffs and whiffs of correlations that may betray something significant amidst the haze.
It is a classic tale of tackling the seemingly unrelated with the fervor of a detective hot on the trail, piecing together an investigative puzzle with the gusto of a physicist seeking to crack the code of the universe. On the surface, one might assume that air quality in Phoenix and kerosene consumption in Cuba are as connected as a fish is to a bicycle – an apocryphal, incongruous affair. Nonetheless, as our research unravels, we find ourselves standing at the crossroads of climatic intricacies and energy consumption quirkiness, pondering the intercontinental reach of environmental influences.
Our study stands as a testament to the marriage of disciplines – a rendezvous between the atmospheric sciences and the fine art of energy accounting, much like a delightful fusion dish concocted from the most unlikely of ingredients. In this endeavor, we invoke the spirits of statistical rigor and scientific curiosity, endeavoring to cast a light on the shadows of correlation and causation, as if we were to wave a scientific torch through the murk and mire of nebulous associations.
As we embark on this expedition into the realm of empirical observation and robust data analysis, we aim not only to decipher the twists and turns of this unexpected dance between air quality in Phoenix and kerosene usage in Cuba, but also to stir the pot of contemplation on the interconnectedness of our planet's environmental dynamics. So, join us in this enlightening pursuit, where we untangle the web of relationships with the fervor of a scientist on the cusp of a groundbreaking discovery, and reveal the intriguing ties that bind atmospheric currents and energy consumption patterns across oceans and continents.

[[RESULTS]]
The analysis of the data yielded intriguing results, unveiling a substantial correlation between air quality in Phoenix, Arizona, and kerosene consumption in Cuba. Quantitatively, our research uncovered a correlation coefficient of 0.7582886, indicating a strong positive relationship between the two variables. This coefficient signifies that as kerosene consumption in Cuba rose or fell, air quality in Phoenix exhibited a corresponding trend, much like a duo engaged in a synchronized dance, albeit one that spans thousands of miles and stratospheric heights.
The coefficient of determination, or R-squared value, stood at 0.5750015, signifying that approximately 57.5% of the variability in air quality in Phoenix can be explained by changes in kerosene consumption in Cuba. The remaining 42.5% of the variability, much like the elusive whispers of the wind, may be influenced by other factors, such as local emissions, meteorological phenomena, and the occasional dust devil throwing a whimsical twist into the mixture.
In conjunction with the correlation coefficient, the p-value of less than 0.01 presents a compelling argument for the significance of the observed relationship. This statistical gem signifies that the likelihood of the relationship occurring by mere happenstance is less than 1%, lending substantial weight to the idea that the connection between air quality in Phoenix and kerosene consumption in Cuba is not merely a coincidental gust, but a deliberate, albeit surprising, confluence of atmospheric and energy dynamics.
To visually encapsulate the robust correlation uncovered in our analysis, we present Figure 1, a scatterplot illustrating the covariation between air quality in Phoenix and kerosene consumption in Cuba. The scatterplot paints a vivid picture of the harmonious ebb and flow of these interconnected variables, akin to a celestial ballet choreographed by the hand of statistical fate.
These results shed a revealing light on the interconnectedness of our planet, suggesting that seemingly disparate phenomena can indeed dance in tandem across global landscapes. The winds of change, it seems, are not bound by traditional geographies and may carry the imprint of kerosene consumption from the shores of distant lands to the skies over the arid expanse of Phoenix. Our findings ignite contemplation on the pervasive effects of energy consumption, sprouting roots as far-reaching as the air quality of a southwestern desert city.
The contours of this correlation offer an invitation for policymakers and environmental stewards to take heed of the far-reaching implications of global energy patterns. As we move forward, embracing a holistic perspective on environmental dynamics, the unexpected dance between air quality in Phoenix and kerosene usage in Cuba beckons us to transcend conventional boundaries and indulge in conversations of international import, "fueling" discussions on sustainability and cooperation, all with a playful nod to the capricious nature of global relationships.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, this study has unraveled a fascinating correlation between air quality in Phoenix and kerosene consumption in Cuba. The statistical findings have brought to light the intriguing dance of intercontinental influence, much like a whimsical tango between two unlikely partners. The robust correlation coefficient and p-value less than 0.01 provide compelling evidence, akin to a sleuth uncovering crucial clues in a mystery novel, lending credence to the significance of this unexpected association.

The interconnectedness of environmental dynamics, as demonstrated by our research, leaves us pondering the far-reaching implications of global energy patterns. It seems that the winds of change carry more than just atmospheric particles; they carry the echoes of kerosene consumption across the vast expanse of the oceans, painting a vivid picture of the intricate interplay of seemingly unrelated phenomena.

As we wrap up this illuminating journey, we must acknowledge the significance of this correlation in urging international collaboration and environmental stewardship. The proverbial ball is now in the court of policymakers and policymakers alike to nurture conversations about sustainability and cooperation, taking into account the capricious nature of global relationships and embracing the unexpected connections that come to light through scientific inquiry.

Ultimately, this study calls for a holistic perspective on environmental dynamics and encourages us to broaden our horizons, not just metaphorically but also statistically. With that said, it is safe to say that further research in this area may yield diminishing returns, much like attempting to squeeze blood from a data stone. It's time to bid adieu to this peculiar pairing of air quality in Phoenix and kerosene consumption in Cuba, for we have unraveled its mysteries and reveled in its unexpected beauty.

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 Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Atmospheric Dynamics and International Energy Markets

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 Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Atmospheric and Geochemical Research and Collaboration

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 Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba with an abstract of In this study, we analyze the curious relationship between air quality in Phoenix, Arizona, and kerosene consumption in Cuba. While the connection between these two seemingly disparate factors may appear as nebulous as smog on a hazy day, our findings unveil a striking correlation. Leveraging data from the Environmental Protection Agency and the Energy Information Administration, we meticulously sifted through decades of records to unearth this unexpected association.
Employing robust statistical methods, our research team identified a correlation coefficient of 0.7582886 and a p-value less than 0.01 for the period spanning 1980 to 2021. These results cast a revealing light on the intertwining dynamics of air quality in Phoenix and kerosene usage in Cuba. Surprisingly, the data suggests that the winds of change may blow far beyond traditional boundaries, carrying the impact of kerosene consumption across the seas to the deserts of the American Southwest.
As we delve deeper into this enigmatic connection, we unravel the intricate interplay of atmospheric currents and energy consumption patterns, shedding light on a complex, global tapestry. Our findings urge policymakers to consider the far-reaching implications of seemingly distant phenomena and to "fuel" discussions about collaborative efforts for environmental stewardship.
So, let us embark on this illuminating journey, exploring the "combustible" relationship between air quality in Phoenix and kerosene use in Cuba, and unveiling the interconnectedness of our planet's environmental dynamics.

ChatGPT:

air quality, Phoenix, Arizona, kerosene consumption, Cuba, correlation, atmospheric currents, energy consumption, environmental impact, global interconnectedness, policymaker implications

*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 quality in Phoenix
Detailed data title: Percentage of days with good air quality in Phoenix-Mesa-Scottsdale, AZ
Source: Environmental Protection Agency
See what else correlates with Air quality in Phoenix

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

Correlation r = 0.7582886 (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 = 0.5750015 (Coefficient of determination)
This means 57.5% of the change in the one variable (i.e., Kerosene used in Cuba) is predictable based on the change in the other (i.e., Air quality in Phoenix) over the 42 years from 1980 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 6.008E-9.^Show 0.0000000060084351261330450000
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 0.76 in 6.008E-7% of random cases. Said differently, if you correlated 166,432,687 random variables^Note You don't actually need 166 million variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

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

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

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

[ 0.59, 0.86 ] 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 quality in Phoenix (Good air quality)	25.0689	17.2603	25.7534	24.3836	9.56284	11.5068	13.1507	18.1818	24.0437	24.3836	27.9452	26.5753	21.8579	27.6712	20.8219	14.2466	15.847	8.49315	9.31507	1.36986	5.7377	8.21918	8.49315	11.7808	16.3934	13.4247	3.0137	6.0274	11.7486	6.84932	16.1644	5.47945	6.28415	8.21918	6.0274	13.9726	7.10383	8.76712	11.5068	13.6986	3.00546	3.0137
Kerosene used in Cuba (Million Barrels/Day)	13.6854	13.9551	15.1011	13.8876	14.3596	14.6292	15	14	13	14	13	12	12	12	13	12	12	4.6	3.2	3	4.70981	3.66381	2.49901	4.04501	7.5188	5.61219	2.83786	1.99074	1.75298	1.65189	1.67307	1.67307	1.67307	1.67307	1.27068	2	2	1.71636	1.6729	1.586	1.39047	1.39047

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([25.0689,17.2603,25.7534,24.3836,9.56284,11.5068,13.1507,18.1818,24.0437,24.3836,27.9452,26.5753,21.8579,27.6712,20.8219,14.2466,15.847,8.49315,9.31507,1.36986,5.7377,8.21918,8.49315,11.7808,16.3934,13.4247,3.0137,6.0274,11.7486,6.84932,16.1644,5.47945,6.28415,8.21918,6.0274,13.9726,7.10383,8.76712,11.5068,13.6986,3.00546,3.0137,])
array_2 = np.array([13.6854,13.9551,15.1011,13.8876,14.3596,14.6292,15,14,13,14,13,12,12,12,13,12,12,4.6,3.2,3,4.70981,3.66381,2.49901,4.04501,7.5188,5.61219,2.83786,1.99074,1.75298,1.65189,1.67307,1.67307,1.67307,1.67307,1.27068,2,2,1.71636,1.6729,1.586,1.39047,1.39047,])
array_1_name = "Air quality in Phoenix"
array_2_name = "Kerosene used in Cuba"

# 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 quality in Phoenix
Line chart for only Kerosene used in Cuba
AI-generated correlation image
The spurious research paper: Connecting the Clouds: Correlating Air Quality in Phoenix with Kerosene Consumption in Cuba

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Correlation ID: 1979 · Black Variable ID: 21062 · Red Variable ID: 24336


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