Spurious correlation #5,560 · 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 Bowling Green, Kentucky and the second variable is The divorce rate in Kentucky. The chart goes from 1999 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 Bowling Green, Kentucky and the second variable is The divorce rate in Kentucky. The chart goes from 1999 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As the air became fresher, it rekindled the spark in marriages, leading to smoother communication. It's as if the cleaner air acted as a breath of fresh air in their relationships, helping them see things more clearly and not feel smogged down by issues.

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a cyberpunk-inspired scene set in Bowling Green, Kentucky. The environment is a futuristic cityscape, enhanced by neon lights and holographic billboards. In the foreground, couples are strolling hand in hand through the revitalized streets lined with technologically advanced buildings. The atmosphere showcases a refreshing contrast of nature reclaiming the urban space, with vibrant greenery and clean air permeating the city. The couples are portrayed engaged in intimate conversations, amid a setting that exudes a sense of revitalization and renewed connection. 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 Bowling Green, Kentucky and The divorce rate in Kentucky. 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: Hyper-realistic Cyberpunk Pop art Art nouveau Futuristic
ChatGPT: Cyberpunk

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 Bowling Green, Kentucky and The divorce rate in Kentucky, in the following situation: As the air became fresher, it rekindled the spark in marriages, leading to smoother communication. It's as if the cleaner air acted as a breath of fresh air in their relationships, helping them see things more clearly and not feel smogged down by issues.. Keep the description simple.
ChatGPT: In Bowling Green, Kentucky, the air clears up after a heavy bout of pollution, creating a fresh, clear atmosphere. Against this backdrop, couples are seen walking hand in hand, smiles on their faces as they engage in deep, uninterrupted conversations. The air seems to have lifted the weight off their shoulders, and they seem more connected than ever.

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: [ Cyberpunk ] and depicting this scene: In Bowling Green, Kentucky, the air clears up after a heavy bout of pollution, creating a fresh, clear atmosphere. Against this backdrop, couples are seen walking hand in hand, smiles on their faces as they engage in deep, uninterrupted conversations. The air seems to have lifted the weight off their shoulders, and they seem more connected than ever. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a cyberpunk-inspired scene set in Bowling Green, Kentucky. The environment is a futuristic cityscape, enhanced by neon lights and holographic billboards. In the foreground, couples are strolling hand in hand through the revitalized streets lined with technologically advanced buildings. The atmosphere showcases a refreshing contrast of nature reclaiming the urban space, with vibrant greenery and clean air permeating the city. The couples are portrayed engaged in intimate conversations, amid a setting that exudes a sense of revitalization and renewed connection.

*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 Bowling Green, Kentucky caused The divorce rate in Kentucky to decrease. Include one good pun.

AI academic paper

(Because p < 0.01)

Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky

The Journal of Sociological Quirkiness

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 Bowling Green, Kentucky and The divorce rate in Kentucky. Make lots of jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then name some movies that you watched that are tangentially related to the topic.

Here is the title and abstract of the paper:
[[TITLE]]
"Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky"

[[ABSTRACT]]
This research paper addresses the unexpected connection between air pollution in Bowling Green, Kentucky, and the divorce rate in the state. Utilizing data from the Environmental Protection Agency and CDC National Vital Statistics, we sought to uncover whether there was a match made in smog. Our findings revealed a surprisingly high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, indicating a strong relationship between the two factors. As we delved into this perplexing partnership, we were abuzz with excitement to uncover the unexpected interplay between air quality and marital status. This study serves as a breath of fresh air in the realm of environmental and social sciences as it unearths an unconventional romance between seemingly unrelated variables. We hope that our findings spark both interest and amusement and pave the way for further investigations into the whimsical world of air pollution and divorce dynamics.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
INTRODUCTION
In the realm of environmental and social sciences, researchers often seek to uncover the hidden connections between seemingly disparate phenomena. One might expect to find correlations between air pollution and respiratory illnesses, or between divorce rates and economic downturns. However, the captivating nature of statistical analysis lies in its ability to reveal unexpected relationships, much like stumbling upon a love connection in the unlikeliest of places.
Our study delves into the charming town of Bowling Green, Kentucky, where we stumbled upon a captivating courtship between air pollution and the dissolution of marriages. Much like star-crossed lovers, these two variables captured our attention and prompted us to embark on a journey to unravel their clandestine affair. As we waltzed through the data from the Environmental Protection Agency and CDC National Vital Statistics, we found ourselves irresistibly drawn deeper into this enchanting tango of environmental quality and marital harmony.
With a song in our hearts and a twinkle in our eyes, we set out to quantify the dance of air pollution and divorce rates. Our analysis revealed a remarkably high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, providing undeniable evidence of a strong relationship between these two enchanting variables. This statistical embrace between air pollution and divorce rates left us in breathless awe, challenging our preconceived notions and reaffirming the boundless potential for delightfully surprising discoveries.
Our findings beckon us to consider the whimsical interplay between environmental factors and social dynamics. The enchanting liaison between air pollution and marital discord takes center stage in our exploration, inviting researchers to expand their horizons and embrace the delightful unpredictability of statistical analysis. As we present our findings, we hope to infuse a dash of amusement and a sprinkle of curiosity into the scholarly discourse, inviting fellow enthusiasts to join us in unearthing the charming romances that lie beneath the surface of seemingly unrelated variables.
As we navigate this captivating terrain of statistical romance, we invite readers to accompany us on this waltz of discovery, where the unexpected delights in challenging our assumptions and tickles our intellectual curiosity. It is our fervent hope that this study will serve as a poetic ode to the enchanting dance between air pollution and the dissolution of marriages, sparking joy and merriment along the way. Join us in this whimsical exploration, where the winds of change and the bonds of matrimony intertwine in a captivating pas de deux unlike any other.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

In "Smith and Doe" the authors find a striking association between air pollution and adverse health outcomes, emphasizing the detrimental effects on respiratory health and overall well-being. Similarly, in "Jones et al.," the researchers delve into the intricate web of social and environmental factors, shedding light on the nuanced relationships that underpin community dynamics.

But let's move beyond the dry academic tomes and venture into the realm of popular non-fiction works. In "Breath: The New Science of a Lost Art," James Nestor takes readers on a journey through the hidden realms of respiratory health, offering insights that are truly a breath of fresh air. Meanwhile, "Polluted Marriage: Navigating the Hazy Union of Air Quality and Relationship Strain" by Dr. Misty Skyes explores the peculiar parallels between environmental pollution and marital discord with a mix of seriousness and whimsy.

As we tiptoe further into the literary landscape, let's not overlook the fictional tales that, with a bit of imagination, could bear relevance to our curious conundrum. Perhaps in Jane Austen's "Pride and Pollution," the characters navigate a world where societal woes intertwine with atmospheric strife. Or in J.R.R. Tolkien's "The Smog of the Rings," we may find ourselves embroiled in an epic quest to purify the air of Middle-earth while also mending fractured relationships.

While we're on the subject of whimsical intersections, consider the cinematic marvels that, albeit tangentially, offer glimpses into the complexities of human interaction and environmental influence. In the film "The Toxic Romance," characters navigate both the polluted cityscape and the murky depths of their relationships, offering a poignant reflection on the entanglement of external surroundings and internal turmoil.

With these eclectic references in mind, we embark on our own scholarly expedition, armed with a sense of wonder and a touch of humor, to unravel the peculiar dance between air pollution and the dissolution of marriages. Let the scholarly tango begin!

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 Bowling Green, Kentucky and The divorce rate in Kentucky. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and CDC National Vital Statistics . You used data from 1999 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]]
"Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky"

[[ABSTRACT]]
This research paper addresses the unexpected connection between air pollution in Bowling Green, Kentucky, and the divorce rate in the state. Utilizing data from the Environmental Protection Agency and CDC National Vital Statistics, we sought to uncover whether there was a match made in smog. Our findings revealed a surprisingly high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, indicating a strong relationship between the two factors. As we delved into this perplexing partnership, we were abuzz with excitement to uncover the unexpected interplay between air quality and marital status. This study serves as a breath of fresh air in the realm of environmental and social sciences as it unearths an unconventional romance between seemingly unrelated variables. We hope that our findings spark both interest and amusement and pave the way for further investigations into the whimsical world of air pollution and divorce dynamics.

[[INTRODUCTION]]
INTRODUCTION
In the realm of environmental and social sciences, researchers often seek to uncover the hidden connections between seemingly disparate phenomena. One might expect to find correlations between air pollution and respiratory illnesses, or between divorce rates and economic downturns. However, the captivating nature of statistical analysis lies in its ability to reveal unexpected relationships, much like stumbling upon a love connection in the unlikeliest of places.
Our study delves into the charming town of Bowling Green, Kentucky, where we stumbled upon a captivating courtship between air pollution and the dissolution of marriages. Much like star-crossed lovers, these two variables captured our attention and prompted us to embark on a journey to unravel their clandestine affair. As we waltzed through the data from the Environmental Protection Agency and CDC National Vital Statistics, we found ourselves irresistibly drawn deeper into this enchanting tango of environmental quality and marital harmony.
With a song in our hearts and a twinkle in our eyes, we set out to quantify the dance of air pollution and divorce rates. Our analysis revealed a remarkably high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, providing undeniable evidence of a strong relationship between these two enchanting variables. This statistical embrace between air pollution and divorce rates left us in breathless awe, challenging our preconceived notions and reaffirming the boundless potential for delightfully surprising discoveries.
Our findings beckon us to consider the whimsical interplay between environmental factors and social dynamics. The enchanting liaison between air pollution and marital discord takes center stage in our exploration, inviting researchers to expand their horizons and embrace the delightful unpredictability of statistical analysis. As we present our findings, we hope to infuse a dash of amusement and a sprinkle of curiosity into the scholarly discourse, inviting fellow enthusiasts to join us in unearthing the charming romances that lie beneath the surface of seemingly unrelated variables.
As we navigate this captivating terrain of statistical romance, we invite readers to accompany us on this waltz of discovery, where the unexpected delights in challenging our assumptions and tickles our intellectual curiosity. It is our fervent hope that this study will serve as a poetic ode to the enchanting dance between air pollution and the dissolution of marriages, sparking joy and merriment along the way. Join us in this whimsical exploration, where the winds of change and the bonds of matrimony intertwine in a captivating pas de deux unlike any other.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

To commence our investigation into the curious connection between air pollution and divorce rates, our research team engaged in a series of methodological maneuvers that would make even the most seasoned statistician raise an eyebrow. We harnessed the power of data mining and statistical wizardry to uncover the secrets lurking within the digital archives of the Environmental Protection Agency and the CDC National Vital Statistics. Our research vessel traversed the vast seas of internet databases, braving the tempestuous waves of information to procure datasets spanning the years 1999 to 2021. With a mix of precision and whimsy, we charted a course through the digital expanse, navigating the bountiful waters of environmental quality and social metrics.

Data Compilation and Environmental Exposure
Armed with an insatiable curiosity and an overwhelming desire to parse through heaps of data, we journeyed through the digital archives of the Environmental Protection Agency like intrepid explorers in search of statistical treasure. Drawing upon a myriad of air quality metrics, including levels of particulate matter, ozone, carbon monoxide, sulfur dioxide, and nitrogen dioxide, our team constructed a comprehensive profile of air pollution in the enchanting locale of Bowling Green, Kentucky. We meticulously combed through datasets and tapped into the quantitative riches, mining nuggets of information that would illuminate the atmospheric landscape of this verdant region.

Marital Dissolution and Demographic Databasing
As we ventured further into the labyrinthine recesses of data repositories, we turned our attention to the realm of marital harmony – or lack thereof. The CDC National Vital Statistics provided a bountiful harvest of demographic data, allowing us to scrutinize divorce rates with a level of scrutiny akin to a detective poring over clues at a crime scene. With meticulous care and methodical precision, we cataloged and cross-referenced the dissolution of marriages, unfurling the intricate tapestry of social dynamics that interwove with the atmospheric musings of our air pollution datasets.

Statistical Courtship: Correlation Analysis and Hypothesis Testing
With our quivers brimming with datasets and our spirits ablaze with statistical fervor, we embarked on the grand challenge of hypothesis testing and correlation analysis. Employing a multitude of statistical tools, including the Pearson correlation coefficient and robust regression analyses, we sought to unravel the enchanting dance between air pollution and divorce rates. Our statistical foray allowed us to quantitatively measure the degree of association between these seemingly incongruous variables, unveiling a partnership that was as surprising as finding a four-leaf clover in a field of statistical probabilities.

Matchmaking with Covariates and Sensitivity Analyses
Knowing that no statistical romance is complete without a touch of complexity, we engaged in covariate matching and sensitivity analyses to ensure the robustness of our findings. Our methodological courtship extended beyond the mere association between air pollution and divorce rates, delving into the influence of covariates such as median household income, educational attainment, and urbanization. With a touch of statistical alchemy, we teased apart the nuanced interplay of variables, ensuring that our findings were as steadfast as the bonds of a reliable regression model.

Limitations and Caveats: Navigating the Shoals of Statistical Adventure
As with any grand expedition into the realm of statistical romance, our research encountered its fair share of limitations and caveats. From the potential for ecological fallacy to the confounding effects of unobserved variables, we navigated the treacherous waters of statistical inference with caution and humility. Recognizing the limitations inherent in our study, we aimed to temper our findings with a healthy dose of scholarly skepticism and a sprinkling of statistical humility.

In the grand tapestry of methodological endeavors, our research embarked upon an adventure that traversed the realms of environmental exposure, social dynamics, and the whimsical interplay of statistical romance. With a blend of precision and humor, we emerged from the labyrinth of statistical analysis with findings that spoke to the enchanting courtship between air pollution and the dissolution of marriages, leaving us in delightful awe at the unexpected connections that dot the expansive landscape of quantitative inquiry.

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

Please make up the results section of an academic research paper presenting the findings of the connection between Air pollution in Bowling Green, Kentucky and The divorce rate in Kentucky. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and CDC National Vital Statistics .

For the time period 1999 to 2021, you found a correlation 0.8179517, r-squared of 0.6690450, 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]]
"Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky"

[[ABSTRACT]]
This research paper addresses the unexpected connection between air pollution in Bowling Green, Kentucky, and the divorce rate in the state. Utilizing data from the Environmental Protection Agency and CDC National Vital Statistics, we sought to uncover whether there was a match made in smog. Our findings revealed a surprisingly high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, indicating a strong relationship between the two factors. As we delved into this perplexing partnership, we were abuzz with excitement to uncover the unexpected interplay between air quality and marital status. This study serves as a breath of fresh air in the realm of environmental and social sciences as it unearths an unconventional romance between seemingly unrelated variables. We hope that our findings spark both interest and amusement and pave the way for further investigations into the whimsical world of air pollution and divorce dynamics.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
INTRODUCTION
In the realm of environmental and social sciences, researchers often seek to uncover the hidden connections between seemingly disparate phenomena. One might expect to find correlations between air pollution and respiratory illnesses, or between divorce rates and economic downturns. However, the captivating nature of statistical analysis lies in its ability to reveal unexpected relationships, much like stumbling upon a love connection in the unlikeliest of places.
Our study delves into the charming town of Bowling Green, Kentucky, where we stumbled upon a captivating courtship between air pollution and the dissolution of marriages. Much like star-crossed lovers, these two variables captured our attention and prompted us to embark on a journey to unravel their clandestine affair. As we waltzed through the data from the Environmental Protection Agency and CDC National Vital Statistics, we found ourselves irresistibly drawn deeper into this enchanting tango of environmental quality and marital harmony.
With a song in our hearts and a twinkle in our eyes, we set out to quantify the dance of air pollution and divorce rates. Our analysis revealed a remarkably high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, providing undeniable evidence of a strong relationship between these two enchanting variables. This statistical embrace between air pollution and divorce rates left us in breathless awe, challenging our preconceived notions and reaffirming the boundless potential for delightfully surprising discoveries.
Our findings beckon us to consider the whimsical interplay between environmental factors and social dynamics. The enchanting liaison between air pollution and marital discord takes center stage in our exploration, inviting researchers to expand their horizons and embrace the delightful unpredictability of statistical analysis. As we present our findings, we hope to infuse a dash of amusement and a sprinkle of curiosity into the scholarly discourse, inviting fellow enthusiasts to join us in unearthing the charming romances that lie beneath the surface of seemingly unrelated variables.
As we navigate this captivating terrain of statistical romance, we invite readers to accompany us on this waltz of discovery, where the unexpected delights in challenging our assumptions and tickles our intellectual curiosity. It is our fervent hope that this study will serve as a poetic ode to the enchanting dance between air pollution and the dissolution of marriages, sparking joy and merriment along the way. Join us in this whimsical exploration, where the winds of change and the bonds of matrimony intertwine in a captivating pas de deux unlike any other.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The results of our analysis unveiled a captivating relationship between air pollution in Bowling Green, Kentucky, and the dissolution of marriages throughout the state. The correlation coefficient of 0.8179517 indicated a striking alignment between these seemingly unrelated variables, akin to a surprise rendezvous at a masquerade ball. This substantial correlation, coupled with the r-squared value of 0.6690450, further emphasized the cozy entanglement of air pollution and divorce rates, much like a pair of lovebirds nesting in the branches of statistical significance.

The presence of a p-value less than 0.01 added an air of certainty to our findings, akin to a gust of wind carrying the sweet scent of academic validation. Indeed, the statistical winds whispered secrets of an unforeseen romance between environmental quality and marital upheaval, drawing us into the beguiling whirlwind of data exploration.

In Figure 1, our scatterplot elegantly portrays the amorous courtship between air pollution and divorce rates, serving as a visual testament to the magnetic allure of this unlikely liaison. The points on the plot embrace each other with a tender snugness, symbolizing the uncanny attraction between these two variables. One can almost hear the gentle rustle of statistical significance as the plot unfolds, beckoning us to ponder the beguiling dance of cause and effect.

As we reflect on the implications of our findings, we are reminded of the whimsical nature of statistical discovery. Much like uncorking a bottle of fine wine, our analysis has uncorked the enthralling complexities of environmental and social dynamics, leaving us intoxicated with both fascination and mirth. Our results stand as a testament to the captivating dalliance between air pollution and marital discord, inviting scholars and enthusiasts alike to embrace the enchanting unpredictability that lies at the heart of statistical inquiry.

This statistical symphony of air pollution and divorce rates in Bowling Green, Kentucky, plays a melodious tune that beckons us to revel in the harmonious and unexpected connections that permeate the fabric of our world. As we gaze upon our findings, we are reminded that beneath the veneer of empirical rigidity lies a whimsical realm where statistical analysis and unexpected romances intertwine, inviting us to waltz in the delightful ballroom of intellectual inquiry.

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the 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 Bowling Green, Kentucky and The divorce rate in Kentucky. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Limit your response to 500 tokens.

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

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

[[TITLE]]
"Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky"

[[ABSTRACT]]
This research paper addresses the unexpected connection between air pollution in Bowling Green, Kentucky, and the divorce rate in the state. Utilizing data from the Environmental Protection Agency and CDC National Vital Statistics, we sought to uncover whether there was a match made in smog. Our findings revealed a surprisingly high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, indicating a strong relationship between the two factors. As we delved into this perplexing partnership, we were abuzz with excitement to uncover the unexpected interplay between air quality and marital status. This study serves as a breath of fresh air in the realm of environmental and social sciences as it unearths an unconventional romance between seemingly unrelated variables. We hope that our findings spark both interest and amusement and pave the way for further investigations into the whimsical world of air pollution and divorce dynamics.

[[LITERATURE REVIEW]]
In "Smith and Doe" the authors find a striking association between air pollution and adverse health outcomes, emphasizing the detrimental effects on respiratory health and overall well-being. Similarly, in "Jones et al.," the researchers delve into the intricate web of social and environmental factors, shedding light on the nuanced relationships that underpin community dynamics.
But let's move beyond the dry academic tomes and venture into the realm of popular non-fiction works. In "Breath: The New Science of a Lost Art," James Nestor takes readers on a journey through the hidden realms of respiratory health, offering insights that are truly a breath of fresh air. Meanwhile, "Polluted Marriage: Navigating the Hazy Union of Air Quality and Relationship Strain" by Dr. Misty Skyes explores the peculiar parallels between environmental pollution and marital discord with a mix of seriousness and whimsy.
As we tiptoe further into the literary landscape, let's not overlook the fictional tales that, with a bit of imagination, could bear relevance to our curious conundrum. Perhaps in Jane Austen's "Pride and Pollution," the characters navigate a world where societal woes intertwine with atmospheric strife. Or in J.R.R. Tolkien's "The Smog of the Rings," we may find ourselves embroiled in an epic quest to purify the air of Middle-earth while also mending fractured relationships.
While we're on the subject of whimsical intersections, consider the cinematic marvels that, albeit tangentially, offer glimpses into the complexities of human interaction and environmental influence. In the film "The Toxic Romance," characters navigate both the polluted cityscape and the murky depths of their relationships, offering a poignant reflection on the entanglement of external surroundings and internal turmoil.
With these eclectic references in mind, we embark on our own scholarly expedition, armed with a sense of wonder and a touch of humor, to unravel the peculiar dance between air pollution and the dissolution of marriages. Let the scholarly tango begin!

[[RESULTS]]
The results of our analysis unveiled a captivating relationship between air pollution in Bowling Green, Kentucky, and the dissolution of marriages throughout the state. The correlation coefficient of 0.8179517 indicated a striking alignment between these seemingly unrelated variables, akin to a surprise rendezvous at a masquerade ball. This substantial correlation, coupled with the r-squared value of 0.6690450, further emphasized the cozy entanglement of air pollution and divorce rates, much like a pair of lovebirds nesting in the branches of statistical significance.
The presence of a p-value less than 0.01 added an air of certainty to our findings, akin to a gust of wind carrying the sweet scent of academic validation. Indeed, the statistical winds whispered secrets of an unforeseen romance between environmental quality and marital upheaval, drawing us into the beguiling whirlwind of data exploration.
In Figure 1, our scatterplot elegantly portrays the amorous courtship between air pollution and divorce rates, serving as a visual testament to the magnetic allure of this unlikely liaison. The points on the plot embrace each other with a tender snugness, symbolizing the uncanny attraction between these two variables. One can almost hear the gentle rustle of statistical significance as the plot unfolds, beckoning us to ponder the beguiling dance of cause and effect.
As we reflect on the implications of our findings, we are reminded of the whimsical nature of statistical discovery. Much like uncorking a bottle of fine wine, our analysis has uncorked the enthralling complexities of environmental and social dynamics, leaving us intoxicated with both fascination and mirth. Our results stand as a testament to the captivating dalliance between air pollution and marital discord, inviting scholars and enthusiasts alike to embrace the enchanting unpredictability that lies at the heart of statistical inquiry.
This statistical symphony of air pollution and divorce rates in Bowling Green, Kentucky, plays a melodious tune that beckons us to revel in the harmonious and unexpected connections that permeate the fabric of our world. As we gaze upon our findings, we are reminded that beneath the veneer of empirical rigidity lies a whimsical realm where statistical analysis and unexpected romances intertwine, inviting us to waltz in the delightful ballroom of intellectual inquiry.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of our study offer a compelling glimpse into the enigmatic relationship between air pollution and the dissolution of marriages in Bowling Green, Kentucky. Our findings not only substantiate the existing scholarly literature but also add a dash of whimsy to the rather staid world of environmental and social sciences.

Firstly, let's hearken back to the literature review, where we playfully toyed with the notion of fictional narratives bearing relevance to our perplexing conundrum. While an air-polluted Middle-earth may remain confined to the realm of fantasy, our research has illuminated a tangible connection between real-world air pollution and marital strain. Furthermore, the cinematic marvel "The Toxic Romance" seemed almost prescient, offering a poignant reflection of the entanglement of external surroundings and internal turmoil, much like the entwined fate of air pollution and divorce rates in our study.

Our study supported previous research, echoing the findings of "Smith and Doe" and "Jones et al.," which emphasized the intricate interplay between environmental factors and social dynamics. Much like the pages of "Breath: The New Science of a Lost Art" and "Polluted Marriage," our analysis has breathed new life into the discourse, revealing the palpable influence of air quality on relationship strain.

The substantial correlation coefficient and the whispering secrets of a low p-value in our statistical winds corroborate the unforeseen romance between environmental quality and marital upheaval. Just as J.R.R. Tolkien's characters embroiled themselves in an epic quest to purify the air of Middle-earth, our scholarly expedition has uncovered a compelling journey through the hidden realms of environmental and social dynamics, highlighting the uncanny allure of this unexpected liaison.

In conclusion, our results not only validate the association between air pollution in Bowling Green, Kentucky, and the dissolution of marriages throughout the state but also inject a sense of unpredictability and whimsy into the world of empirical investigation. This whimsical waltz between air pollution and marital discord invites scholars and enthusiasts alike to revel in the harmonious and unexpected connections that permeate the fabric of our world, challenging us to embrace the enchanting unpredictability that lies at the heart of statistical inquiry.

As we bask in the afterglow of this academic dalliance, we are reminded that beneath the sheen of empirical rigor lies a whimsical realm where statistical analysis and unexpected romances intertwine, beckoning us to pirouette in the delightful ballroom of intellectual inquiry.

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the 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 Bowling Green, Kentucky and The divorce rate in Kentucky. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
"Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky"

[[ABSTRACT]]
This research paper addresses the unexpected connection between air pollution in Bowling Green, Kentucky, and the divorce rate in the state. Utilizing data from the Environmental Protection Agency and CDC National Vital Statistics, we sought to uncover whether there was a match made in smog. Our findings revealed a surprisingly high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, indicating a strong relationship between the two factors. As we delved into this perplexing partnership, we were abuzz with excitement to uncover the unexpected interplay between air quality and marital status. This study serves as a breath of fresh air in the realm of environmental and social sciences as it unearths an unconventional romance between seemingly unrelated variables. We hope that our findings spark both interest and amusement and pave the way for further investigations into the whimsical world of air pollution and divorce dynamics.

[[INTRDUCTION]]
INTRODUCTION
In the realm of environmental and social sciences, researchers often seek to uncover the hidden connections between seemingly disparate phenomena. One might expect to find correlations between air pollution and respiratory illnesses, or between divorce rates and economic downturns. However, the captivating nature of statistical analysis lies in its ability to reveal unexpected relationships, much like stumbling upon a love connection in the unlikeliest of places.
Our study delves into the charming town of Bowling Green, Kentucky, where we stumbled upon a captivating courtship between air pollution and the dissolution of marriages. Much like star-crossed lovers, these two variables captured our attention and prompted us to embark on a journey to unravel their clandestine affair. As we waltzed through the data from the Environmental Protection Agency and CDC National Vital Statistics, we found ourselves irresistibly drawn deeper into this enchanting tango of environmental quality and marital harmony.
With a song in our hearts and a twinkle in our eyes, we set out to quantify the dance of air pollution and divorce rates. Our analysis revealed a remarkably high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, providing undeniable evidence of a strong relationship between these two enchanting variables. This statistical embrace between air pollution and divorce rates left us in breathless awe, challenging our preconceived notions and reaffirming the boundless potential for delightfully surprising discoveries.
Our findings beckon us to consider the whimsical interplay between environmental factors and social dynamics. The enchanting liaison between air pollution and marital discord takes center stage in our exploration, inviting researchers to expand their horizons and embrace the delightful unpredictability of statistical analysis. As we present our findings, we hope to infuse a dash of amusement and a sprinkle of curiosity into the scholarly discourse, inviting fellow enthusiasts to join us in unearthing the charming romances that lie beneath the surface of seemingly unrelated variables.
As we navigate this captivating terrain of statistical romance, we invite readers to accompany us on this waltz of discovery, where the unexpected delights in challenging our assumptions and tickles our intellectual curiosity. It is our fervent hope that this study will serve as a poetic ode to the enchanting dance between air pollution and the dissolution of marriages, sparking joy and merriment along the way. Join us in this whimsical exploration, where the winds of change and the bonds of matrimony intertwine in a captivating pas de deux unlike any other.

[[RESULTS]]
The results of our analysis unveiled a captivating relationship between air pollution in Bowling Green, Kentucky, and the dissolution of marriages throughout the state. The correlation coefficient of 0.8179517 indicated a striking alignment between these seemingly unrelated variables, akin to a surprise rendezvous at a masquerade ball. This substantial correlation, coupled with the r-squared value of 0.6690450, further emphasized the cozy entanglement of air pollution and divorce rates, much like a pair of lovebirds nesting in the branches of statistical significance.
The presence of a p-value less than 0.01 added an air of certainty to our findings, akin to a gust of wind carrying the sweet scent of academic validation. Indeed, the statistical winds whispered secrets of an unforeseen romance between environmental quality and marital upheaval, drawing us into the beguiling whirlwind of data exploration.
In Figure 1, our scatterplot elegantly portrays the amorous courtship between air pollution and divorce rates, serving as a visual testament to the magnetic allure of this unlikely liaison. The points on the plot embrace each other with a tender snugness, symbolizing the uncanny attraction between these two variables. One can almost hear the gentle rustle of statistical significance as the plot unfolds, beckoning us to ponder the beguiling dance of cause and effect.
As we reflect on the implications of our findings, we are reminded of the whimsical nature of statistical discovery. Much like uncorking a bottle of fine wine, our analysis has uncorked the enthralling complexities of environmental and social dynamics, leaving us intoxicated with both fascination and mirth. Our results stand as a testament to the captivating dalliance between air pollution and marital discord, inviting scholars and enthusiasts alike to embrace the enchanting unpredictability that lies at the heart of statistical inquiry.
This statistical symphony of air pollution and divorce rates in Bowling Green, Kentucky, plays a melodious tune that beckons us to revel in the harmonious and unexpected connections that permeate the fabric of our world. As we gaze upon our findings, we are reminded that beneath the veneer of empirical rigidity lies a whimsical realm where statistical analysis and unexpected romances intertwine, inviting us to waltz in the delightful ballroom of intellectual inquiry.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

CONCLUSION

In conclusion, our research has uncovered a captivating courtship between air pollution in Bowling Green, Kentucky, and the dissolution of marriages throughout the state. The robust correlation coefficient and p-value less than 0.01 have left us in awe, much like discovering a love letter hidden between the pages of a dry statistical tome. The dance of statistical significance has revealed an unexpectedly delightful duet between environmental quality and marital discord, surpassing even the most enchanting telenovela in its mesmerizing appeal.

As we bid adieu to this mesmerizing tango of data analysis, we are left with a lingering sense of wonder and amusement. It is as if the data itself has donned a masquerade mask, inviting us to revel in the playful intricacies of statistical exploration. Our findings, much like a bouquet of statistical roses, beckon us to appreciate the whimsical romance that unfolds in the unlikeliest of statistical pairings.

With an air of whimsy and a touch of statistical charm, we assert that no further research is needed in this area -- at least until we find another surprising statistical courtship to explore.

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 Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Sociological Quirkiness

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 Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky. Respond only with the name of a fictional organization.

ChatGPT:

The Center for Environmental and Sociological Studies

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 Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky with an abstract of This research paper addresses the unexpected connection between air pollution in Bowling Green, Kentucky, and the divorce rate in the state. Utilizing data from the Environmental Protection Agency and CDC National Vital Statistics, we sought to uncover whether there was a match made in smog. Our findings revealed a surprisingly high correlation coefficient of 0.8179517 and a p-value less than 0.01 from 1999 to 2021, indicating a strong relationship between the two factors. As we delved into this perplexing partnership, we were abuzz with excitement to uncover the unexpected interplay between air quality and marital status. This study serves as a breath of fresh air in the realm of environmental and social sciences as it unearths an unconventional romance between seemingly unrelated variables. We hope that our findings spark both interest and amusement and pave the way for further investigations into the whimsical world of air pollution and divorce dynamics.

ChatGPT:

Marriage Dissolution, Air Pollution, Bowling Green, Kentucky, Divorce Rate, Environmental Protection Agency, CDC National Vital Statistics, correlation coefficient, p-value, air quality, marital status, social sciences, environmental sciences, divorce dynamics

*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 Bowling Green, Kentucky
Detailed data title: Percentage of days with moderate or worse air quality in Bowling Green, KY
Source: Environmental Protection Agency
See what else correlates with Air pollution in Bowling Green, Kentucky

The divorce rate in Kentucky
Source: CDC National Vital Statistics
See what else correlates with The divorce rate in Kentucky

Correlation r = 0.8179517 (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 = 0.6690450 (Coefficient of determination)
This means 66.9% of the change in the one variable (i.e., The divorce rate in Kentucky) is predictable based on the change in the other (i.e., Air pollution in Bowling Green, Kentucky) over the 23 years from 1999 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.9E-6.^Show 0.0000018688971212506903000000
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 0.82 in 0.00019% of random cases. Said differently, if you correlated 535,075 random variables^Note You don't actually need 535 thousand 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 22 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 22 because we have two variables measured over a period of 23 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.

[ 0.61, 0.92 ] 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.

	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 Bowling Green, Kentucky (Bad air quality days)	0.531856	0.491803	0.40274	0.386301	0.378082	0.319672	0.4	0.339726	0.528767	0.382514	0.29589	0.394521	0.39726	0.314208	0.230137	0.219178	0.145205	0.224044	0.257534	0.232877	0.265753	0.150273	0.227397
The divorce rate in Kentucky (Divorce rate)	5.5	5.1	5.1	5.2	5	4.9	4.6	5	4.6	4.6	4.6	4.5	4.4	4.1	4.16263	3.84914	3.7023	3.78817	3.7266	3.54422	3.43311	3.13228	3.31064

Why this works

Data dredging: I have 25,237 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 636,906,169 correlation calculations! This is called “data dredging.” Instead of starting with a hypothesis and testing it, I instead abused the data to see what correlations shake out. It’s a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random.
Lack of causal connection: There is probably^Note Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple^Note Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
p-value calculation does not take this into account, so mathematically it appears less probable than it really is.

Try it yourself

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

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([0.531856,0.491803,0.40274,0.386301,0.378082,0.319672,0.4,0.339726,0.528767,0.382514,0.29589,0.394521,0.39726,0.314208,0.230137,0.219178,0.145205,0.224044,0.257534,0.232877,0.265753,0.150273,0.227397,])
array_2 = np.array([5.5,5.1,5.1,5.2,5,4.9,4.6,5,4.6,4.6,4.6,4.5,4.4,4.1,4.16263,3.84914,3.7023,3.78817,3.7266,3.54422,3.43311,3.13228,3.31064,])
array_1_name = "Air pollution in Bowling Green, Kentucky"
array_2_name = "The divorce rate in Kentucky"

# 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 Bowling Green, Kentucky
Line chart for only The divorce rate in Kentucky
AI-generated correlation image
The spurious research paper: Marriage Dissolution and Air Pollution: A Matching Pair in Bowling Green, Kentucky

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Correlation ID: 5560 · Black Variable ID: 21725 · Red Variable ID: 19801


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