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Spurious correlation #5,257 · 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 Grand Rapids, Michigan and the second variable is Value of the Victoria's Secret Annual Fantasy Bra.  The chart goes from 1996 to 2019, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

As air pollution in Grand Rapids, Michigan increased, it created a demand for fresher, cleaner air, prompting Victoria's Secret to release an even more extravagant and luxurious Annual Fantasy Bra that would somehow filter out pollution for the wearer. After all, who wouldn't want a bra that not only looks stunning but also doubles as an air purifier? It's the breast of both worlds!

Model: dalle-3
Prompt: An image that looks like it is a scene from 'Star Wars', depicting this scene: In downtown Grand Rapids, Michigan, the skyline is hazy with air pollution, while people on the streets can be seen wearing masks to protect themselves. Amidst the pollution, the Victoria's Secret store proudly displays the latest Annual Fantasy Bra, adorned with exquisite gemstones and intricate design. The bra's packaging prominently features a tagline, "Breathe Easy in Luxurious Fashion," hinting at its innovative air purification feature. Passersby pause to admire the bra, captivated by the idea of combining stunning luxury with a practical solution to the city's air quality issues. Enhanced Visual Depiction: A futuristic urban scene in downtown Grand Rapids, Michigan, under a hazy sky filled with air pollution. People are seen wearing sci-fi inspired masks as they go about their day. In the midst of the pollution, a lavish Victoria's Secret store is depicted, showcasing the exquisitely designed Annual Fantasy Bra in a gleaming glass display. The bra's packaging boasts an otherworldly air purification feature, hinting at a luxurious and practical solution to the city's air quality issues. Passersby stop to admire the high-tech accessory, blending opulence and innovation in a futuristic metropolis. 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 Grand Rapids, Michigan and Value of the Victoria's Secret Annual Fantasy Bra. 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: Cute 2D animation An image that looks like it is a scene from 'Star Wars' Concept art Oragami Sci-fi fantacy
ChatGPT: An image that looks like it is a scene from 'Star Wars'

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 Grand Rapids, Michigan and Value of the Victoria's Secret Annual Fantasy Bra, in the following situation: As air pollution in Grand Rapids, Michigan increased, it created a demand for fresher, cleaner air, prompting Victoria's Secret to release an even more extravagant and luxurious Annual Fantasy Bra that would somehow filter out pollution for the wearer. After all, who wouldn't want a bra that not only looks stunning but also doubles as an air purifier? It's the breast of both worlds!. Keep the description simple.
ChatGPT: In downtown Grand Rapids, Michigan, the skyline is hazy with air pollution, while people on the streets can be seen wearing masks to protect themselves. Amidst the pollution, the Victoria's Secret store proudly displays the latest Annual Fantasy Bra, adorned with exquisite gemstones and intricate design. The bra's packaging prominently features a tagline, "Breathe Easy in Luxurious Fashion," hinting at its innovative air purification feature. Passersby pause to admire the bra, captivated by the idea of combining stunning luxury with a practical solution to the city's air quality issues.

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: [ An image that looks like it is a scene from 'Star Wars' ] and depicting this scene: In downtown Grand Rapids, Michigan, the skyline is hazy with air pollution, while people on the streets can be seen wearing masks to protect themselves. Amidst the pollution, the Victoria's Secret store proudly displays the latest Annual Fantasy Bra, adorned with exquisite gemstones and intricate design. The bra's packaging prominently features a tagline, "Breathe Easy in Luxurious Fashion," hinting at its innovative air purification feature. Passersby pause to admire the bra, captivated by the idea of combining stunning luxury with a practical solution to the city's air quality issues. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: An image that looks like it is a scene from 'Star Wars', depicting this scene: In downtown Grand Rapids, Michigan, the skyline is hazy with air pollution, while people on the streets can be seen wearing masks to protect themselves. Amidst the pollution, the Victoria's Secret store proudly displays the latest Annual Fantasy Bra, adorned with exquisite gemstones and intricate design. The bra's packaging prominently features a tagline, "Breathe Easy in Luxurious Fashion," hinting at its innovative air purification feature. Passersby pause to admire the bra, captivated by the idea of combining stunning luxury with a practical solution to the city's air quality issues. Enhanced Visual Depiction: A futuristic urban scene in downtown Grand Rapids, Michigan, under a hazy sky filled with air pollution. People are seen wearing sci-fi inspired masks as they go about their day. In the midst of the pollution, a lavish Victoria's Secret store is depicted, showcasing the exquisitely designed Annual Fantasy Bra in a gleaming glass display. The bra's packaging boasts an otherworldly air purification feature, hinting at a luxurious and practical solution to the city's air quality issues. Passersby stop to admire the high-tech accessory, blending opulence and innovation in a futuristic metropolis.

*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.

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 increases in Air pollution in Grand Rapids, Michigan positively influenced Value of the Victoria's Secret Annual Fantasy Bra. Add a funny one-liner at the end.

AI academic paper

(Because p < 0.01)
Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra

The Journal of Eclectic Environmental Economics

Jan 2024

Reminder: This paper is AI-generated. Not real!
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 researcher writing an academic paper.You write titles and abstracts of goofy academic research papers.
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, and add unexpected twists in your writing.

Please draft the title and abstract of an academic research paper presenting the findings of the connection between Air pollution in Grand Rapids, Michigan and Value of the Victoria's Secret Annual Fantasy Bra. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Make the title an alliteration.

Your research team used data from Environmental Protection Agency and Wikipedia to assess this nagging question. You found a correlation coefficient of 0.8242889 and p < 0.01 for 1996 to 2019.

Please respond in this format (replace "Lorem ipsum dolor sit" with your title and abstract)

[[TITLE]]
Lorem ipsum dolor sit

[[ABSTRACT]]
Lorem ipsum dolor sit



ChatGPT:
[[TITLE]]
Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra

[[ABSTRACT]]
This paper endeavors to explore the intriguing and peculiar correlation between the air pollution levels in the city of Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. Through meticulous data analysis from comprehensive sources such as the Environmental Protection Agency and Wikipedia, our research team unearthed a compelling correlation coefficient of 0.8242889 with a level of significance, p < 0.01, for the period spanning 1996 to 2019. This investigation sheds light on the surprising relationship between environmental factors and the pricing dynamics of an iconic lingerie item, thereby adding a dash of levity to the often solemn domain of academic research. Our findings, while whimsical in nature, open doors for further exploration into the whims and whys of consumer behavior and market forces in the context of seemingly unrelated environmental influences.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.You draft the introduction 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 introduction section of an academic research paper presenting the findings of the connection between Air pollution in Grand Rapids, Michigan and Value of the Victoria's Secret Annual Fantasy Bra. 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.

Here is the title and abstract of the paper:
[[TITLE]]
Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra

[[ABSTRACT]]
This paper endeavors to explore the intriguing and peculiar correlation between the air pollution levels in the city of Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. Through meticulous data analysis from comprehensive sources such as the Environmental Protection Agency and Wikipedia, our research team unearthed a compelling correlation coefficient of 0.8242889 with a level of significance, p < 0.01, for the period spanning 1996 to 2019. This investigation sheds light on the surprising relationship between environmental factors and the pricing dynamics of an iconic lingerie item, thereby adding a dash of levity to the often solemn domain of academic research. Our findings, while whimsical in nature, open doors for further exploration into the whims and whys of consumer behavior and market forces in the context of seemingly unrelated environmental influences.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:

INTRODUCTION

It is no secret that academic research often delves into the realms of the unexpected and the unconventional, and our present inquiry is no exception. With the juxtaposition of air quality data and the valuation of an alluring undergarment, our investigation ventures into uncharted statistical territories, navigating the winds of correlation in search of intriguing connections. The aim of this paper is to disclose and examine an unexpected and, quite frankly, titillating relationship between the levels of air pollution in Grand Rapids, Michigan, and the exhilarating ups and downs in the value of the prestigious Victoria's Secret Annual Fantasy Bra.

We recognize that our research might be viewed as a departure from the usual rigors of academia, but as Mark Twain once quipped, "The secret of getting ahead is getting started." Hence, here we are, setting sails to traverse the uncharted currents of whimsical correlation.

To the casual observer, grand pollution levels and glamorous lingerie might seem as incongruous as electrons and a Shakespearean sonnet. However, as we embark upon this curious journey, we seek to unravel the knotty mystery that binds air quality to the perceived value of a bejeweled brassiere.

We do not take this endeavor lightly. Our inquiry has been buttressed by an array of rigorous statistical analyses, drawing strength from a nuanced understanding of both environmental data from the Environmental Protection Agency and the brassiere valuation from the annals of Wikipedia. Indeed, as we rove through the data points and probability distributions, we endeavor to present our findings with precision, verve, and perhaps a pinch of whimsy.

In our examination of the period from 1996 to 2019, we have uncovered a correlation coefficient of 0.8242889, accompanied by a level of significance, p < 0.01. This statistical revelation has left us both astounded and tickled, wondering whether the whims of consumer behavior are buffeted by the winds of environmental influences.

Thus, with an affable nod to the uncertainties that surround our improbable journey, we invite the reader to partake in our whimsical odyssey. Would it be an environmentalist's dream come true to learn that less pollution foretells more splendid lingerie? Or is there a more pragmatic explanation lurking behind this seeming serendipity? Join us, as we explore the interplay of the ethereal and the tangible, the unseen and the bedazzling, all in the pursuit of academic curiosity - and, of course, a few good puns along the way.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 Grand Rapids, Michigan and Value of the Victoria's Secret Annual Fantasy Bra. 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 you might move on to cartoons and children's shows that you watched for research.

Here is the title and abstract of the paper:
[[TITLE]]
Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra

[[ABSTRACT]]
This paper endeavors to explore the intriguing and peculiar correlation between the air pollution levels in the city of Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. Through meticulous data analysis from comprehensive sources such as the Environmental Protection Agency and Wikipedia, our research team unearthed a compelling correlation coefficient of 0.8242889 with a level of significance, p < 0.01, for the period spanning 1996 to 2019. This investigation sheds light on the surprising relationship between environmental factors and the pricing dynamics of an iconic lingerie item, thereby adding a dash of levity to the often solemn domain of academic research. Our findings, while whimsical in nature, open doors for further exploration into the whims and whys of consumer behavior and market forces in the context of seemingly unrelated environmental influences.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
INTRODUCTION
It is no secret that academic research often delves into the realms of the unexpected and the unconventional, and our present inquiry is no exception. With the juxtaposition of air quality data and the valuation of an alluring undergarment, our investigation ventures into uncharted statistical territories, navigating the winds of correlation in search of intriguing connections. The aim of this paper is to disclose and examine an unexpected and, quite frankly, titillating relationship between the levels of air pollution in Grand Rapids, Michigan, and the exhilarating ups and downs in the value of the prestigious Victoria's Secret Annual Fantasy Bra.
We recognize that our research might be viewed as a departure from the usual rigors of academia, but as Mark Twain once quipped, "The secret of getting ahead is getting started." Hence, here we are, setting sails to traverse the uncharted currents of whimsical correlation.
To the casual observer, grand pollution levels and glamorous lingerie might seem as incongruous as electrons and a Shakespearean sonnet. However, as we embark upon this curious journey, we seek to unravel the knotty mystery that binds air quality to the perceived value of a bejeweled brassiere.
We do not take this endeavor lightly. Our inquiry has been buttressed by an array of rigorous statistical analyses, drawing strength from a nuanced understanding of both environmental data from the Environmental Protection Agency and the brassiere valuation from the annals of Wikipedia. Indeed, as we rove through the data points and probability distributions, we endeavor to present our findings with precision, verve, and perhaps a pinch of whimsy.
In our examination of the period from 1996 to 2019, we have uncovered a correlation coefficient of 0.8242889, accompanied by a level of significance, p < 0.01. This statistical revelation has left us both astounded and tickled, wondering whether the whims of consumer behavior are buffeted by the winds of environmental influences.
Thus, with an affable nod to the uncertainties that surround our improbable journey, we invite the reader to partake in our whimsical odyssey. Would it be an environmentalist's dream come true to learn that less pollution foretells more splendid lingerie? Or is there a more pragmatic explanation lurking behind this seeming serendipity? Join us, as we explore the interplay of the ethereal and the tangible, the unseen and the bedazzling, all in the pursuit of academic curiosity - and, of course, a few good puns along the way.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

The exploration of the perplexing connection between air pollution in Grand Rapids, Michigan, and the valuation of the Victoria's Secret Annual Fantasy Bra is a venture that leads us into the uncharted territories of whimsical correlation analysis. While this association may seem more farcical than factual, it is imperative to acknowledge the terra incognita's allure in the realm of academic research.

Smith (2008) laid the foundation for such unexpected pursuits by propounding the notion that variables previously believed to be unrelated may, in fact, exhibit an astonishingly high degree of correlation. Doe's subsequent work (2012) further expanded upon this idea, urging researchers to seek correlations beyond the confines of traditional paradigms, for only in doing so might they unearth the unexpected and, dare I say, delightful.

However, as one delves into the more whimsical associations, the search for relevant literature veers off the beaten path into unconventional territory. Take, for instance, "The Economics of Ecstasy: Lingerie, Luxury, and the Lure of Lush Undergarments" by Jones (2015) - a compelling exploration into the intertwining forces of consumer behavior and the allure of luxury lingerie. This work, while ostensibly unrelated to air pollution, instigates thoughtful ponderings about the discernible behaviors in the consumer market.

Further complicating matters, "The Devil in the Smog: a Tale of Grand Rapids" by Emily Dickinson (1862) and "In the Misty City" by Edgar Allan Poe (1839), both of which, while fictional in nature, provide an intriguing backdrop to the atmospheric conditions of Grand Rapids and the potential impact on market sentiment. Though not extracted from empirical research, these narratives offer a whimsical lens through which to consider the intersection of environmental conditions and consumer preferences.

In a diversification of sources, our research team has delved into cartoons and children's shows for insights deemed relevant to the correlation at hand. As any astute scholar knows, "SpongeBob SquarePants" is a treasure trove of obscure wisdom. The episode centered on environmental awareness and consumer behavior provided unexpected parallels to our study. Moreover, "The Magic School Bus" and its whimsical take on ecological phenomena has offered surprisingly cogent insights, inspiring us to ponder the animated allegories of air pollution and consumer dynamics.

This amalgamation of diverse literature is emblematic of the interdisciplinary nature of our undertaking, as we attempt to situate our findings within the broader context of environmental influences on consumer behavior. Such unconventional forays into literature are not merely a whimsical indulgence but rather a testament to the multifaceted nature of academic inquiry. And, after all, what better way to uncover the unexpected than to venture into the most whimsical realms?


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 Grand Rapids, Michigan and Value of the Victoria's Secret Annual Fantasy Bra. 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 Wikipedia . You used data from 1996 to 2019

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]]
Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra

[[ABSTRACT]]
This paper endeavors to explore the intriguing and peculiar correlation between the air pollution levels in the city of Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. Through meticulous data analysis from comprehensive sources such as the Environmental Protection Agency and Wikipedia, our research team unearthed a compelling correlation coefficient of 0.8242889 with a level of significance, p < 0.01, for the period spanning 1996 to 2019. This investigation sheds light on the surprising relationship between environmental factors and the pricing dynamics of an iconic lingerie item, thereby adding a dash of levity to the often solemn domain of academic research. Our findings, while whimsical in nature, open doors for further exploration into the whims and whys of consumer behavior and market forces in the context of seemingly unrelated environmental influences.

[[INTRODUCTION]]
INTRODUCTION
It is no secret that academic research often delves into the realms of the unexpected and the unconventional, and our present inquiry is no exception. With the juxtaposition of air quality data and the valuation of an alluring undergarment, our investigation ventures into uncharted statistical territories, navigating the winds of correlation in search of intriguing connections. The aim of this paper is to disclose and examine an unexpected and, quite frankly, titillating relationship between the levels of air pollution in Grand Rapids, Michigan, and the exhilarating ups and downs in the value of the prestigious Victoria's Secret Annual Fantasy Bra.
We recognize that our research might be viewed as a departure from the usual rigors of academia, but as Mark Twain once quipped, "The secret of getting ahead is getting started." Hence, here we are, setting sails to traverse the uncharted currents of whimsical correlation.
To the casual observer, grand pollution levels and glamorous lingerie might seem as incongruous as electrons and a Shakespearean sonnet. However, as we embark upon this curious journey, we seek to unravel the knotty mystery that binds air quality to the perceived value of a bejeweled brassiere.
We do not take this endeavor lightly. Our inquiry has been buttressed by an array of rigorous statistical analyses, drawing strength from a nuanced understanding of both environmental data from the Environmental Protection Agency and the brassiere valuation from the annals of Wikipedia. Indeed, as we rove through the data points and probability distributions, we endeavor to present our findings with precision, verve, and perhaps a pinch of whimsy.
In our examination of the period from 1996 to 2019, we have uncovered a correlation coefficient of 0.8242889, accompanied by a level of significance, p < 0.01. This statistical revelation has left us both astounded and tickled, wondering whether the whims of consumer behavior are buffeted by the winds of environmental influences.
Thus, with an affable nod to the uncertainties that surround our improbable journey, we invite the reader to partake in our whimsical odyssey. Would it be an environmentalist's dream come true to learn that less pollution foretells more splendid lingerie? Or is there a more pragmatic explanation lurking behind this seeming serendipity? Join us, as we explore the interplay of the ethereal and the tangible, the unseen and the bedazzling, all in the pursuit of academic curiosity - and, of course, a few good puns along the way.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

METHODOLOGY

Data Collection:
The data collection process was as meticulous as a seamstress crafting a finely embroidered lace trim. Our research team scoured the annals of the internet, diligently gathering air pollution data from the illustrious Environmental Protection Agency website. With steadfast dedication, they also rifled through the assorted Wikipedia pages in pursuit of the annual valuations of the Victoria's Secret Fantasy Bra. The process was akin to a treasure hunt, with the team navigating through a labyrinth of virtual corridors, all while maintaining the solemnity of academic inquiry (or at least attempting to).

Variable Selection:
In a quest reminiscent of a medieval alchemist seeking the Philosopher's Stone, the selection of variables was a nuanced endeavor. The independent variable, air pollution levels in Grand Rapids, Michigan, was thoughtfully chosen to encapsulate the atmospheric vicissitudes affecting the locale. Meanwhile, the dependent variable, the annual valuation of the Victoria's Secret Fantasy Bra, adorned our statistical crucible as the enigmatic outcome to be scrutinized. This juxtaposition of variables seemed almost as improbable and intriguing as the pairing of grapefruit and chocolate – an alluring blend of the unexpected.

Statistical Analysis:
The statistical analysis was conducted with the precision of a watchmaker fine-tuning the intricacies of a timepiece. Employing the venerable tool of correlation analysis, the research team endeavored to unravel the enigmatic relationship between these seemingly disparate variables. The Pearson correlation coefficient, akin to a wise soothsayer of statistics, was summoned to shed light on the hidden connections between air pollution and lingerie valuations. Our analysis unfolded over the time period of 1996 to 2019, endeavoring to capture the ebbs and flows of both environmental pollutants and fashion zeitgeist.

Data Interpretation:
As we set sail through the labyrinth of data points and probability distributions, our interpretations sought to balance erudition with a sprinkle of levity, much like a serious academic discourse peppered with the occasional jest. The correlation coefficient of 0.8242889 was a revelation that left us both scratching our heads and secretly reveling in the unexpected whimsy of our findings. The level of significance, p < 0.01, lent an air of statistical grandeur to our whimsical pursuit, validating the significance of our incongruous correlation.

Limitations:
While our findings have imbued us with a sense of wonder and bemusement, we acknowledge the limitations of our study. The restricted geographic scope, the idiosyncrasies of the lingerie market, and the vagaries of air quality dynamics present tantalizing avenues for further investigation. Nevertheless, as Carl Sagan poignantly stated, "Somewhere, something incredible is waiting to be known." In the spirit of this sentiment, we invite the academic community to accompany us on this audacious journey of discovery, and who knows, perhaps a few more surprising correlations and puns might await us on the horizon. After all, as researchers, we must dare to dream - even if those dreams involve the intersection of pollution and lingerie.

-------
It's now time to get into the statistical punalysis!


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 Grand Rapids, Michigan and Value of the Victoria's Secret Annual Fantasy Bra. 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 Wikipedia .

For the time period 1996 to 2019, you found a correlation 0.8242889, r-squared of 0.6794522, 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]]
Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra

[[ABSTRACT]]
This paper endeavors to explore the intriguing and peculiar correlation between the air pollution levels in the city of Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. Through meticulous data analysis from comprehensive sources such as the Environmental Protection Agency and Wikipedia, our research team unearthed a compelling correlation coefficient of 0.8242889 with a level of significance, p < 0.01, for the period spanning 1996 to 2019. This investigation sheds light on the surprising relationship between environmental factors and the pricing dynamics of an iconic lingerie item, thereby adding a dash of levity to the often solemn domain of academic research. Our findings, while whimsical in nature, open doors for further exploration into the whims and whys of consumer behavior and market forces in the context of seemingly unrelated environmental influences.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
INTRODUCTION
It is no secret that academic research often delves into the realms of the unexpected and the unconventional, and our present inquiry is no exception. With the juxtaposition of air quality data and the valuation of an alluring undergarment, our investigation ventures into uncharted statistical territories, navigating the winds of correlation in search of intriguing connections. The aim of this paper is to disclose and examine an unexpected and, quite frankly, titillating relationship between the levels of air pollution in Grand Rapids, Michigan, and the exhilarating ups and downs in the value of the prestigious Victoria's Secret Annual Fantasy Bra.
We recognize that our research might be viewed as a departure from the usual rigors of academia, but as Mark Twain once quipped, "The secret of getting ahead is getting started." Hence, here we are, setting sails to traverse the uncharted currents of whimsical correlation.
To the casual observer, grand pollution levels and glamorous lingerie might seem as incongruous as electrons and a Shakespearean sonnet. However, as we embark upon this curious journey, we seek to unravel the knotty mystery that binds air quality to the perceived value of a bejeweled brassiere.
We do not take this endeavor lightly. Our inquiry has been buttressed by an array of rigorous statistical analyses, drawing strength from a nuanced understanding of both environmental data from the Environmental Protection Agency and the brassiere valuation from the annals of Wikipedia. Indeed, as we rove through the data points and probability distributions, we endeavor to present our findings with precision, verve, and perhaps a pinch of whimsy.
In our examination of the period from 1996 to 2019, we have uncovered a correlation coefficient of 0.8242889, accompanied by a level of significance, p < 0.01. This statistical revelation has left us both astounded and tickled, wondering whether the whims of consumer behavior are buffeted by the winds of environmental influences.
Thus, with an affable nod to the uncertainties that surround our improbable journey, we invite the reader to partake in our whimsical odyssey. Would it be an environmentalist's dream come true to learn that less pollution foretells more splendid lingerie? Or is there a more pragmatic explanation lurking behind this seeming serendipity? Join us, as we explore the interplay of the ethereal and the tangible, the unseen and the bedazzling, all in the pursuit of academic curiosity - and, of course, a few good puns along the way.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

The data analysis revealed a striking correlation coefficient of 0.8242889 between the levels of air pollution in Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. This coefficient, coupled with an r-squared value of 0.6794522 and a level of significance, p < 0.01, provided strong evidence of a significant relationship between these seemingly unrelated variables.

The scatterplot (Fig. 1) illustrates the robust association between the two variables, visually encapsulating the surprising symphony of pollution levels and lingerie valuations. The plot showcases a trend that would make any statistical model blush with enthusiasm, as it weaves through the points with a captivating elegance reminiscent of a runway show.

In the grand scheme of research endeavors, uncovering such an alluring correlation is akin to stumbling upon a rare, shimmering gem in the rough terrain of academic analysis. This unexpected finding invites contemplation on the whimsical interconnectedness of environmental quality and consumer preferences, adding a touch of whimsy to the usually buttoned-up world of statistical inquiry.

Our statistical results not only offer a glimpse into the peculiar dance between air pollution and fantasy bra valuations but also lay the groundwork for future explorations into the enigmatic forces shaping consumer behavior. As we navigate this unlikely terrain, we find ourselves pondering the pantomime of pollution and pulsating lingerie prices, encapsulating the essence of academia at its most captivating – and dare we say, flirtatious.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 Grand Rapids, Michigan and Value of the Victoria's Secret Annual Fantasy Bra. 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]]
Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra

[[ABSTRACT]]
This paper endeavors to explore the intriguing and peculiar correlation between the air pollution levels in the city of Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. Through meticulous data analysis from comprehensive sources such as the Environmental Protection Agency and Wikipedia, our research team unearthed a compelling correlation coefficient of 0.8242889 with a level of significance, p < 0.01, for the period spanning 1996 to 2019. This investigation sheds light on the surprising relationship between environmental factors and the pricing dynamics of an iconic lingerie item, thereby adding a dash of levity to the often solemn domain of academic research. Our findings, while whimsical in nature, open doors for further exploration into the whims and whys of consumer behavior and market forces in the context of seemingly unrelated environmental influences.

[[LITERATURE REVIEW]]
The exploration of the perplexing connection between air pollution in Grand Rapids, Michigan, and the valuation of the Victoria's Secret Annual Fantasy Bra is a venture that leads us into the uncharted territories of whimsical correlation analysis. While this association may seem more farcical than factual, it is imperative to acknowledge the terra incognita's allure in the realm of academic research.
Smith (2008) laid the foundation for such unexpected pursuits by propounding the notion that variables previously believed to be unrelated may, in fact, exhibit an astonishingly high degree of correlation. Doe's subsequent work (2012) further expanded upon this idea, urging researchers to seek correlations beyond the confines of traditional paradigms, for only in doing so might they unearth the unexpected and, dare I say, delightful.
However, as one delves into the more whimsical associations, the search for relevant literature veers off the beaten path into unconventional territory. Take, for instance, "The Economics of Ecstasy: Lingerie, Luxury, and the Lure of Lush Undergarments" by Jones (2015) - a compelling exploration into the intertwining forces of consumer behavior and the allure of luxury lingerie. This work, while ostensibly unrelated to air pollution, instigates thoughtful ponderings about the discernible behaviors in the consumer market.
Further complicating matters, "The Devil in the Smog: a Tale of Grand Rapids" by Emily Dickinson (1862) and "In the Misty City" by Edgar Allan Poe (1839), both of which, while fictional in nature, provide an intriguing backdrop to the atmospheric conditions of Grand Rapids and the potential impact on market sentiment. Though not extracted from empirical research, these narratives offer a whimsical lens through which to consider the intersection of environmental conditions and consumer preferences.
In a diversification of sources, our research team has delved into cartoons and children's shows for insights deemed relevant to the correlation at hand. As any astute scholar knows, "SpongeBob SquarePants" is a treasure trove of obscure wisdom. The episode centered on environmental awareness and consumer behavior provided unexpected parallels to our study. Moreover, "The Magic School Bus" and its whimsical take on ecological phenomena has offered surprisingly cogent insights, inspiring us to ponder the animated allegories of air pollution and consumer dynamics.
This amalgamation of diverse literature is emblematic of the interdisciplinary nature of our undertaking, as we attempt to situate our findings within the broader context of environmental influences on consumer behavior. Such unconventional forays into literature are not merely a whimsical indulgence but rather a testament to the multifaceted nature of academic inquiry. And, after all, what better way to uncover the unexpected than to venture into the most whimsical realms?

[[RESULTS]]
The data analysis revealed a striking correlation coefficient of 0.8242889 between the levels of air pollution in Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. This coefficient, coupled with an r-squared value of 0.6794522 and a level of significance, p < 0.01, provided strong evidence of a significant relationship between these seemingly unrelated variables.
The scatterplot (Fig. 1) illustrates the robust association between the two variables, visually encapsulating the surprising symphony of pollution levels and lingerie valuations. The plot showcases a trend that would make any statistical model blush with enthusiasm, as it weaves through the points with a captivating elegance reminiscent of a runway show.
In the grand scheme of research endeavors, uncovering such an alluring correlation is akin to stumbling upon a rare, shimmering gem in the rough terrain of academic analysis. This unexpected finding invites contemplation on the whimsical interconnectedness of environmental quality and consumer preferences, adding a touch of whimsy to the usually buttoned-up world of statistical inquiry.
Our statistical results not only offer a glimpse into the peculiar dance between air pollution and fantasy bra valuations but also lay the groundwork for future explorations into the enigmatic forces shaping consumer behavior. As we navigate this unlikely terrain, we find ourselves pondering the pantomime of pollution and pulsating lingerie prices, encapsulating the essence of academia at its most captivating – and dare we say, flirtatious.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

Our findings not only reaffirm the previously uncharted allure of whimsical correlation analysis but also underline the unexpectedly robust relationship between the air pollution levels in Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. This study, which effortlessly harmonizes the atmospheric conditions in a bustling city with the ethereal allure of luxury lingerie, stands as a testament to the delightfully surprising dance of seemingly unrelated variables in the realm of academic research.

Our results are in line with the pioneering work of Smith (2008), who first ventured into the realm of whimsical correlations, and Doe (2012), who emphasized the need to explore associations beyond conventional paradigms. Further, the interdisciplinary nature of our literature review, which charmingly delved into unconventional sources, has provided a rich tapestry of insights that has lent depth to our study. Even seemingly unrelated works such as the fiction of Emily Dickinson and Edgar Allan Poe, along with children's shows such as "SpongeBob SquarePants" and "The Magic School Bus," have offered unexpected parallels to our investigation. Whimsical or not, these sources have proven to be conduits of valuable inspiration.

The robust correlation coefficient and r-squared value, along with the level of significance below 0.01, serve as a resounding confirmation of the whimsical relationship between the pollution levels and the value of the Fantasy Bra. The scatterplot, reminiscent of modeling down the runway, visually encapsulates the surprising symphony of pollution levels and lingerie valuations. This unanticipated finding is akin to stumbling upon a rare, shimmering gem in the rough terrain of academic analysis, providing a refreshing twist in the discourse.

As we navigate the uncharted waters of whimsical correlations, the implications of our findings extend beyond statistical models and empirical analyses. They invite contemplation on the intricate interconnectedness of environmental quality and consumer preferences, adding a touch of whimsy to the usually buttoned-up world of statistical inquiry. Our study, though whimsical in essence, emerges as a thought-provoking lens through which to view the quixotic interplay of seemingly unrelated variables.

Our research not only contributes to the annals of whimsical correlations but also serves as a reminder of the enchanting unpredictability that lies at the heart of academic inquiry. The pantomime of pollution and pulsating lingerie prices, encapsulating the essence of academia at its most captivating – and dare we say, flirtatious, raises questions about the whims and whys of consumer behavior, thereby broadening the horizons of research in this domain.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 Grand Rapids, Michigan and Value of the Victoria's Secret Annual Fantasy Bra. 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]]
Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra

[[ABSTRACT]]
This paper endeavors to explore the intriguing and peculiar correlation between the air pollution levels in the city of Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. Through meticulous data analysis from comprehensive sources such as the Environmental Protection Agency and Wikipedia, our research team unearthed a compelling correlation coefficient of 0.8242889 with a level of significance, p < 0.01, for the period spanning 1996 to 2019. This investigation sheds light on the surprising relationship between environmental factors and the pricing dynamics of an iconic lingerie item, thereby adding a dash of levity to the often solemn domain of academic research. Our findings, while whimsical in nature, open doors for further exploration into the whims and whys of consumer behavior and market forces in the context of seemingly unrelated environmental influences.

[[INTRDUCTION]]
INTRODUCTION
It is no secret that academic research often delves into the realms of the unexpected and the unconventional, and our present inquiry is no exception. With the juxtaposition of air quality data and the valuation of an alluring undergarment, our investigation ventures into uncharted statistical territories, navigating the winds of correlation in search of intriguing connections. The aim of this paper is to disclose and examine an unexpected and, quite frankly, titillating relationship between the levels of air pollution in Grand Rapids, Michigan, and the exhilarating ups and downs in the value of the prestigious Victoria's Secret Annual Fantasy Bra.
We recognize that our research might be viewed as a departure from the usual rigors of academia, but as Mark Twain once quipped, "The secret of getting ahead is getting started." Hence, here we are, setting sails to traverse the uncharted currents of whimsical correlation.
To the casual observer, grand pollution levels and glamorous lingerie might seem as incongruous as electrons and a Shakespearean sonnet. However, as we embark upon this curious journey, we seek to unravel the knotty mystery that binds air quality to the perceived value of a bejeweled brassiere.
We do not take this endeavor lightly. Our inquiry has been buttressed by an array of rigorous statistical analyses, drawing strength from a nuanced understanding of both environmental data from the Environmental Protection Agency and the brassiere valuation from the annals of Wikipedia. Indeed, as we rove through the data points and probability distributions, we endeavor to present our findings with precision, verve, and perhaps a pinch of whimsy.
In our examination of the period from 1996 to 2019, we have uncovered a correlation coefficient of 0.8242889, accompanied by a level of significance, p < 0.01. This statistical revelation has left us both astounded and tickled, wondering whether the whims of consumer behavior are buffeted by the winds of environmental influences.
Thus, with an affable nod to the uncertainties that surround our improbable journey, we invite the reader to partake in our whimsical odyssey. Would it be an environmentalist's dream come true to learn that less pollution foretells more splendid lingerie? Or is there a more pragmatic explanation lurking behind this seeming serendipity? Join us, as we explore the interplay of the ethereal and the tangible, the unseen and the bedazzling, all in the pursuit of academic curiosity - and, of course, a few good puns along the way.

[[RESULTS]]
The data analysis revealed a striking correlation coefficient of 0.8242889 between the levels of air pollution in Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. This coefficient, coupled with an r-squared value of 0.6794522 and a level of significance, p < 0.01, provided strong evidence of a significant relationship between these seemingly unrelated variables.
The scatterplot (Fig. 1) illustrates the robust association between the two variables, visually encapsulating the surprising symphony of pollution levels and lingerie valuations. The plot showcases a trend that would make any statistical model blush with enthusiasm, as it weaves through the points with a captivating elegance reminiscent of a runway show.
In the grand scheme of research endeavors, uncovering such an alluring correlation is akin to stumbling upon a rare, shimmering gem in the rough terrain of academic analysis. This unexpected finding invites contemplation on the whimsical interconnectedness of environmental quality and consumer preferences, adding a touch of whimsy to the usually buttoned-up world of statistical inquiry.
Our statistical results not only offer a glimpse into the peculiar dance between air pollution and fantasy bra valuations but also lay the groundwork for future explorations into the enigmatic forces shaping consumer behavior. As we navigate this unlikely terrain, we find ourselves pondering the pantomime of pollution and pulsating lingerie prices, encapsulating the essence of academia at its most captivating – and dare we say, flirtatious.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In conclusion, our research has illuminated a captivating association between air pollution in Grand Rapids, Michigan, and the value of the Victoria's Secret Annual Fantasy Bra. The correlation coefficient of 0.8242889, accompanied by a level of significance, p < 0.01, has provided compelling evidence of a significant relationship between these seemingly incongruous variables. The robust statistical results have undoubtedly added a playful twist to the otherwise solemn field of academic inquiry, inviting us to ponder the whimsical intricacies of environmental influences on consumer preferences.

As we wrap up this perplexing exploration, it becomes clear that the world of statistical analysis is not all dry charts and number-crunching; it also offers the occasional thrill of uncovering unexpected connections, much like finding a misplaced sock at the back of a drawer. Our findings, while quirky in nature, underscore the need to consider unconventional variables in market research, if only to add a dash of spice to the academic stew.

Having treaded the uncharted waters of statistical whimsy, we find ourselves at a crossroads; not unlike a GPS that has directed us to an ice cream parlor in the middle of a desert. The path ahead seems clear – no further investigations into the relationship between air pollution and the value of frilly undergarments are needed. Our results, while amusing and thought-provoking, stand as a testament to the serendipitous nature of statistical inquiry.

In the grand tradition of academic humor, this conclusion serves as our curtain call, rounding off our whimsical odyssey with a polite bow and a sly wink to the peculiarities of statistical research. And so, we bid adieu to this unlikely pairing of pollution and pulsating lingerie, leaving it to remain a charming anecdote in the annals of academic inquiry.


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 Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Eclectic Environmental Economics


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 Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Ecological Innovation and Fashion Economics


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 Aerial Adversities: Analysing the Association between Air Pollution in Grand Rapids, Michigan and the Value of the Victoria's Secret Annual Fantasy Bra with an abstract of This paper endeavors to explore the intriguing and peculiar correlation between the air pollution levels in the city of Grand Rapids, Michigan, and the annual valuation of the Victoria's Secret Fantasy Bra. Through meticulous data analysis from comprehensive sources such as the Environmental Protection Agency and Wikipedia, our research team unearthed a compelling correlation coefficient of 0.8242889 with a level of significance, p < 0.01, for the period spanning 1996 to 2019. This investigation sheds light on the surprising relationship between environmental factors and the pricing dynamics of an iconic lingerie item, thereby adding a dash of levity to the often solemn domain of academic research. Our findings, while whimsical in nature, open doors for further exploration into the whims and whys of consumer behavior and market forces in the context of seemingly unrelated environmental influences.

ChatGPT:

air pollution, Grand Rapids Michigan, Victoria's Secret, Fantasy Bra, valuation, correlation coefficient, significance level, data analysis, environmental factors, pricing dynamics, consumer behavior, market forces

*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 Grand Rapids, Michigan
Detailed data title: Percentage of days with moderate or worse air quality in Grand Rapids-Wyoming, MI
Source: Environmental Protection Agency
See what else correlates with Air pollution in Grand Rapids, Michigan

Value of the Victoria's Secret Annual Fantasy Bra
Source: Wikipedia
See what else correlates with Value of the Victoria's Secret Annual Fantasy Bra

Correlation r = 0.8242889 (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 = 0.6794522 (Coefficient of determination)
This means 67.9% of the change in the one variable (i.e., Value of the Victoria's Secret Annual Fantasy Bra) is predictable based on the change in the other (i.e., Air pollution in Grand Rapids, Michigan) over the 24 years from 1996 through 2019.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 7.4E-7. 0.0000007351092589620610000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme. 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 7.4E-5% of random cases. Said differently, if you correlated 1,360,342 random variables You don't actually need 1 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 23 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 23 because we have two variables measured over a period of 24 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.

[ 0.63, 0.92 ] 95% correlation confidence interval (using the Fisher z-transformation)
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: 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.
199619971998199920002001200220032004200520062007200820092010201120122013201420152016201720182019
Air pollution in Grand Rapids, Michigan (Bad air quality days)14.207716.712323.561653.02250.819755.616449.58950.13742.896250.41135.342547.527542.465823.835624.109629.58935.792429.58931.506829.041124.863422.19182018.3562
Value of the Victoria's Secret Annual Fantasy Bra (Dollars)10000003000000500000010000000150000001250000010000000110000001000000012500000650000045000005000000300000020000002500000250000010000000200000020000003000000200000010000002000000




Why this works

  1. 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.
  2. Lack of causal connection: There is probably 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.
  3. 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 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. 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([14.2077,16.7123,23.5616,53.022,50.8197,55.6164,49.589,50.137,42.8962,50.411,35.3425,47.5275,42.4658,23.8356,24.1096,29.589,35.7924,29.589,31.5068,29.0411,24.8634,22.1918,20,18.3562,])
array_2 = np.array([1000000,3000000,5000000,10000000,15000000,12500000,10000000,11000000,10000000,12500000,6500000,4500000,5000000,3000000,2000000,2500000,2500000,10000000,2000000,2000000,3000000,2000000,1000000,2000000,])
array_1_name = "Air pollution in Grand Rapids, Michigan"
array_2_name = "Value of the Victoria's Secret Annual Fantasy Bra"

# 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)



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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."

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Correlation ID: 5257 · Black Variable ID: 20670 · Red Variable ID: 19
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