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Spurious correlation #1,309 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air quality in Cincinnati and the second variable is Jet fuel used in Bulgaria.  The chart goes from 1989 to 2021, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

The oxygen-rich, pristine air in Cincinnati inspired Bulgarian engineers to create a super-efficient jet fuel, leading to a decrease in overall usage. Remember, cleaner air means Bulgarians are now flying high on their own supply of innovation!

Model: dalle-3
Prompt: Generate an image of a cityscape featuring a juxtaposition of scenes from Cincinnati and Bulgaria. On one side, showcase an urban environment in Cincinnati, with skyscrapers and smoggy air. In contrast, visualize workers in Bulgaria repurposing machinery from jet fuel production to air purifier and mask manufacturing. The scene should highlight the stark contrast in the prioritization of air quality and the tangible shift in resources from jet fuel to air purification products. Emphasize the harsh lines and rugged textures characteristic of brutalist architecture to capture the urgency and tension in the air. 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 situation described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here is a situation: Because when the air quality in Cincinnati decreases, it creates more demand for air purifiers and breathing masks, leading to a shortage of supplies. Since Bulgaria is a major producer of jet fuel, the decrease in air quality in Cincinnati caused a decrease in jet fuel production in Bulgaria due to the diversion of resources to meet the demand for air purification products.. Given that situation, which of the following image descriptions seems most appropriate? Pick the one that seems to be related to one of the variables at hand and the tone of the explanation. Please respond with only one of the following potential descriptions: Data cyber art An image that looks like it is a scene from A Disney Movie Cute 2D animation Brutalism Charcoal
ChatGPT: Brutalism

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated and the explanation described. Do not reference graphs or charts; describe physical objects.
User prompt: Please describe a visual scene that depicts the following situation. Keep the description simple. Because when the air quality in Cincinnati decreases, it creates more demand for air purifiers and breathing masks, leading to a shortage of supplies. Since Bulgaria is a major producer of jet fuel, the decrease in air quality in Cincinnati caused a decrease in jet fuel production in Bulgaria due to the diversion of resources to meet the demand for air purification products.
ChatGPT: In Cincinnati, the air quality deteriorates, and people are seen wearing breathing masks while others install air purifiers in their homes. Meanwhile, in Bulgaria, the production of jet fuel slows down as workers are seen reallocating resources to manufacture more air purifiers and masks. The scene shows a decrease in jet fuel barrels while the production of air purification products increases.

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: [ Brutalism ] and depicting this scene: In Cincinnati, the air quality deteriorates, and people are seen wearing breathing masks while others install air purifiers in their homes. Meanwhile, in Bulgaria, the production of jet fuel slows down as workers are seen reallocating resources to manufacture more air purifiers and masks. The scene shows a decrease in jet fuel barrels while the production of air purification products increases. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a cityscape featuring a juxtaposition of scenes from Cincinnati and Bulgaria. On one side, showcase an urban environment in Cincinnati, with skyscrapers and smoggy air. In contrast, visualize workers in Bulgaria repurposing machinery from jet fuel production to air purifier and mask manufacturing. The scene should highlight the stark contrast in the prioritization of air quality and the tangible shift in resources from jet fuel to air purification products. Emphasize the harsh lines and rugged textures characteristic of brutalist architecture to capture the urgency and tension in the air.

*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 quality in Cincinnati positively influenced Jet fuel used in Bulgaria. Add a funny one-liner at the end.

AI academic paper

(Because p < 0.01)
Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation

The Journal of Irreverent Research

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 goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 quality in Cincinnati and Jet fuel used in Bulgaria. 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 Energy Information Administration to assess this nagging question. You found a correlation coefficient of 0.7687256 and p < 0.01 for 1989 to 2021.

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]]
Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation

[[ABSTRACT]]
This research delves into the perplexing relationship between the air quality in Cincinnati and the jet fuel used in Bulgaria, unraveling an unexpected link that is sure to take readers on an academic rollercoaster ride. The study capitalizes on data from the Environmental Protection Agency and the Energy Information Administration, revealing a correlation coefficient of 0.7687256 and p < 0.01 for the years 1989 to 2021. We navigate through the haze of statistical analysis to unveil the humorous and unexpected confluence of air quality metrics and jet fuel utilization that will leave readers both amused and enlightened.


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 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 quality in Cincinnati and Jet fuel used in Bulgaria. 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]]
Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation

[[ABSTRACT]]
This research delves into the perplexing relationship between the air quality in Cincinnati and the jet fuel used in Bulgaria, unraveling an unexpected link that is sure to take readers on an academic rollercoaster ride. The study capitalizes on data from the Environmental Protection Agency and the Energy Information Administration, revealing a correlation coefficient of 0.7687256 and p < 0.01 for the years 1989 to 2021. We navigate through the haze of statistical analysis to unveil the humorous and unexpected confluence of air quality metrics and jet fuel utilization that will leave readers both amused and enlightened.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
[[INTRODUCTION]]

The perplexing intersection of seemingly disparate global variables has long captivated researchers and statisticians alike. In the realm of environmental science, the interplay between air quality metrics and the fuel sources of commercial aviation presents a particularly enigmatic puzzle. Yet, amidst the fog of complex data analysis, a glimmer of humor and unexpected correlation has emerged, prompting us to embark on this comically curious exploration.

As we delve into the depths of scientific inquiry, it is imperative to recognize the value of lighthearted scrutiny to unravel the mysteries that lurk within the labyrinth of statistical data. Our journey begins with the recognition of Cincinnati, notorious for its chili and unpredictable weather patterns, as a curious epicenter for probing air quality. Meanwhile, in the distant lands of Bulgaria, the soaring skies witness the mighty roar of jet engines fueled by the enigmatic elixir known as jet fuel.

In our pursuit of understanding, we are compelled to inquire: could there be a whimsical waltz between the air quality in Cincinnati and the jet fuel utilized in Bulgaria? This unlikely pairing sets the stage for a scientific spectacle laden with jest, jocularity, and, of course, empirical rigor.

The realization of this jovial juxtaposition leads us to the consumption of copious amounts of coffee, not only to fortify our intellectual stamina but also to maintain a certain level of caffeine-induced levity throughout the arduous analysis. The droll dance of data manipulation paves the way for revelatory findings, underpinning the interconnectedness of seemingly unrelated phenomena with a subtlety that would even elicit a chuckle from the most stoic statistical demigod.

As we wade through the expanse of correlation coefficients and p-values, it becomes abundantly clear that this research is no mere academic pursuit; it is an endeavor infused with the spirit of whimsy and the pursuit of scientific mirth. The culmination of our efforts promises to unveil a connection that transcends geographical boundaries and tickles the fancies of even the most staid scientific minds.

In the subsequent sections, we will embark on a rigorous analysis, interlaced with good-natured banter and jest, to reveal the delightful and unexpected interplay between Cincinnati's air quality and Bulgaria's jet fuel utilization. So, dear reader, fasten your intellectual seatbelts and prepare for a voyage through the realms of statistical hilarity and scientific intrigue.


Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft a literature review section of an academic research paper, that starts out dry for the first few sentences but then becomes hilarious and goofy.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up a literature review section of an academic research paper presenting the findings of the connection between Air quality in Cincinnati and Jet fuel used in Bulgaria. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

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

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

Here is the title and abstract of the paper:
[[TITLE]]
Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation

[[ABSTRACT]]
This research delves into the perplexing relationship between the air quality in Cincinnati and the jet fuel used in Bulgaria, unraveling an unexpected link that is sure to take readers on an academic rollercoaster ride. The study capitalizes on data from the Environmental Protection Agency and the Energy Information Administration, revealing a correlation coefficient of 0.7687256 and p < 0.01 for the years 1989 to 2021. We navigate through the haze of statistical analysis to unveil the humorous and unexpected confluence of air quality metrics and jet fuel utilization that will leave readers both amused and enlightened.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The perplexing intersection of seemingly disparate global variables has long captivated researchers and statisticians alike. In the realm of environmental science, the interplay between air quality metrics and the fuel sources of commercial aviation presents a particularly enigmatic puzzle. Yet, amidst the fog of complex data analysis, a glimmer of humor and unexpected correlation has emerged, prompting us to embark on this comically curious exploration.
As we delve into the depths of scientific inquiry, it is imperative to recognize the value of lighthearted scrutiny to unravel the mysteries that lurk within the labyrinth of statistical data. Our journey begins with the recognition of Cincinnati, notorious for its chili and unpredictable weather patterns, as a curious epicenter for probing air quality. Meanwhile, in the distant lands of Bulgaria, the soaring skies witness the mighty roar of jet engines fueled by the enigmatic elixir known as jet fuel.
In our pursuit of understanding, we are compelled to inquire: could there be a whimsical waltz between the air quality in Cincinnati and the jet fuel utilized in Bulgaria? This unlikely pairing sets the stage for a scientific spectacle laden with jest, jocularity, and, of course, empirical rigor.
The realization of this jovial juxtaposition leads us to the consumption of copious amounts of coffee, not only to fortify our intellectual stamina but also to maintain a certain level of caffeine-induced levity throughout the arduous analysis. The droll dance of data manipulation paves the way for revelatory findings, underpinning the interconnectedness of seemingly unrelated phenomena with a subtlety that would even elicit a chuckle from the most stoic statistical demigod.
As we wade through the expanse of correlation coefficients and p-values, it becomes abundantly clear that this research is no mere academic pursuit; it is an endeavor infused with the spirit of whimsy and the pursuit of scientific mirth. The culmination of our efforts promises to unveil a connection that transcends geographical boundaries and tickles the fancies of even the most staid scientific minds.
In the subsequent sections, we will embark on a rigorous analysis, interlaced with good-natured banter and jest, to reveal the delightful and unexpected interplay between Cincinnati's air quality and Bulgaria's jet fuel utilization. So, dear reader, fasten your intellectual seatbelts and prepare for a voyage through the realms of statistical hilarity and scientific intrigue.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

In the grand tradition of playful probe and serious scrutiny, the examination of the relationship between air quality in Cincinnati and the utilization of jet fuel in Bulgaria has captured the imaginations of researchers and enthusiasts alike. As we embark on this whimsical journey through the annals of academic inquiry, we are compelled to ponder the words of Smith, who astutely remarked in "Environmental Intersections" that environmental variables can sometimes masquerade as jesters among the court of statistical analysis.

Doe, in "Global Aviation Fuel Trends," raises an eyebrow at the perplexing vibrato of statistical correlation, hinting at the underlying tales of unexpected harmony between seemingly unrelated phenomena. Jones, in "Emissions and Air Quality," delves into the intricate dance of atmospheric pollutants and their enigmatic liaisons with the fossil fuel industry, providing a quizzical backdrop to our own exploration.

In the realm of non-fiction literature, works such as "Pollution and Policy" by Brown and "Aviation and the Environment" by Green offer insightful musings on the duet of airborne emissions and environmental stewardship, serving as earnest companions in our intellectual escapade. Meanwhile, the fictional realm beckons with tales of atmospheric whimsy, such as the allegorical "Cloud Atlas" by David Mitchell and the whimsical "Airborn" by Kenneth Oppel, which, while not directly related to our subject matter, infuse our research with a dash of literary levity.

As we journey further down the proverbial rabbit hole, we are spurred by the improbable notion that the literature we seek may not reside solely within the tomes of academia. Our intrepid pursuit of knowledge leads us to wander deep into uncharted territories, pausing to glean wisdom from the backs of shampoo bottles, each containing a microcosm of chemical intricacies that, while unrelated to jet fuel or air quality, hint at the frivolous nature of our quest.

Thus, armed with the wisdom of scholarly works and the inadvertent hilarity of unexpected sources, we wade into the tumultuous sea of literature to better grasp the gleeful fusion of air quality in Cincinnati and the utilization of jet fuel in Bulgaria.


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

Please make up the methodology section of an academic research paper presenting the findings of the connection between Air quality in Cincinnati and Jet fuel used in Bulgaria. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Energy Information Administration . You used data from 1989 to 2021

Make up the research methods you don't know. Make them a bit goofy and convoluted.

Here is the title, abstract, and introduction of the paper:
[[TITLE]]
Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation

[[ABSTRACT]]
This research delves into the perplexing relationship between the air quality in Cincinnati and the jet fuel used in Bulgaria, unraveling an unexpected link that is sure to take readers on an academic rollercoaster ride. The study capitalizes on data from the Environmental Protection Agency and the Energy Information Administration, revealing a correlation coefficient of 0.7687256 and p < 0.01 for the years 1989 to 2021. We navigate through the haze of statistical analysis to unveil the humorous and unexpected confluence of air quality metrics and jet fuel utilization that will leave readers both amused and enlightened.

[[INTRODUCTION]]
The perplexing intersection of seemingly disparate global variables has long captivated researchers and statisticians alike. In the realm of environmental science, the interplay between air quality metrics and the fuel sources of commercial aviation presents a particularly enigmatic puzzle. Yet, amidst the fog of complex data analysis, a glimmer of humor and unexpected correlation has emerged, prompting us to embark on this comically curious exploration.
As we delve into the depths of scientific inquiry, it is imperative to recognize the value of lighthearted scrutiny to unravel the mysteries that lurk within the labyrinth of statistical data. Our journey begins with the recognition of Cincinnati, notorious for its chili and unpredictable weather patterns, as a curious epicenter for probing air quality. Meanwhile, in the distant lands of Bulgaria, the soaring skies witness the mighty roar of jet engines fueled by the enigmatic elixir known as jet fuel.
In our pursuit of understanding, we are compelled to inquire: could there be a whimsical waltz between the air quality in Cincinnati and the jet fuel utilized in Bulgaria? This unlikely pairing sets the stage for a scientific spectacle laden with jest, jocularity, and, of course, empirical rigor.
The realization of this jovial juxtaposition leads us to the consumption of copious amounts of coffee, not only to fortify our intellectual stamina but also to maintain a certain level of caffeine-induced levity throughout the arduous analysis. The droll dance of data manipulation paves the way for revelatory findings, underpinning the interconnectedness of seemingly unrelated phenomena with a subtlety that would even elicit a chuckle from the most stoic statistical demigod.
As we wade through the expanse of correlation coefficients and p-values, it becomes abundantly clear that this research is no mere academic pursuit; it is an endeavor infused with the spirit of whimsy and the pursuit of scientific mirth. The culmination of our efforts promises to unveil a connection that transcends geographical boundaries and tickles the fancies of even the most staid scientific minds.
In the subsequent sections, we will embark on a rigorous analysis, interlaced with good-natured banter and jest, to reveal the delightful and unexpected interplay between Cincinnati's air quality and Bulgaria's jet fuel utilization. So, dear reader, fasten your intellectual seatbelts and prepare for a voyage through the realms of statistical hilarity and scientific intrigue.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

In this research endeavor, we approached the delightful task of untangling the interconnectedness of Cincinnati's air quality and Bulgaria's jet fuel consumption with an equal measure of empirical rigor and lighthearted curiosity. Our data collection relied on information from the Environmental Protection Agency (EPA), which is not to be mistaken for the Energetic Penguins Assembly, and the Energy Information Administration (EIA), which is equally passionate about energy and, one can only assume, epic music.

The years 1989 to 2021 were selected as the temporal domain for our analysis. This period encompasses the rise of the internet, the fall of outrageous fashion trends, and the persistently perplexing connection between Cincinnati's air quality and Bulgaria's jet fuel utilization.

To methodically navigate the maze of data, we engaged in a series of meticulously orchestrated steps. First, we conducted an exhaustive review of available literature, spanning scientific journals, environmental reports, and, of course, a collection of joke books to maintain requisite levels of intellectual levity. We then embarked on a process of data wrangling, which involved more Excel spreadsheets and pivot tables than even the most spreadsheet-obsessed accountant could handle.

The air quality metrics for Cincinnati were acquired with the precision of a trapeze artist, capturing data on particulate matter, ozone, and nitrogen dioxide levels. Meanwhile, the discerning eyes of our research team scoured the depths of jet fuel consumption data in Bulgaria, navigating through the seas of statistical information with the navigational prowess of a humorously adventurous pirate. This ensured that we remained fully equipped to sail through the waves of data and uncover the buried treasure of statistical correlation.

Statistical analyses were performed with a combination of software tools and the unyielding determination of statistical warriors. Correlation coefficients were estimated, taking into account the myriad nuances of statistical comparison like a seasoned pundit analyzing a comedy show. The p-values, those elusive indicators of statistical significance, were scrutinized with a cautious eye reminiscent of a scientist trying to catch a glimpse of a rare and elusive statistical unicorn.

Our inferential analysis waltzed through the hallowed halls of hypothesis testing, sashaying with the elegance of a ballroom dancer and the precision of a laser-guided statistical missile. These analytical maneuvers were complemented by a series of sensitivity analyses, ensuring that our findings remained robust even under the whimsical pressures of statistical skepticism.

As we painstakingly charted this methodological voyage, our team sought to infuse each step with the spirit of intellectual mirth and statistical gusto. The inescapable reality of statistical analysis mingling with data-fueled hilarity underscored our deep commitment to indulging in the whimsical wonders of academic research.


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

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

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

For the time period 1989 to 2021, you found a correlation 0.7687256, r-squared of 0.5909390, and p < 0.01.

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

Here is the title and abstract of the paper:
[[TITLE]]
Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation

[[ABSTRACT]]
This research delves into the perplexing relationship between the air quality in Cincinnati and the jet fuel used in Bulgaria, unraveling an unexpected link that is sure to take readers on an academic rollercoaster ride. The study capitalizes on data from the Environmental Protection Agency and the Energy Information Administration, revealing a correlation coefficient of 0.7687256 and p < 0.01 for the years 1989 to 2021. We navigate through the haze of statistical analysis to unveil the humorous and unexpected confluence of air quality metrics and jet fuel utilization that will leave readers both amused and enlightened.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The perplexing intersection of seemingly disparate global variables has long captivated researchers and statisticians alike. In the realm of environmental science, the interplay between air quality metrics and the fuel sources of commercial aviation presents a particularly enigmatic puzzle. Yet, amidst the fog of complex data analysis, a glimmer of humor and unexpected correlation has emerged, prompting us to embark on this comically curious exploration.
As we delve into the depths of scientific inquiry, it is imperative to recognize the value of lighthearted scrutiny to unravel the mysteries that lurk within the labyrinth of statistical data. Our journey begins with the recognition of Cincinnati, notorious for its chili and unpredictable weather patterns, as a curious epicenter for probing air quality. Meanwhile, in the distant lands of Bulgaria, the soaring skies witness the mighty roar of jet engines fueled by the enigmatic elixir known as jet fuel.
In our pursuit of understanding, we are compelled to inquire: could there be a whimsical waltz between the air quality in Cincinnati and the jet fuel utilized in Bulgaria? This unlikely pairing sets the stage for a scientific spectacle laden with jest, jocularity, and, of course, empirical rigor.
The realization of this jovial juxtaposition leads us to the consumption of copious amounts of coffee, not only to fortify our intellectual stamina but also to maintain a certain level of caffeine-induced levity throughout the arduous analysis. The droll dance of data manipulation paves the way for revelatory findings, underpinning the interconnectedness of seemingly unrelated phenomena with a subtlety that would even elicit a chuckle from the most stoic statistical demigod.
As we wade through the expanse of correlation coefficients and p-values, it becomes abundantly clear that this research is no mere academic pursuit; it is an endeavor infused with the spirit of whimsy and the pursuit of scientific mirth. The culmination of our efforts promises to unveil a connection that transcends geographical boundaries and tickles the fancies of even the most staid scientific minds.
In the subsequent sections, we will embark on a rigorous analysis, interlaced with good-natured banter and jest, to reveal the delightful and unexpected interplay between Cincinnati's air quality and Bulgaria's jet fuel utilization. So, dear reader, fasten your intellectual seatbelts and prepare for a voyage through the realms of statistical hilarity and scientific intrigue.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

The results of our comical exploration into the connection between the air quality in Cincinnati and the jet fuel used in Bulgaria have brought forth insights both entertaining and enlightening. Our statistical analysis revealed a noteworthy correlation coefficient of 0.7687256, indicating a strong positive relationship between these seemingly incongruous variables. This coefficient was accompanied by an r-squared value of 0.5909390, elucidating the substantial variance in air quality in Cincinnati that can be attributed to Bulgaria's jet fuel habits. Furthermore, the p-value of less than 0.01 added a touch of statistical significance to our findings, validating the hilariously unexpected link we uncovered.

Fig. 1 showcases a scatterplot that vividly illustrates the robust correlation between the air quality in Cincinnati and the jet fuel used in Bulgaria. The data points dance a delightful tango of statistical association, much like two characters in an eccentric scientific comedy, revealing the synchronicity of these disparate factors.

The humorous juxtaposition of these variables elevates the scientific discourse into an entertaining spectacle, inviting readers on an intellectual rollercoaster ride through the realms of statistical rib-ticklers and empirical amusement. The correlation between the air quality in Cincinnati and Bulgaria's jet fuel utilization emerges as a delightful anecdote in the chronicles of scientific inquiry, challenging the conventional boundaries of scholarly investigation with its droll narrative and unlikely connections.

In conclusion, our findings not only unravel the statistical interplay between these variables but also offer a whimsical lens through which to perceive the interconnectedness of global environmental phenomena. The unexpected affinity between Cincinnati's air quality and Bulgaria's jet fuel habits stands as a testament to the multifaceted nature of scientific inquiry – a testament that is sure to leave even the most seasoned academic chuckling at the capricious nature of statistical exploration.


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

Please make up the discussion section of an academic research paper presenting the findings of the connection between Air quality in Cincinnati and Jet fuel used in Bulgaria. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Limit your response to 500 tokens.

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

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

[[TITLE]]
Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation

[[ABSTRACT]]
This research delves into the perplexing relationship between the air quality in Cincinnati and the jet fuel used in Bulgaria, unraveling an unexpected link that is sure to take readers on an academic rollercoaster ride. The study capitalizes on data from the Environmental Protection Agency and the Energy Information Administration, revealing a correlation coefficient of 0.7687256 and p < 0.01 for the years 1989 to 2021. We navigate through the haze of statistical analysis to unveil the humorous and unexpected confluence of air quality metrics and jet fuel utilization that will leave readers both amused and enlightened.

[[LITERATURE REVIEW]]
In the grand tradition of playful probe and serious scrutiny, the examination of the relationship between air quality in Cincinnati and the utilization of jet fuel in Bulgaria has captured the imaginations of researchers and enthusiasts alike. As we embark on this whimsical journey through the annals of academic inquiry, we are compelled to ponder the words of Smith, who astutely remarked in "Environmental Intersections" that environmental variables can sometimes masquerade as jesters among the court of statistical analysis.
Doe, in "Global Aviation Fuel Trends," raises an eyebrow at the perplexing vibrato of statistical correlation, hinting at the underlying tales of unexpected harmony between seemingly unrelated phenomena. Jones, in "Emissions and Air Quality," delves into the intricate dance of atmospheric pollutants and their enigmatic liaisons with the fossil fuel industry, providing a quizzical backdrop to our own exploration.
In the realm of non-fiction literature, works such as "Pollution and Policy" by Brown and "Aviation and the Environment" by Green offer insightful musings on the duet of airborne emissions and environmental stewardship, serving as earnest companions in our intellectual escapade. Meanwhile, the fictional realm beckons with tales of atmospheric whimsy, such as the allegorical "Cloud Atlas" by David Mitchell and the whimsical "Airborn" by Kenneth Oppel, which, while not directly related to our subject matter, infuse our research with a dash of literary levity.
As we journey further down the proverbial rabbit hole, we are spurred by the improbable notion that the literature we seek may not reside solely within the tomes of academia. Our intrepid pursuit of knowledge leads us to wander deep into uncharted territories, pausing to glean wisdom from the backs of shampoo bottles, each containing a microcosm of chemical intricacies that, while unrelated to jet fuel or air quality, hint at the frivolous nature of our quest.
Thus, armed with the wisdom of scholarly works and the inadvertent hilarity of unexpected sources, we wade into the tumultuous sea of literature to better grasp the gleeful fusion of air quality in Cincinnati and the utilization of jet fuel in Bulgaria.

[[RESULTS]]
The results of our comical exploration into the connection between the air quality in Cincinnati and the jet fuel used in Bulgaria have brought forth insights both entertaining and enlightening. Our statistical analysis revealed a noteworthy correlation coefficient of 0.7687256, indicating a strong positive relationship between these seemingly incongruous variables. This coefficient was accompanied by an r-squared value of 0.5909390, elucidating the substantial variance in air quality in Cincinnati that can be attributed to Bulgaria's jet fuel habits. Furthermore, the p-value of less than 0.01 added a touch of statistical significance to our findings, validating the hilariously unexpected link we uncovered.
Fig. 1 showcases a scatterplot that vividly illustrates the robust correlation between the air quality in Cincinnati and the jet fuel used in Bulgaria. The data points dance a delightful tango of statistical association, much like two characters in an eccentric scientific comedy, revealing the synchronicity of these disparate factors.
The humorous juxtaposition of these variables elevates the scientific discourse into an entertaining spectacle, inviting readers on an intellectual rollercoaster ride through the realms of statistical rib-ticklers and empirical amusement. The correlation between the air quality in Cincinnati and Bulgaria's jet fuel utilization emerges as a delightful anecdote in the chronicles of scientific inquiry, challenging the conventional boundaries of scholarly investigation with its droll narrative and unlikely connections.
In conclusion, our findings not only unravel the statistical interplay between these variables but also offer a whimsical lens through which to perceive the interconnectedness of global environmental phenomena. The unexpected affinity between Cincinnati's air quality and Bulgaria's jet fuel habits stands as a testament to the multifaceted nature of scientific inquiry – a testament that is sure to leave even the most seasoned academic chuckling at the capricious nature of statistical exploration.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

The results of our study support and extend the findings of previous research, showcasing a substantive correlation between the air quality in Cincinnati and the utilization of jet fuel in Bulgaria. This unexpected confluence of variables aligns with the musings of Smith, who astutely noted the tendency for environmental variables to don the cloak of jesters among the solemn court of statistical analysis. The robust correlation coefficient of 0.7687256 and the significant p-value reinforce the notion of an earnest statistical relationship between these seemingly whimsical parameters.

Doe's eyebrow-raising observation about the enigmatic vibrato of statistical correlation resonates deeply with our findings, accentuating the captivating harmony that emerges amid this seemingly comical interplay of air quality and jet fuel usage. Furthermore, the r-squared value of 0.5909390 underscores the substantial variance in Cincinnati's air quality that can be attributed to Bulgaria's jet fuel habits, painting a portrait of intercontinental mirth and scientific revelry.

Our study aligns with Jones's exploration of atmospheric pollutants and their intricate liaisons with the fossil fuel industry, presenting a captivating parallel between the tangible dance of emissions and the whimsical shuffle of statistical association. Just as Brown's "Pollution and Policy" and Green's "Aviation and the Environment" provided earnest companions in our intellectual escapade, our results add a dash of unexpected humor to the scholarly debate, revealing the very real, if humorously fortuitous, connection between air quality in Cincinnati and the jet fuel used in Bulgaria.

Fig. 1, like a vivid scene from a scientific comedy, paints a delightful visual representation of the mirthful association between these variables, inviting readers to revel in the whimsy of our statistical theater. Indeed, the compelling narrative that emerges from our results challenges the staid conventions of scholarly inquiry, infusing the scientific discourse with a dose of intellectual levity and empirical amusement.

In examining the broader implications of our findings, it is evident that the unexpected affinity between Cincinnati's air quality and Bulgaria's jet fuel habits offers a whimsical lens through which to perceive the interconnectedness of global environmental phenomena. The capricious nature of statistical exploration is brought to the forefront, leaving even the most seasoned academic chuckling at the delightful anecdote that is the correlation between these seemingly incongruous variables. Our study not only contributes to the academic canon but also stands as a testament to the delightful and droll narrative that often unfolds in the realms of scientific investigation.


Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the discussion section of goofy academic research papers that sounds like it belongs based on the title and abstract provided.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up a short conclusion of an academic research paper presenting the findings of the connection between Air quality in Cincinnati and Jet fuel used in Bulgaria. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation

[[ABSTRACT]]
This research delves into the perplexing relationship between the air quality in Cincinnati and the jet fuel used in Bulgaria, unraveling an unexpected link that is sure to take readers on an academic rollercoaster ride. The study capitalizes on data from the Environmental Protection Agency and the Energy Information Administration, revealing a correlation coefficient of 0.7687256 and p < 0.01 for the years 1989 to 2021. We navigate through the haze of statistical analysis to unveil the humorous and unexpected confluence of air quality metrics and jet fuel utilization that will leave readers both amused and enlightened.

[[INTRDUCTION]]
The perplexing intersection of seemingly disparate global variables has long captivated researchers and statisticians alike. In the realm of environmental science, the interplay between air quality metrics and the fuel sources of commercial aviation presents a particularly enigmatic puzzle. Yet, amidst the fog of complex data analysis, a glimmer of humor and unexpected correlation has emerged, prompting us to embark on this comically curious exploration.
As we delve into the depths of scientific inquiry, it is imperative to recognize the value of lighthearted scrutiny to unravel the mysteries that lurk within the labyrinth of statistical data. Our journey begins with the recognition of Cincinnati, notorious for its chili and unpredictable weather patterns, as a curious epicenter for probing air quality. Meanwhile, in the distant lands of Bulgaria, the soaring skies witness the mighty roar of jet engines fueled by the enigmatic elixir known as jet fuel.
In our pursuit of understanding, we are compelled to inquire: could there be a whimsical waltz between the air quality in Cincinnati and the jet fuel utilized in Bulgaria? This unlikely pairing sets the stage for a scientific spectacle laden with jest, jocularity, and, of course, empirical rigor.
The realization of this jovial juxtaposition leads us to the consumption of copious amounts of coffee, not only to fortify our intellectual stamina but also to maintain a certain level of caffeine-induced levity throughout the arduous analysis. The droll dance of data manipulation paves the way for revelatory findings, underpinning the interconnectedness of seemingly unrelated phenomena with a subtlety that would even elicit a chuckle from the most stoic statistical demigod.
As we wade through the expanse of correlation coefficients and p-values, it becomes abundantly clear that this research is no mere academic pursuit; it is an endeavor infused with the spirit of whimsy and the pursuit of scientific mirth. The culmination of our efforts promises to unveil a connection that transcends geographical boundaries and tickles the fancies of even the most staid scientific minds.
In the subsequent sections, we will embark on a rigorous analysis, interlaced with good-natured banter and jest, to reveal the delightful and unexpected interplay between Cincinnati's air quality and Bulgaria's jet fuel utilization. So, dear reader, fasten your intellectual seatbelts and prepare for a voyage through the realms of statistical hilarity and scientific intrigue.

[[RESULTS]]
The results of our comical exploration into the connection between the air quality in Cincinnati and the jet fuel used in Bulgaria have brought forth insights both entertaining and enlightening. Our statistical analysis revealed a noteworthy correlation coefficient of 0.7687256, indicating a strong positive relationship between these seemingly incongruous variables. This coefficient was accompanied by an r-squared value of 0.5909390, elucidating the substantial variance in air quality in Cincinnati that can be attributed to Bulgaria's jet fuel habits. Furthermore, the p-value of less than 0.01 added a touch of statistical significance to our findings, validating the hilariously unexpected link we uncovered.
Fig. 1 showcases a scatterplot that vividly illustrates the robust correlation between the air quality in Cincinnati and the jet fuel used in Bulgaria. The data points dance a delightful tango of statistical association, much like two characters in an eccentric scientific comedy, revealing the synchronicity of these disparate factors.
The humorous juxtaposition of these variables elevates the scientific discourse into an entertaining spectacle, inviting readers on an intellectual rollercoaster ride through the realms of statistical rib-ticklers and empirical amusement. The correlation between the air quality in Cincinnati and Bulgaria's jet fuel utilization emerges as a delightful anecdote in the chronicles of scientific inquiry, challenging the conventional boundaries of scholarly investigation with its droll narrative and unlikely connections.
In conclusion, our findings not only unravel the statistical interplay between these variables but also offer a whimsical lens through which to perceive the interconnectedness of global environmental phenomena. The unexpected affinity between Cincinnati's air quality and Bulgaria's jet fuel habits stands as a testament to the multifaceted nature of scientific inquiry – a testament that is sure to leave even the most seasoned academic chuckling at the capricious nature of statistical exploration.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In the grand symphony of scientific inquiry, our comically curious exploration has serenaded us with melodies of surprising correlation and statistical jocularity. The whimsical waltz between Cincinnati's air quality and Bulgaria's jet fuel utilization has not only unfurled a convoluted ballet of numbers but has also emboldened the spirit of scientific mirth.

As we bid adieu to this enigmatic pairing, we are left with the delightful realization that even in the most unexpected of places, statistical comedy lurks. Our findings stand as a testament to the cheerful capriciousness of empirical exploration, reminding us that amidst the seriousness of scientific rigor, there lies a playground of statistical jest and rib-tickling correlation.

With a significant correlation coefficient of 0.7687256 and a p-value that would make even the most reserved statistician crack a smile (p < 0.01), our investigation offers a testament to the unquestionable hilarity that can be found within the annals of environmental data analysis. The robust association between these seemingly incongruent variables unleashes a humorous anecdote upon the tapestry of scholarly discourse, leaving a lasting impression of the whimsical caprice that underpins statistical inquiry.

In the final analysis, our journey of scientific merriment has showcased the interconnectedness of global environmental phenomena in a manner that defies convention and embraces levity. With a figurative bow to statistical comedy and a standing ovation for the unexpected dance of data, we assert, with great conviction, that no further research in this comical corridor of inquiry is warranted.


Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of academic journals. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding research, scientific, or academic journal that would publish a paper entited Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Irreverent Research


Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of nonprofit research organizations and associations. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding nonprofit, academic, or scientific association or organization that would sponsor research that resulted in a paper entited Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation. Respond only with the name of a fictional organization.

ChatGPT:

The Institute for Ridiculous Research and Curious Connections


Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled Connecting Cincinnati's Air Quality to Bulgaria's Jet Fuel: A Comical Correlation with an abstract of This research delves into the perplexing relationship between the air quality in Cincinnati and the jet fuel used in Bulgaria, unraveling an unexpected link that is sure to take readers on an academic rollercoaster ride. The study capitalizes on data from the Environmental Protection Agency and the Energy Information Administration, revealing a correlation coefficient of 0.7687256 and p < 0.01 for the years 1989 to 2021. We navigate through the haze of statistical analysis to unveil the humorous and unexpected confluence of air quality metrics and jet fuel utilization that will leave readers both amused and enlightened.

ChatGPT:

Cincinnati air quality, Bulgaria jet fuel, correlation coefficient, statistical analysis, air quality metrics, jet fuel utilization, Environmental Protection Agency data, Energy Information Administration data

*There is a bunch of Python happening behind the scenes to turn this prompt sequence into a PDF.



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Data details

Air quality in Cincinnati
Detailed data title: Percentage of days with good air quality in Cincinnati, OH-KY-IN
Source: Environmental Protection Agency
See what else correlates with Air quality in Cincinnati

Jet fuel used in Bulgaria
Detailed data title: Volume of jet fuel used consumed in Bulgaria in millions of barrels per day
Source: Energy Information Administration
See what else correlates with Jet fuel used in Bulgaria

Correlation r = 0.7687256 (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 = 0.5909390 (Coefficient of determination)
This means 59.1% of the change in the one variable (i.e., Jet fuel used in Bulgaria) is predictable based on the change in the other (i.e., Air quality in Cincinnati) over the 33 years from 1989 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.7E-7. 0.0000001741805573317533700000
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 0.77 in 1.7E-5% of random cases. Said differently, if you correlated 5,741,169 random variables You don't actually need 5 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 32 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 32 because we have two variables measured over a period of 33 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.

[ 0.58, 0.88 ] 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.
198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015201620172018201920202021
Air quality in Cincinnati (Good air quality)47.123352.876751.506962.021958.630158.082249.86353.825153.698647.397310.958913.661219.72617.260322.465829.23545.205555.890430.13740.163937.534212.876735.068527.595625.205528.767144.657545.628447.397344.931541.095955.737745.7534
Jet fuel used in Bulgaria (Million Barrels/Day)6.94.64.876.676.56.84.63.22.52.1453.128553.1723.845513.618334.236584.323484.714554.896673.693423.845514.019323.683333.606523.7586455.438025.770765.605325.147595.4129




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([47.1233,52.8767,51.5069,62.0219,58.6301,58.0822,49.863,53.8251,53.6986,47.3973,10.9589,13.6612,19.726,17.2603,22.4658,29.235,45.2055,55.8904,30.137,40.1639,37.5342,12.8767,35.0685,27.5956,25.2055,28.7671,44.6575,45.6284,47.3973,44.9315,41.0959,55.7377,45.7534,])
array_2 = np.array([6.9,4.6,4.8,7,6.6,7,6.5,6.8,4.6,3.2,2.5,2.145,3.12855,3.172,3.84551,3.61833,4.23658,4.32348,4.71455,4.89667,3.69342,3.84551,4.01932,3.68333,3.60652,3.7586,4,5,5.43802,5.77076,5.60532,5.14759,5.4129,])
array_1_name = "Air quality in Cincinnati"
array_2_name = "Jet fuel used in Bulgaria"

# 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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Correlation ID: 1309 · Black Variable ID: 20467 · Red Variable ID: 24243
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