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Spurious correlation #3,025 · 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 Columbus, Georgia and the second variable is Barclays' stock price (BCS).  The chart goes from 2002 to 2023, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

As air pollution in Columbus, Georgia increased, it led to the production of more airborne particles. These particles, being excellent reflectors of sunlight, acted as a makeshift barrier, reducing the amount of sunlight reaching the ground. This unexpected shade created localized cooling, leading residents to use their air conditioners less frequently. The decreased demand for electricity meant lower operational costs for businesses, including Barclays. With reduced expenses, Barclays' bottom line improved, boosting investor confidence and ultimately lifting their stock price. It's like Mother Nature decided to give Barclays a breath of fresh (albeit polluted) air!

Model: dalle-3
Prompt: Generate an image of a futuristic and vibrant city skyline of Columbus, Georgia, where clean, clear blue skies are visible. People can be seen gathered outdoors, engaging in picnics and barbecues in vibrant green parks beneath the clear skies. The air is filled with the aroma of sizzling barbecue, and a soaring demand for barbecue sauce is visually represented. Additionally, incorporate a digital stock exchange board displaying the rapid climb of Barclays' stock price (BCS) as a result of their successful investment in a BBQ sauce startup. 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 Columbus, Georgia and Barclays' stock price (BCS). 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: Whimsical illustration High-tech Sci-fi fantacy Voxel art Brutalism
ChatGPT: High-tech

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 Columbus, Georgia and Barclays' stock price (BCS), in the following situation: Because as air pollution decreased in Columbus, Georgia, people started spending more time outdoors, leading to an increase in barbecues. As a result, the demand for barbeque sauce skyrocketed, boosting the stock prices of companies like Barclays, who just so happened to recently invest in a BBQ sauce startup.. Keep the description simple.
ChatGPT: In Columbus, Georgia, the skyline clears as air pollution decreases. People gather outdoors, enjoying picnics and barbecues under clear blue skies. The aroma of sizzling barbecue fills the air as the demand for barbecue sauce soars. Meanwhile, on the stock exchange, Barclays' stock price (BCS) climbs rapidly as the company's recent investment in a BBQ sauce startup pays off.

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: [ High-tech ] and depicting this scene: In Columbus, Georgia, the skyline clears as air pollution decreases. People gather outdoors, enjoying picnics and barbecues under clear blue skies. The aroma of sizzling barbecue fills the air as the demand for barbecue sauce soars. Meanwhile, on the stock exchange, Barclays' stock price (BCS) climbs rapidly as the company's recent investment in a BBQ sauce startup pays off. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a futuristic and vibrant city skyline of Columbus, Georgia, where clean, clear blue skies are visible. People can be seen gathered outdoors, engaging in picnics and barbecues in vibrant green parks beneath the clear skies. The air is filled with the aroma of sizzling barbecue, and a soaring demand for barbecue sauce is visually represented. Additionally, incorporate a digital stock exchange board displaying the rapid climb of Barclays' stock price (BCS) as a result of their successful investment in a BBQ sauce startup.

*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 Columbus, Georgia positively influenced Barclays' stock price (BCS).

AI academic paper

(Because p < 0.01)
The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price

The Journal of Financial Atmospheric Science

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 silly 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 Columbus, Georgia and Barclays' stock price (BCS). Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Make the title punny if you can come up with clever pun. If not, make it sound serious.

Your research team used data from Environmental Protection Agency and LSEG Analytics (Refinitiv) to assess this nagging question. You found a correlation coefficient of 0.9366056 and p < 0.01 for 2002 to 2023.

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]]
The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price

[[ABSTRACT]]
In this study, we examine the potentially smoggy relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). Harnessing data from the Environmental Protection Agency and LSEG Analytics. Our findings indicated a remarkably robust correlation coefficient of 0.9366056, with a significance level of p < 0.01, covering the period from 2002 to 2023. The results suggest that the impact of air pollution extends beyond respiratory health, reaching into the financial realm, quite literally "fouling the air" of the stock market. We delve into the potential implications of these findings, offering a breath of fresh air in understanding the connection between environmental factors and financial markets.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 Columbus, Georgia and Barclays' stock price (BCS). Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Here is the title and abstract of the paper:
[[TITLE]]
The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price

[[ABSTRACT]]
In this study, we examine the potentially smoggy relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). Harnessing data from the Environmental Protection Agency and LSEG Analytics. Our findings indicated a remarkably robust correlation coefficient of 0.9366056, with a significance level of p < 0.01, covering the period from 2002 to 2023. The results suggest that the impact of air pollution extends beyond respiratory health, reaching into the financial realm, quite literally "fouling the air" of the stock market. We delve into the potential implications of these findings, offering a breath of fresh air in understanding the connection between environmental factors and financial markets.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
[[INTRODUCTION]]

The intersection of environmental factors and financial markets has long been a subject of intrigue and debate. The notion that air pollution, a seemingly distant and ethereal phenomenon, could have tangible effects on the stock market may raise a few eyebrows, perhaps even prompting one to exclaim, "Are we really blowing this out of proportion?" However, as we take a deep breath and explore the link between air pollution levels in Columbus, Georgia and the stock price of Barclays (BCS), we begin to uncover a narrative that may very well leave us gasping for air.

The city of Columbus, Georgia, located alongside the Chattahoochee River, has experienced its fair share of industrial activity and vehicular emissions, creating an atmospheric backdrop that is not without its smoggy character. Meanwhile, Barclays, a global financial institution with a presence on the London Stock Exchange, has ridden the waves of market tumult and economic volatility. If one were to take a deep inhale and ponder the possibility of these seemingly disparate entities coming together in an unexpected dance, akin to a tango between Wall Street and Main Street, the resulting connection may just leave them breathless.

In this study, we endeavor to unravel the interplay between these two seemingly unrelated domains. By weaving together data on air pollution levels in Columbus, Georgia, sourced from the Environmental Protection Agency's meticulous records, with stock price history from LSEG Analytics, we aim to shine a light on a correlation that may have previously been obscured by the hazy clouds of speculation. Our findings, showcasing a correlation coefficient of 0.9366056, pique curiosity and prompt us to ponder whether we are indeed sniffing out a significant relationship or merely experiencing a statistical mirage.

As we embark on this journey, let us not underestimate the potential implications of our discoveries. Could the impact of air pollution extend beyond respiratory health, infiltrating the financial realm with an unexpected and unwelcome presence? Might we find that, through environmental footprints and stock market footfalls, we are bearing witness to a connection that is not only nose-worthy but also has far-reaching ramifications?

Upon this curious crossroads of air quality and stock prices, we invite you to join us in unpacking the implications of our findings, offering a breath of fresh air in understanding the relationship between environmental factors and financial markets. So, sit back, take a deep breath, and prepare yourself for a journey that may leave you not only pondering economic indicators but also contemplating the literal winds of change.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 Columbus, Georgia and Barclays' stock price (BCS). 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. Perhaps you also got inspiration from some board games that are vaugely related.

Here is the title and abstract of the paper:
[[TITLE]]
The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price

[[ABSTRACT]]
In this study, we examine the potentially smoggy relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). Harnessing data from the Environmental Protection Agency and LSEG Analytics. Our findings indicated a remarkably robust correlation coefficient of 0.9366056, with a significance level of p < 0.01, covering the period from 2002 to 2023. The results suggest that the impact of air pollution extends beyond respiratory health, reaching into the financial realm, quite literally "fouling the air" of the stock market. We delve into the potential implications of these findings, offering a breath of fresh air in understanding the connection between environmental factors and financial markets.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The intersection of environmental factors and financial markets has long been a subject of intrigue and debate. The notion that air pollution, a seemingly distant and ethereal phenomenon, could have tangible effects on the stock market may raise a few eyebrows, perhaps even prompting one to exclaim, "Are we really blowing this out of proportion?" However, as we take a deep breath and explore the link between air pollution levels in Columbus, Georgia and the stock price of Barclays (BCS), we begin to uncover a narrative that may very well leave us gasping for air.
The city of Columbus, Georgia, located alongside the Chattahoochee River, has experienced its fair share of industrial activity and vehicular emissions, creating an atmospheric backdrop that is not without its smoggy character. Meanwhile, Barclays, a global financial institution with a presence on the London Stock Exchange, has ridden the waves of market tumult and economic volatility. If one were to take a deep inhale and ponder the possibility of these seemingly disparate entities coming together in an unexpected dance, akin to a tango between Wall Street and Main Street, the resulting connection may just leave them breathless.
In this study, we endeavor to unravel the interplay between these two seemingly unrelated domains. By weaving together data on air pollution levels in Columbus, Georgia, sourced from the Environmental Protection Agency's meticulous records, with stock price history from LSEG Analytics, we aim to shine a light on a correlation that may have previously been obscured by the hazy clouds of speculation. Our findings, showcasing a correlation coefficient of 0.9366056, pique curiosity and prompt us to ponder whether we are indeed sniffing out a significant relationship or merely experiencing a statistical mirage.
As we embark on this journey, let us not underestimate the potential implications of our discoveries. Could the impact of air pollution extend beyond respiratory health, infiltrating the financial realm with an unexpected and unwelcome presence? Might we find that, through environmental footprints and stock market footfalls, we are bearing witness to a connection that is not only nose-worthy but also has far-reaching ramifications?
Upon this curious crossroads of air quality and stock prices, we invite you to join us in unpacking the implications of our findings, offering a breath of fresh air in understanding the relationship between environmental factors and financial markets. So, sit back, take a deep breath, and prepare yourself for a journey that may leave you not only pondering economic indicators but also contemplating the literal winds of change.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

The present study represents a groundbreaking endeavor to investigate the intersection of environmental factors and financial markets, focusing on the relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). We wish to inhale the sweet aroma of knowledge and exhale the scents of insight in delving into this unexplored territory. Our review of the existing literature uncovers a trove of research that expands upon the nuanced interplay between air quality and financial valuations, painting a picture that is not only intriguing but also flush with potential implications.

Smith and Doe (2015) conducted a comprehensive analysis of air pollution's impact on economic indicators, exposing the hidden costs of environmental degradation. Their findings shed light on the smoggy specter that looms over financial markets, hinting at a tailwind of consequences that may have been previously overlooked. Meanwhile, Jones et al. (2018) offer a detailed examination of the reverberations of air pollution on urban centers, presenting a canvas of insights that extends beyond the mere visibility of skyscrapers. Their work underscores the importance of considering the atmospherics of financial hubs when evaluating market trends, elevating the discourse to a level that is, dare we say, breath-taking.

Building upon this foundation, we draw inspiration from non-fiction tomes that delve into the intricacies of environmental economics and market forces. "The Economics of Pollution" by Smith (2019) brings an analytical lens to the conversation, dissecting the ramifications of pollution on economic vitality. In a similar vein, "Environmental Regulations and Stock Market Performance" by Doe (2020) delves into the regulatory landscape and its impact on financial valuations, providing a panoramic view that extends beyond the horizon of traditional market analyses.

In a delightful departure from the expected, we encounter fiction works that, while not rooted in empirical data, offer a whimsical reflection of the interplay between air quality and financial fortitude. "Mist and Markets: A Tale of Two Fogs" by Forster (1920) transports readers to a world where the misty tendrils of smog intertwine with the ebbs and flows of market dynamics, inviting us to ponder the foggy implications of environmental factors on financial destinies. Similarly, "The Airborne Alchemist" by Rowling (1999) weaves a spellbinding narrative that fuses the alchemy of air quality with the sorcery of stock prices, creating a concoction that is both intoxicating and mystifying.

Additionally, we draw upon the insights offered by board games that tangentially relate to our investigation. "Pollution Peril: The Board Game" compels players to navigate the treacherous terrain of pollution management and financial risk, consistently reminding us that the winds of change may carry a scent that is not easily ignored.

As we embark on this comedic stroll through the literature, we implore readers to suspend their disbelief and embrace the wondrous tapestry of knowledge that emerges when we merge the serious with the lighthearted. Our journey is just beginning, and we invite you to join us in inhaling the fragrant possibilities that arise when unconventional connections are brought to light. Keep your sense of humor close at hand – after all, when it comes to the relationship between air pollution and stock prices, the forecast may just be a mix of wit and whimsy.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 Columbus, Georgia and Barclays' stock price (BCS). Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and LSEG Analytics (Refinitiv) . You used data from 2002 to 2023

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]]
The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price

[[ABSTRACT]]
In this study, we examine the potentially smoggy relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). Harnessing data from the Environmental Protection Agency and LSEG Analytics. Our findings indicated a remarkably robust correlation coefficient of 0.9366056, with a significance level of p < 0.01, covering the period from 2002 to 2023. The results suggest that the impact of air pollution extends beyond respiratory health, reaching into the financial realm, quite literally "fouling the air" of the stock market. We delve into the potential implications of these findings, offering a breath of fresh air in understanding the connection between environmental factors and financial markets.

[[INTRODUCTION]]
The intersection of environmental factors and financial markets has long been a subject of intrigue and debate. The notion that air pollution, a seemingly distant and ethereal phenomenon, could have tangible effects on the stock market may raise a few eyebrows, perhaps even prompting one to exclaim, "Are we really blowing this out of proportion?" However, as we take a deep breath and explore the link between air pollution levels in Columbus, Georgia and the stock price of Barclays (BCS), we begin to uncover a narrative that may very well leave us gasping for air.
The city of Columbus, Georgia, located alongside the Chattahoochee River, has experienced its fair share of industrial activity and vehicular emissions, creating an atmospheric backdrop that is not without its smoggy character. Meanwhile, Barclays, a global financial institution with a presence on the London Stock Exchange, has ridden the waves of market tumult and economic volatility. If one were to take a deep inhale and ponder the possibility of these seemingly disparate entities coming together in an unexpected dance, akin to a tango between Wall Street and Main Street, the resulting connection may just leave them breathless.
In this study, we endeavor to unravel the interplay between these two seemingly unrelated domains. By weaving together data on air pollution levels in Columbus, Georgia, sourced from the Environmental Protection Agency's meticulous records, with stock price history from LSEG Analytics, we aim to shine a light on a correlation that may have previously been obscured by the hazy clouds of speculation. Our findings, showcasing a correlation coefficient of 0.9366056, pique curiosity and prompt us to ponder whether we are indeed sniffing out a significant relationship or merely experiencing a statistical mirage.
As we embark on this journey, let us not underestimate the potential implications of our discoveries. Could the impact of air pollution extend beyond respiratory health, infiltrating the financial realm with an unexpected and unwelcome presence? Might we find that, through environmental footprints and stock market footfalls, we are bearing witness to a connection that is not only nose-worthy but also has far-reaching ramifications?
Upon this curious crossroads of air quality and stock prices, we invite you to join us in unpacking the implications of our findings, offering a breath of fresh air in understanding the relationship between environmental factors and financial markets. So, sit back, take a deep breath, and prepare yourself for a journey that may leave you not only pondering economic indicators but also contemplating the literal winds of change.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

To investigate the potentially foggy relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS), a comprehensive and multi-faceted approach was adopted. The data collection process resembled a treasure hunt as we scoured the digital seas, with the Environmental Protection Agency and LSEG Analytics (Refinitiv) serving as our trusty treasure maps.

First, we cast our net wide to catch the historical air quality data in Columbus, Georgia, from the Environmental Protection Agency's voluminous records. This involved navigating through a sea of digital data, akin to venturing through the fog of a misty morning, and extracting pertinent air pollution data such as particulate matter (PM2.5 and PM10), nitrogen dioxide (NO2), sulfur dioxide (SO2), and ozone (O3) concentrations. We then performed rigorous quality checks, ensuring that our dataset was as clean and pure as the fresh country air, or at least as close as we could get in the realm of data collection.

Meanwhile, as the sun rose over the financial markets, we sauntered through the stock price history of Barclays (BCS) using the LSEG Analytics (Refinitiv) platform. This journey resembled navigating the ebbs and flows of the tides, with each stock price movement akin to the gentle lapping of waves against the shore. We collected the daily closing prices of Barclays (BCS) stock from 2002 to 2023, ensuring that our dataset was as robust as the financial institution it represented.

With our data sets in hand, we subjected them to a battery of statistical analyses that would have made any arithmetic enthusiast raise their eyebrows in interest. We calculated daily averages of air pollution levels and examined how they related to the corresponding daily stock prices, employing correlation analyses with the gravitas of a detective solving a mystery. Additionally, we injected some econometric models to account for potential confounding factors, ensuring that our findings were as crystal clear as a breath of fresh air.

This methodology allowed us to uncover a relationship that went beyond the mere statistical correlation, navigating through the headwinds and tailwinds of methodological rigor to provide an expansive view of the relationship between air pollution in Columbus, Georgia, and Barclays' stock price. So, as we set sail on this methodological voyage, we present our findings with a hearty dose of statistical confidence and a touch of whimsy, inviting fellow explorers to join us in unlocking the mysteries of this curious crossroads.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 Columbus, Georgia and Barclays' stock price (BCS). Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and LSEG Analytics (Refinitiv) .

For the time period 2002 to 2023, you found a correlation 0.9366056, r-squared of 0.8772300, 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]]
The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price

[[ABSTRACT]]
In this study, we examine the potentially smoggy relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). Harnessing data from the Environmental Protection Agency and LSEG Analytics. Our findings indicated a remarkably robust correlation coefficient of 0.9366056, with a significance level of p < 0.01, covering the period from 2002 to 2023. The results suggest that the impact of air pollution extends beyond respiratory health, reaching into the financial realm, quite literally "fouling the air" of the stock market. We delve into the potential implications of these findings, offering a breath of fresh air in understanding the connection between environmental factors and financial markets.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The intersection of environmental factors and financial markets has long been a subject of intrigue and debate. The notion that air pollution, a seemingly distant and ethereal phenomenon, could have tangible effects on the stock market may raise a few eyebrows, perhaps even prompting one to exclaim, "Are we really blowing this out of proportion?" However, as we take a deep breath and explore the link between air pollution levels in Columbus, Georgia and the stock price of Barclays (BCS), we begin to uncover a narrative that may very well leave us gasping for air.
The city of Columbus, Georgia, located alongside the Chattahoochee River, has experienced its fair share of industrial activity and vehicular emissions, creating an atmospheric backdrop that is not without its smoggy character. Meanwhile, Barclays, a global financial institution with a presence on the London Stock Exchange, has ridden the waves of market tumult and economic volatility. If one were to take a deep inhale and ponder the possibility of these seemingly disparate entities coming together in an unexpected dance, akin to a tango between Wall Street and Main Street, the resulting connection may just leave them breathless.
In this study, we endeavor to unravel the interplay between these two seemingly unrelated domains. By weaving together data on air pollution levels in Columbus, Georgia, sourced from the Environmental Protection Agency's meticulous records, with stock price history from LSEG Analytics, we aim to shine a light on a correlation that may have previously been obscured by the hazy clouds of speculation. Our findings, showcasing a correlation coefficient of 0.9366056, pique curiosity and prompt us to ponder whether we are indeed sniffing out a significant relationship or merely experiencing a statistical mirage.
As we embark on this journey, let us not underestimate the potential implications of our discoveries. Could the impact of air pollution extend beyond respiratory health, infiltrating the financial realm with an unexpected and unwelcome presence? Might we find that, through environmental footprints and stock market footfalls, we are bearing witness to a connection that is not only nose-worthy but also has far-reaching ramifications?
Upon this curious crossroads of air quality and stock prices, we invite you to join us in unpacking the implications of our findings, offering a breath of fresh air in understanding the relationship between environmental factors and financial markets. So, sit back, take a deep breath, and prepare yourself for a journey that may leave you not only pondering economic indicators but also contemplating the literal winds of change.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

Our analysis of the connection between air pollution levels in Columbus, Georgia and the stock price of Barclays (BCS) yielded some intriguing and, dare we say, breath-taking results. Over the period from 2002 to 2023, we unearthed a robust correlation coefficient of 0.9366056 between these seemingly unrelated entities. This indicates a remarkably strong positive linear relationship between the two variables, nearly as striking as the brisk inhales of a competitive marathon runner.

Furthermore, the coefficient of determination (r-squared) stood at an impressive 0.8772300, suggesting that approximately 87.7% of the variation in Barclays' stock price can be explained by the concurrent fluctuations in air pollution levels in Columbus. It seems the nebulous tendrils of air pollution may not only affect the lungs but also wrap around stock prices with a remarkably tight grip.

To add weight to our findings, the significance level (p-value) was found to be less than 0.01, signifying a high degree of confidence in the strength of the relationship. This level of statistical significance provides a robust foundation for our argument, not unlike a sturdy pair of lungs in the face of pollution.

These results are visually represented in Figure 1, which elucidates the compelling correlation between air pollution levels in Columbus, Georgia, and Barclays' stock price. The scatterplot showcases a clear and decisive pattern that may lead one to exclaim, "That's quite an 'air'-tight relationship!" While our findings may not clear the smog surrounding the causality of these two factors, they certainly offer a breath of fresh air in understanding their interplay.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 Columbus, Georgia and Barclays' stock price (BCS). Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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]]
The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price

[[ABSTRACT]]
In this study, we examine the potentially smoggy relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). Harnessing data from the Environmental Protection Agency and LSEG Analytics. Our findings indicated a remarkably robust correlation coefficient of 0.9366056, with a significance level of p < 0.01, covering the period from 2002 to 2023. The results suggest that the impact of air pollution extends beyond respiratory health, reaching into the financial realm, quite literally "fouling the air" of the stock market. We delve into the potential implications of these findings, offering a breath of fresh air in understanding the connection between environmental factors and financial markets.

[[LITERATURE REVIEW]]
The present study represents a groundbreaking endeavor to investigate the intersection of environmental factors and financial markets, focusing on the relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). We wish to inhale the sweet aroma of knowledge and exhale the scents of insight in delving into this unexplored territory. Our review of the existing literature uncovers a trove of research that expands upon the nuanced interplay between air quality and financial valuations, painting a picture that is not only intriguing but also flush with potential implications.
Smith and Doe (2015) conducted a comprehensive analysis of air pollution's impact on economic indicators, exposing the hidden costs of environmental degradation. Their findings shed light on the smoggy specter that looms over financial markets, hinting at a tailwind of consequences that may have been previously overlooked. Meanwhile, Jones et al. (2018) offer a detailed examination of the reverberations of air pollution on urban centers, presenting a canvas of insights that extends beyond the mere visibility of skyscrapers. Their work underscores the importance of considering the atmospherics of financial hubs when evaluating market trends, elevating the discourse to a level that is, dare we say, breath-taking.
Building upon this foundation, we draw inspiration from non-fiction tomes that delve into the intricacies of environmental economics and market forces. "The Economics of Pollution" by Smith (2019) brings an analytical lens to the conversation, dissecting the ramifications of pollution on economic vitality. In a similar vein, "Environmental Regulations and Stock Market Performance" by Doe (2020) delves into the regulatory landscape and its impact on financial valuations, providing a panoramic view that extends beyond the horizon of traditional market analyses.
In a delightful departure from the expected, we encounter fiction works that, while not rooted in empirical data, offer a whimsical reflection of the interplay between air quality and financial fortitude. "Mist and Markets: A Tale of Two Fogs" by Forster (1920) transports readers to a world where the misty tendrils of smog intertwine with the ebbs and flows of market dynamics, inviting us to ponder the foggy implications of environmental factors on financial destinies. Similarly, "The Airborne Alchemist" by Rowling (1999) weaves a spellbinding narrative that fuses the alchemy of air quality with the sorcery of stock prices, creating a concoction that is both intoxicating and mystifying.
Additionally, we draw upon the insights offered by board games that tangentially relate to our investigation. "Pollution Peril: The Board Game" compels players to navigate the treacherous terrain of pollution management and financial risk, consistently reminding us that the winds of change may carry a scent that is not easily ignored.
As we embark on this comedic stroll through the literature, we implore readers to suspend their disbelief and embrace the wondrous tapestry of knowledge that emerges when we merge the serious with the lighthearted. Our journey is just beginning, and we invite you to join us in inhaling the fragrant possibilities that arise when unconventional connections are brought to light. Keep your sense of humor close at hand – after all, when it comes to the relationship between air pollution and stock prices, the forecast may just be a mix of wit and whimsy.

[[RESULTS]]
Our analysis of the connection between air pollution levels in Columbus, Georgia and the stock price of Barclays (BCS) yielded some intriguing and, dare we say, breath-taking results. Over the period from 2002 to 2023, we unearthed a robust correlation coefficient of 0.9366056 between these seemingly unrelated entities. This indicates a remarkably strong positive linear relationship between the two variables, nearly as striking as the brisk inhales of a competitive marathon runner.
Furthermore, the coefficient of determination (r-squared) stood at an impressive 0.8772300, suggesting that approximately 87.7% of the variation in Barclays' stock price can be explained by the concurrent fluctuations in air pollution levels in Columbus. It seems the nebulous tendrils of air pollution may not only affect the lungs but also wrap around stock prices with a remarkably tight grip.
To add weight to our findings, the significance level (p-value) was found to be less than 0.01, signifying a high degree of confidence in the strength of the relationship. This level of statistical significance provides a robust foundation for our argument, not unlike a sturdy pair of lungs in the face of pollution.
These results are visually represented in Figure 1, which elucidates the compelling correlation between air pollution levels in Columbus, Georgia, and Barclays' stock price. The scatterplot showcases a clear and decisive pattern that may lead one to exclaim, "That's quite an 'air'-tight relationship!" While our findings may not clear the smog surrounding the causality of these two factors, they certainly offer a breath of fresh air in understanding their interplay.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

Our findings not only exhale the tantalizing aroma of correlation between air pollution in Columbus, Georgia, and Barclays' stock price (BCS) but also blow away the haze surrounding the potential implications of these interrelated factors. The statistically robust correlation coefficient of 0.9366056, akin to a breath of fresh air in the world of financial research, adds weight to prior literature supporting the impact of air quality on financial markets.

Drawing a deep breath from the literature review, we recall the swoon-worthy findings of Smith and Doe (2015) - a "breathtaking" revelation of the unseen costs of environmental degradation, and the revelatory insights of Jones et al. (2018) that hinted at the "air-mongous" consequences of air pollution on urban environments. Our results paint an eerily similar picture, underscoring the "air-resistible" influence of polluted air on the valuation of Barclays' stock. Perhaps the winds of change truly carry a scent that is not easily ignored, even in the environment of a bustling financial hub.

Delving deeper, the coefficient of determination (r-squared) of 0.8772300 sashays in with an aura of confidence, revealing that approximately 87.7% of the variation in Barclays' stock price can be elucidated by the fluctuations in air pollution levels in Columbus. It seems that the invisible tendrils of air pollution may not only affect the lungs but also wrap around stock prices with a remarkably tight grip, akin to the grip of a trusty ol' pair of lungs in the face of smog.

With a significance level (p-value) of less than 0.01, our study embraces an air of certitude, showcasing a high degree of confidence in the "air-tight" relationship between air pollution and Barclays' stock price. The scatterplot visually captures this compelling correlation, almost as mesmerizing as the misty tendrils of smog intertwining with market dynamics in Forster's "Mist and Markets: A Tale of Two Fogs".

In closing, the bewitching correlations uncovered in this study not only inhale the sweet aroma of novel insights but also offer a smog-free window into the unconventional yet spellbinding connections between environmental factors and financial markets. After all, when it comes to the relationship between air pollution and stock prices, the forecast may indeed be a mix of wit, whimsy, and a dash of he-“air”-y allure.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 Columbus, Georgia and Barclays' stock price (BCS). Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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]]
The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price

[[ABSTRACT]]
In this study, we examine the potentially smoggy relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). Harnessing data from the Environmental Protection Agency and LSEG Analytics. Our findings indicated a remarkably robust correlation coefficient of 0.9366056, with a significance level of p < 0.01, covering the period from 2002 to 2023. The results suggest that the impact of air pollution extends beyond respiratory health, reaching into the financial realm, quite literally "fouling the air" of the stock market. We delve into the potential implications of these findings, offering a breath of fresh air in understanding the connection between environmental factors and financial markets.

[[INTRDUCTION]]
The intersection of environmental factors and financial markets has long been a subject of intrigue and debate. The notion that air pollution, a seemingly distant and ethereal phenomenon, could have tangible effects on the stock market may raise a few eyebrows, perhaps even prompting one to exclaim, "Are we really blowing this out of proportion?" However, as we take a deep breath and explore the link between air pollution levels in Columbus, Georgia and the stock price of Barclays (BCS), we begin to uncover a narrative that may very well leave us gasping for air.
The city of Columbus, Georgia, located alongside the Chattahoochee River, has experienced its fair share of industrial activity and vehicular emissions, creating an atmospheric backdrop that is not without its smoggy character. Meanwhile, Barclays, a global financial institution with a presence on the London Stock Exchange, has ridden the waves of market tumult and economic volatility. If one were to take a deep inhale and ponder the possibility of these seemingly disparate entities coming together in an unexpected dance, akin to a tango between Wall Street and Main Street, the resulting connection may just leave them breathless.
In this study, we endeavor to unravel the interplay between these two seemingly unrelated domains. By weaving together data on air pollution levels in Columbus, Georgia, sourced from the Environmental Protection Agency's meticulous records, with stock price history from LSEG Analytics, we aim to shine a light on a correlation that may have previously been obscured by the hazy clouds of speculation. Our findings, showcasing a correlation coefficient of 0.9366056, pique curiosity and prompt us to ponder whether we are indeed sniffing out a significant relationship or merely experiencing a statistical mirage.
As we embark on this journey, let us not underestimate the potential implications of our discoveries. Could the impact of air pollution extend beyond respiratory health, infiltrating the financial realm with an unexpected and unwelcome presence? Might we find that, through environmental footprints and stock market footfalls, we are bearing witness to a connection that is not only nose-worthy but also has far-reaching ramifications?
Upon this curious crossroads of air quality and stock prices, we invite you to join us in unpacking the implications of our findings, offering a breath of fresh air in understanding the relationship between environmental factors and financial markets. So, sit back, take a deep breath, and prepare yourself for a journey that may leave you not only pondering economic indicators but also contemplating the literal winds of change.

[[RESULTS]]
Our analysis of the connection between air pollution levels in Columbus, Georgia and the stock price of Barclays (BCS) yielded some intriguing and, dare we say, breath-taking results. Over the period from 2002 to 2023, we unearthed a robust correlation coefficient of 0.9366056 between these seemingly unrelated entities. This indicates a remarkably strong positive linear relationship between the two variables, nearly as striking as the brisk inhales of a competitive marathon runner.
Furthermore, the coefficient of determination (r-squared) stood at an impressive 0.8772300, suggesting that approximately 87.7% of the variation in Barclays' stock price can be explained by the concurrent fluctuations in air pollution levels in Columbus. It seems the nebulous tendrils of air pollution may not only affect the lungs but also wrap around stock prices with a remarkably tight grip.
To add weight to our findings, the significance level (p-value) was found to be less than 0.01, signifying a high degree of confidence in the strength of the relationship. This level of statistical significance provides a robust foundation for our argument, not unlike a sturdy pair of lungs in the face of pollution.
These results are visually represented in Figure 1, which elucidates the compelling correlation between air pollution levels in Columbus, Georgia, and Barclays' stock price. The scatterplot showcases a clear and decisive pattern that may lead one to exclaim, "That's quite an 'air'-tight relationship!" While our findings may not clear the smog surrounding the causality of these two factors, they certainly offer a breath of fresh air in understanding their interplay.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]
In conclusion, our study has shed light on the unexpected yet robust relationship between air pollution levels in Columbus, Georgia and the stock price of Barclays (BCS). The remarkably strong correlation coefficient, akin to the force of a gusty wind, highlights the potential influence of environmental factors on financial markets, leaving us not only scratching our heads but also perhaps reaching for our inhalers. The significance level of our findings suggests a high degree of confidence in the connection, prompting us to consider the possibility of air pollution wafting its way into the very fabric of stock prices, much like an unwelcome scent that just won't dissipate.

As we contemplate the implications of these findings, it becomes clear that the impact of air pollution may extend beyond the atmospheric realm, reaching into the intricate web of financial dealings and market dynamics. This unexpected correlation serves as a reminder that, in the world of economics, one must be prepared to navigate through the maze of unexpected twists and turns, much like maneuvering through a hazy cityscape under the influence of smog.

However, it is important to note that our study has its limitations, much like a dust mask not fully protecting against the onslaught of pollutants. The causality of this relationship remains shrouded in uncertainty, much like trying to decipher a message written in fog on a windowpane. Nonetheless, our findings offer a breath of fresh air in advocating for further exploration of the intersection between environmental factors and financial markets, although one could argue that we have already breathed in quite enough smog for one research endeavor.

In light of our findings, we dare say that no further research in this area is needed, as we have certainly exhaled all available insights and puns relating to this topic, leaving our readers both enlightened and slightly out of breath.


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 The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Financial Atmospheric Science


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 The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price. Respond only with the name of a fictional organization.

ChatGPT:

The Association for Environmental Economics and Financial Analysis


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 The Polluted Stock Market: A Breath of Fresh Air on the Link Between Air Pollution in Columbus, Georgia and Barclays' Stock Price with an abstract of In this study, we examine the potentially smoggy relationship between air pollution levels in Columbus, Georgia, and the stock price of Barclays (BCS). Harnessing data from the Environmental Protection Agency and LSEG Analytics. Our findings indicated a remarkably robust correlation coefficient of 0.9366056, with a significance level of p < 0.01, covering the period from 2002 to 2023. The results suggest that the impact of air pollution extends beyond respiratory health, reaching into the financial realm, quite literally "fouling the air" of the stock market. We delve into the potential implications of these findings, offering a breath of fresh air in understanding the connection between environmental factors and financial markets.

ChatGPT:

air pollution, stock market, Columbus Georgia, Barclays stock price, correlation coefficient, Environmental Protection Agency data, LSEG Analytics, financial markets, environmental factors, pollution impact, financial realm

*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 Columbus, Georgia
Detailed data title: Percentage of days with air quality at 'unhealthy for sensitive groups' or worse in Columbus, GA-AL
Source: Environmental Protection Agency
See what else correlates with Air pollution in Columbus, Georgia

Barclays' stock price (BCS)
Detailed data title: Opening price of Barclays (BCS) on the first trading day of the year
Source: LSEG Analytics (Refinitiv)
Additional Info: Via Microsoft Excel Stockhistory function

See what else correlates with Barclays' stock price (BCS)

Correlation r = 0.9366056 (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 = 0.8772300 (Coefficient of determination)
This means 87.7% of the change in the one variable (i.e., Barclays' stock price (BCS)) is predictable based on the change in the other (i.e., Air pollution in Columbus, Georgia) over the 22 years from 2002 through 2023.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.5E-10. 0.0000000001454254623964589000
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 0.94 in 1.5E-8% of random cases. Said differently, if you correlated 6,876,374,904 random variables You don't actually need 6 billion variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

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

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

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 21 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 21 because we have two variables measured over a period of 22 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.

[ 0.85, 0.97 ] 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.
2002200320042005200620072008200920102011201220132014201520162017201820192020202120222023
Air pollution in Columbus, Georgia (Bad air quality days)2.430561.58733.363914.109594.657536.849322.732240.5479451.369861.369860.8196720.2739730.5479450.5509641.373630000.2732241.095890.5479451.0989
Barclays' stock price (BCS) (Stock price)30.5422.9533.8142.3639.3954.7537.878.3616.715.410.5616.5418.115.112.6311.3810.987.49.697.9410.497.93




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([2.43056,1.5873,3.36391,4.10959,4.65753,6.84932,2.73224,0.547945,1.36986,1.36986,0.819672,0.273973,0.547945,0.550964,1.37363,0,0,0,0.273224,1.09589,0.547945,1.0989,])
array_2 = np.array([30.54,22.95,33.81,42.36,39.39,54.75,37.87,8.36,16.7,15.4,10.56,16.54,18.1,15.1,12.63,11.38,10.98,7.4,9.69,7.94,10.49,7.93,])
array_1_name = "Air pollution in Columbus, Georgia"
array_2_name = "Barclays' stock price (BCS)"

# 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: 3025 · Black Variable ID: 20491 · Red Variable ID: 1839
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