Spurious correlation #4,275 · 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 Harrison, Arkansas and the second variable is Biogen's stock price (BIIB). The chart goes from 2002 to 2023, and the two variables track closely in value over that time.

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air quality in Harrison, Arkansas and the second variable is Biogen's stock price (BIIB). The chart goes from 2002 to 2023, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As the air quality improved in Harrison, Arkansas, the local population experienced a surge in energy and mental clarity. This led to a sudden spike in demand for outdoor activities, including a newfound enthusiasm for biogenetic-themed LARPing (live-action role-playing). With more people dressing up as their favorite DNA strands and reenacting cellular processes in the fresh, clean air, there was an unexpected uptick in Biogen's stock price as enthusiasts sought to embody their biotechnological heroes. It seems like cleaner air isn't just good for lungs, but also for the whimsical world of biogenetic finance!

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a low-poly landscape that showcases a group of LARPers enthusiastically enacting biogenetic-themed scenarios in a lush forest clearing in Harrison, Arkansas. The scene should be set under a clear sky, with the participants immersed in portraying DNA strands and mimicking cellular processes. The atmosphere of the forest should be fresh and vibrant, reflecting the participants' energy and determination. Additionally, incorporate a subtle representation of the unexpected uptick in Biogen's stock price, reflecting the growing enthusiasm for biogenetic-themed LARPing. 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 quality in Harrison, Arkansas and Biogen's stock price (BIIB). 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: Low poly Photorealism Cybernetic art Macabre An image that looks like it is a scene from A Disney Movie
ChatGPT: Low poly

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 quality in Harrison, Arkansas and Biogen's stock price (BIIB), in the following situation: As the air quality improved in Harrison, Arkansas, the local population experienced a surge in energy and mental clarity. This led to a sudden spike in demand for outdoor activities, including a newfound enthusiasm for biogenetic-themed LARPing (live-action role-playing). With more people dressing up as their favorite DNA strands and reenacting cellular processes in the fresh, clean air, there was an unexpected uptick in Biogen's stock price as enthusiasts sought to embody their biotechnological heroes. It seems like cleaner air isn't just good for lungs, but also for the whimsical world of biogenetic finance!. Keep the description simple.
ChatGPT: In a clear sky over Harrison, Arkansas, a group of LARPers are gathered in a lush forest clearing. The air is crisp and fresh, and the participants are full of energy as they enthusiastically portray their favorite DNA strands and mimic cellular processes. The excitement in the air is palpable as Biogen's stock price experiences an unexpected uptick, reflecting the newfound enthusiasm for biogenetic-themed LARPing spurred by the improved air quality.

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: [ Low poly ] and depicting this scene: In a clear sky over Harrison, Arkansas, a group of LARPers are gathered in a lush forest clearing. The air is crisp and fresh, and the participants are full of energy as they enthusiastically portray their favorite DNA strands and mimic cellular processes. The excitement in the air is palpable as Biogen's stock price experiences an unexpected uptick, reflecting the newfound enthusiasm for biogenetic-themed LARPing spurred by the improved air quality. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a low-poly landscape that showcases a group of LARPers enthusiastically enacting biogenetic-themed scenarios in a lush forest clearing in Harrison, Arkansas. The scene should be set under a clear sky, with the participants immersed in portraying DNA strands and mimicking cellular processes. The atmosphere of the forest should be fresh and vibrant, reflecting the participants' energy and determination. Additionally, incorporate a subtle representation of the unexpected uptick in Biogen's stock price, reflecting the growing enthusiasm for biogenetic-themed LARPing.

*Variations in the User Prompts from chart to chart are just the result of random number generation in Python. I wrote a few arrays of various styles and methods to ask questions to change up the results. Every time this site writes an explanation or generates an image, the script picks from each at random.

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.
^{Show prompt for explanation} Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how an increase in Air quality in Harrison, Arkansas caused Biogen's stock price (BIIB) to increase.

AI academic paper

(Because p < 0.01)

Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price

The Journal of Environmental Economics and Stock Market Dynamics

Jan 2024

Reminder: This paper is AI-generated. Not real!

^{Show prompt used to generate this paper} Quick note: This sequence is long and repetitive. That's how the prompt engineering works for this one. I manage the output in Python to format it into this PDF.

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

Please make up a literature review section of an academic research paper presenting the findings of the connection between Air quality in Harrison, Arkansas and Biogen's stock price (BIIB). Make lots of jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Perhaps you also got inspiration from some board games that are vaugely related.

Here is the title and abstract of the paper:
[[TITLE]]
"Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price"

[[ABSTRACT]]
The relationship between air quality and stock prices has long been a topic of interest in both environmental and financial domains, but its dynamics continue to elude researchers and investors alike. Our study delves into this conundrum by examining the correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB), a leading biotechnology company. Utilizing data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), we conducted a rigorous analysis spanning the years 2002 to 2023. Surprisingly, our findings reveal a striking correlation coefficient of 0.8657366 and a statistically significant p-value of less than 0.01. While Harrison, Arkansas may be famous for its scenic beauty, the impact of its air quality on the stock market proves to be nothing short of breathtaking. Our study not only sheds light on this unexpected connection but also emphasizes the need for investors to consider the air they breathe alongside the stocks they trade.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The relationship between environmental factors and financial markets has always piqued the curiosity of researchers and investors alike. While air quality may seem as ethereal as a passing breeze, its impact on stock prices is nothing to sneeze at! In this paper, we embark on a whimsical journey to explore the surprising correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB). As we delve into the depths of statistical analysis, let's don our metaphorical oxygen masks and prepare for an exhilarating ride through the realms of data and finance.

Air quality, a topic that often floats through the corridors of environmental research, takes center stage in our exploration. Harrison, Arkansas, with its charming scenery and picturesque landscapes, sets the backdrop for our investigation. However, beneath the serene façade lays a tale of airborne particles and gaseous compounds that intertwine with the whims of the stock market.
Venturing into the midst of air quality data collected by the Environmental Protection Agency, we traverse through the ozone levels, particulate matter, and volatile organic compounds. As we navigate through the labyrinth of air pollution statistics, the correlation with Biogen's stock price emerges like a beacon of fresh air in a sea of statistical haze.

Enter Biogen, a leading biotechnology company that, much like a strand of DNA, embodies the complex interplay of scientific innovation and stock market valuations. As we scrutinize its stock price through the lens of LSEG Analytics (Refinitiv), we witness a molecular dance of financial fortunes, poised at the intersection of scientific breakthroughs and market dynamics.
Our exploration transcends the traditional boundaries of research, as we juxtapose the arcane world of air quality with the enigmatic domain of stock prices. Through rigorous statistical analysis spanning over two decades, we peel back the layers of uncertainty to unveil a correlation coefficient as robust as a cloned gene - a staggering 0.8657366. Yes, you read that right - air quality in Harrison, Arkansas and Biogen's stock price are not merely acquaintances but statistically significant bedfellows.

As our findings ripple through the waters of academia and finance, it becomes evident that the connection between air quality in Harrison, Arkansas, and Biogen's stock price is more than a mere coincidence. It is a revelation that transcends the boundaries of conventional wisdom and breathes new life into the intricacies of environmental and financial interplay.
In conclusion, our study not only provides a breezy insight into this unexpected correlation but also underscores the need for investors to consider the air they breathe alongside the stocks they trade. So, fasten your statistical seatbelts and prepare for a bumpy yet exhilarating ride through the gusts of empirical evidence and financial foresight.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The correlation between air quality and stock prices has been the subject of scholarly inquiry for decades. Smith et al. (2015) examined the impact of air pollution on stock market volatility, finding a significant relationship between particulate matter levels and changes in stock prices. Similarly, Doe and Jones (2018) investigated the association between air quality index and the stock performance of biotechnology companies, shedding light on the potential influence of environmental factors on financial markets.

However, as we navigate the labyrinth of literature on this topic, it becomes apparent that the whimsical correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen introduces a refreshing gust of curiosity into this scholarly realm. With our metaphorical noses twitching like stock market indicators, we embark on a literary adventure that transcends the boundaries of conventional research.

In "Air Purity and Market Prosperity," Lorem and Ipsum (2020) present a compelling analysis of the impact of air quality on stock prices, likening the relationship to the delicate balance of a chemical equation. Their findings not only corroborate our own but also create a whimsical synergy between empirical evidence and scholarly musings.

As we make a comedic pivot, we turn our attention to non-fiction works that, although unrelated to our topic, add a touch of literary flair to our scholarly escapade. "The Economics of Clean Air" by William Nordhaus may not delve into the intricacies of stock market correlations, but its title evokes a sense of relevance to our research. Similarly, "Biophysics for Dummies" by Carlos Bustamante may offer insights into the world of biotechnology, albeit without a direct link to our specific investigation.

Enlisting fictional works for a dose of literary levity, we draw inspiration from "The Air Affair" by Jasper Fforde, a delightful work of speculative fiction that, despite its lack of empirical rigor, provides a whimsical parallel to our research journey. Furthermore, "Stockholm Syndrome" by Richard Doyle, though unrelated to financial markets, serves as a tongue-in-cheek nod to the captivation we experience when unravelling the mysteries of stock price correlations.

Turning our attention to the world of board games, the classic "Monopoly" offers a playful allegory to the whims of financial markets, where players rival for dominance amidst fluctuating fortunes. Conversely, "Photosynthesis" brings a breath of fresh air to our academic discussion, offering a whimsical reminder of the interconnectedness of environmental factors and financial endeavors.

In this scholarly romp through the realms of literature and research, we not only seek to elucidate the connection between air quality in Harrison and Biogen's stock price but also to infuse our exploration with a touch of whimsy and pizzazz. Our aim is to turn the dry, statistical realm of academic research into a tantalizing academic adventure – one where scholarly musings and empirical evidence intertwine like strands of DNA, creating a captivating tale of whimsical correlation between the ethereal air in Harrison, Arkansas and the tantalizing dance of Biogen's stock price. So, fasten your metaphorical seatbelts and prepare for an exhilarating ride through the whims of literature and scholarly inquiry!

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the 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 Harrison, Arkansas and Biogen's stock price (BIIB). Make lots of 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 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]]
"Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price"

[[ABSTRACT]]
The relationship between air quality and stock prices has long been a topic of interest in both environmental and financial domains, but its dynamics continue to elude researchers and investors alike. Our study delves into this conundrum by examining the correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB), a leading biotechnology company. Utilizing data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), we conducted a rigorous analysis spanning the years 2002 to 2023. Surprisingly, our findings reveal a striking correlation coefficient of 0.8657366 and a statistically significant p-value of less than 0.01. While Harrison, Arkansas may be famous for its scenic beauty, the impact of its air quality on the stock market proves to be nothing short of breathtaking. Our study not only sheds light on this unexpected connection but also emphasizes the need for investors to consider the air they breathe alongside the stocks they trade.

[[INTRODUCTION]]
The relationship between environmental factors and financial markets has always piqued the curiosity of researchers and investors alike. While air quality may seem as ethereal as a passing breeze, its impact on stock prices is nothing to sneeze at! In this paper, we embark on a whimsical journey to explore the surprising correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB). As we delve into the depths of statistical analysis, let's don our metaphorical oxygen masks and prepare for an exhilarating ride through the realms of data and finance.

Air quality, a topic that often floats through the corridors of environmental research, takes center stage in our exploration. Harrison, Arkansas, with its charming scenery and picturesque landscapes, sets the backdrop for our investigation. However, beneath the serene façade lays a tale of airborne particles and gaseous compounds that intertwine with the whims of the stock market.
Venturing into the midst of air quality data collected by the Environmental Protection Agency, we traverse through the ozone levels, particulate matter, and volatile organic compounds. As we navigate through the labyrinth of air pollution statistics, the correlation with Biogen's stock price emerges like a beacon of fresh air in a sea of statistical haze.

Enter Biogen, a leading biotechnology company that, much like a strand of DNA, embodies the complex interplay of scientific innovation and stock market valuations. As we scrutinize its stock price through the lens of LSEG Analytics (Refinitiv), we witness a molecular dance of financial fortunes, poised at the intersection of scientific breakthroughs and market dynamics.
Our exploration transcends the traditional boundaries of research, as we juxtapose the arcane world of air quality with the enigmatic domain of stock prices. Through rigorous statistical analysis spanning over two decades, we peel back the layers of uncertainty to unveil a correlation coefficient as robust as a cloned gene - a staggering 0.8657366. Yes, you read that right - air quality in Harrison, Arkansas and Biogen's stock price are not merely acquaintances but statistically significant bedfellows.

As our findings ripple through the waters of academia and finance, it becomes evident that the connection between air quality in Harrison, Arkansas, and Biogen's stock price is more than a mere coincidence. It is a revelation that transcends the boundaries of conventional wisdom and breathes new life into the intricacies of environmental and financial interplay.
In conclusion, our study not only provides a breezy insight into this unexpected correlation but also underscores the need for investors to consider the air they breathe alongside the stocks they trade. So, fasten your statistical seatbelts and prepare for a bumpy yet exhilarating ride through the gusts of empirical evidence and financial foresight.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

In this study, our research team employed a blend of scientific rigor and financial acumen to unravel the conundrum surrounding the connection between air quality in Harrison, Arkansas, and Biogen's stock price. Like intrepid explorers, we navigated through the vast expanse of environmental data and financial market analytics, employing methodologies that were as robust as they were whimsically inventive.

First, we harnessed the power of data compilation from the Environmental Protection Agency, drawing upon a treasure trove of air quality measurements spanning over two decades. We ventured into the realms of ozone levels, particulate matter, and volatile organic compounds, carefully sifting through the statistical haze to extract the nuggets of information that would illuminate the correlation under scrutiny.

Simultaneously, we set sail across the volatile sea of financial data, anchoring our analysis in the stock price fluctuations of Biogen (BIIB) sourced from LSEG Analytics (Refinitiv). As we charted the course of Biogen's stock price, we remained vigilant for the subtle tides of market dynamics that could sway the correlation under investigation.

Our statistical analysis, akin to an alchemist's cauldron, stirred together the disparate elements of air quality data and stock price movements. Through the enchanting incantations of correlation analysis, we unearthed a robust correlation coefficient of 0.8657366, akin to a scientific breakthrough in the realm of empirical finance. With a statistically significant p-value of less than 0.01, the evidence of connection between these seemingly disparate variables emerged as clear as the Arkansas sky after a cleansing rain.

To further fortify our findings, we employed a time series analysis that wove together the intricate threads of air quality fluctuations and stock price movements over the years. This approach allowed us to capture the ebbs and flows of correlation, painting a vivid tapestry of the intertwining forces at play.

Lastly, we conducted a sensitivity analysis, probing the resilience of our findings to variations and perturbations in the data. Like a gentle gust testing the sturdiness of a windmill, this exercise ensured that our conclusions stood firm against the whims of statistical chance and environmental variance.

By undertaking this multifaceted approach, we not only illuminated the connection between air quality in Harrison, Arkansas, and Biogen's stock price but also showcased the intersection of scientific inquiry and financial insight. Like a pair of eccentric tango dancers, air quality and stock prices twirled in a mesmerizing display of correlation that defied the conventional boundaries of academic inquiry.

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

Please make up the results section of an academic research paper presenting the findings of the connection between Air quality in Harrison, Arkansas and Biogen's stock price (BIIB). Make lots of 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 LSEG Analytics (Refinitiv) .

For the time period 2002 to 2023, you found a correlation 0.8657366, r-squared of 0.7494998, 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]]
"Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price"

[[ABSTRACT]]
The relationship between air quality and stock prices has long been a topic of interest in both environmental and financial domains, but its dynamics continue to elude researchers and investors alike. Our study delves into this conundrum by examining the correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB), a leading biotechnology company. Utilizing data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), we conducted a rigorous analysis spanning the years 2002 to 2023. Surprisingly, our findings reveal a striking correlation coefficient of 0.8657366 and a statistically significant p-value of less than 0.01. While Harrison, Arkansas may be famous for its scenic beauty, the impact of its air quality on the stock market proves to be nothing short of breathtaking. Our study not only sheds light on this unexpected connection but also emphasizes the need for investors to consider the air they breathe alongside the stocks they trade.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The relationship between environmental factors and financial markets has always piqued the curiosity of researchers and investors alike. While air quality may seem as ethereal as a passing breeze, its impact on stock prices is nothing to sneeze at! In this paper, we embark on a whimsical journey to explore the surprising correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB). As we delve into the depths of statistical analysis, let's don our metaphorical oxygen masks and prepare for an exhilarating ride through the realms of data and finance.

Air quality, a topic that often floats through the corridors of environmental research, takes center stage in our exploration. Harrison, Arkansas, with its charming scenery and picturesque landscapes, sets the backdrop for our investigation. However, beneath the serene façade lays a tale of airborne particles and gaseous compounds that intertwine with the whims of the stock market.
Venturing into the midst of air quality data collected by the Environmental Protection Agency, we traverse through the ozone levels, particulate matter, and volatile organic compounds. As we navigate through the labyrinth of air pollution statistics, the correlation with Biogen's stock price emerges like a beacon of fresh air in a sea of statistical haze.

Enter Biogen, a leading biotechnology company that, much like a strand of DNA, embodies the complex interplay of scientific innovation and stock market valuations. As we scrutinize its stock price through the lens of LSEG Analytics (Refinitiv), we witness a molecular dance of financial fortunes, poised at the intersection of scientific breakthroughs and market dynamics.
Our exploration transcends the traditional boundaries of research, as we juxtapose the arcane world of air quality with the enigmatic domain of stock prices. Through rigorous statistical analysis spanning over two decades, we peel back the layers of uncertainty to unveil a correlation coefficient as robust as a cloned gene - a staggering 0.8657366. Yes, you read that right - air quality in Harrison, Arkansas and Biogen's stock price are not merely acquaintances but statistically significant bedfellows.

As our findings ripple through the waters of academia and finance, it becomes evident that the connection between air quality in Harrison, Arkansas, and Biogen's stock price is more than a mere coincidence. It is a revelation that transcends the boundaries of conventional wisdom and breathes new life into the intricacies of environmental and financial interplay.
In conclusion, our study not only provides a breezy insight into this unexpected correlation but also underscores the need for investors to consider the air they breathe alongside the stocks they trade. So, fasten your statistical seatbelts and prepare for a bumpy yet exhilarating ride through the gusts of empirical evidence and financial foresight.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The results of our investigation yield a striking correlation between air quality in Harrison, Arkansas, and Biogen's stock price (BIIB) that can only be described as breathtaking. Our statistical analysis reveals a correlation coefficient of 0.8657366, indicating a strong positive relationship between the two variables. This correlation coefficient is accompanied by an r-squared value of 0.7494998, suggesting that approximately 74.95% of the variability in Biogen's stock price can be explained by changes in air quality in Harrison, Arkansas. The p-value of less than 0.01 indicates that this correlation is statistically significant, demonstrating that the relationship between air quality in Harrison, Arkansas and Biogen's stock price is not merely a statistical fluke.

In Fig. 1, we present a scatterplot that vividly illustrates the robust correlation between air quality in Harrison, Arkansas and Biogen's stock price. As we gaze upon this figure, it's as if the data points are whispering to us, revealing the hidden dance between environmental factors and financial markets. The scatterplot serves as a visual testament to the unyielding bond between these seemingly disparate entities, much like the unlikely pairing of peanut butter and jelly.

Our findings not only highlight the unexpected connection between air quality in Harrison, Arkansas, and Biogen's stock price but also serve as a playful nudge to remind investors that even the most unlikely variables can sway the stock market. It appears that in the quest for financial success, it pays off to have a breath of fresh air – quite literally.

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 Harrison, Arkansas and Biogen's stock price (BIIB). Make lots of 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]]
"Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price"

[[ABSTRACT]]
The relationship between air quality and stock prices has long been a topic of interest in both environmental and financial domains, but its dynamics continue to elude researchers and investors alike. Our study delves into this conundrum by examining the correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB), a leading biotechnology company. Utilizing data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), we conducted a rigorous analysis spanning the years 2002 to 2023. Surprisingly, our findings reveal a striking correlation coefficient of 0.8657366 and a statistically significant p-value of less than 0.01. While Harrison, Arkansas may be famous for its scenic beauty, the impact of its air quality on the stock market proves to be nothing short of breathtaking. Our study not only sheds light on this unexpected connection but also emphasizes the need for investors to consider the air they breathe alongside the stocks they trade.

[[LITERATURE REVIEW]]
The correlation between air quality and stock prices has been the subject of scholarly inquiry for decades. Smith et al. (2015) examined the impact of air pollution on stock market volatility, finding a significant relationship between particulate matter levels and changes in stock prices. Similarly, Doe and Jones (2018) investigated the association between air quality index and the stock performance of biotechnology companies, shedding light on the potential influence of environmental factors on financial markets.
However, as we navigate the labyrinth of literature on this topic, it becomes apparent that the whimsical correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen introduces a refreshing gust of curiosity into this scholarly realm. With our metaphorical noses twitching like stock market indicators, we embark on a literary adventure that transcends the boundaries of conventional research.
In "Air Purity and Market Prosperity," Lorem and Ipsum (2020) present a compelling analysis of the impact of air quality on stock prices, likening the relationship to the delicate balance of a chemical equation. Their findings not only corroborate our own but also create a whimsical synergy between empirical evidence and scholarly musings.
As we make a comedic pivot, we turn our attention to non-fiction works that, although unrelated to our topic, add a touch of literary flair to our scholarly escapade. "The Economics of Clean Air" by William Nordhaus may not delve into the intricacies of stock market correlations, but its title evokes a sense of relevance to our research. Similarly, "Biophysics for Dummies" by Carlos Bustamante may offer insights into the world of biotechnology, albeit without a direct link to our specific investigation.
Enlisting fictional works for a dose of literary levity, we draw inspiration from "The Air Affair" by Jasper Fforde, a delightful work of speculative fiction that, despite its lack of empirical rigor, provides a whimsical parallel to our research journey. Furthermore, "Stockholm Syndrome" by Richard Doyle, though unrelated to financial markets, serves as a tongue-in-cheek nod to the captivation we experience when unravelling the mysteries of stock price correlations.
Turning our attention to the world of board games, the classic "Monopoly" offers a playful allegory to the whims of financial markets, where players rival for dominance amidst fluctuating fortunes. Conversely, "Photosynthesis" brings a breath of fresh air to our academic discussion, offering a whimsical reminder of the interconnectedness of environmental factors and financial endeavors.
In this scholarly romp through the realms of literature and research, we not only seek to elucidate the connection between air quality in Harrison and Biogen's stock price but also to infuse our exploration with a touch of whimsy and pizzazz. Our aim is to turn the dry, statistical realm of academic research into a tantalizing academic adventure – one where scholarly musings and empirical evidence intertwine like strands of DNA, creating a captivating tale of whimsical correlation between the ethereal air in Harrison, Arkansas and the tantalizing dance of Biogen's stock price. So, fasten your metaphorical seatbelts and prepare for an exhilarating ride through the whims of literature and scholarly inquiry!

[[RESULTS]]
The results of our investigation yield a striking correlation between air quality in Harrison, Arkansas, and Biogen's stock price (BIIB) that can only be described as breathtaking. Our statistical analysis reveals a correlation coefficient of 0.8657366, indicating a strong positive relationship between the two variables. This correlation coefficient is accompanied by an r-squared value of 0.7494998, suggesting that approximately 74.95% of the variability in Biogen's stock price can be explained by changes in air quality in Harrison, Arkansas. The p-value of less than 0.01 indicates that this correlation is statistically significant, demonstrating that the relationship between air quality in Harrison, Arkansas and Biogen's stock price is not merely a statistical fluke.
In Fig. 1, we present a scatterplot that vividly illustrates the robust correlation between air quality in Harrison, Arkansas and Biogen's stock price. As we gaze upon this figure, it's as if the data points are whispering to us, revealing the hidden dance between environmental factors and financial markets. The scatterplot serves as a visual testament to the unyielding bond between these seemingly disparate entities, much like the unlikely pairing of peanut butter and jelly.
Our findings not only highlight the unexpected connection between air quality in Harrison, Arkansas, and Biogen's stock price but also serve as a playful nudge to remind investors that even the most unlikely variables can sway the stock market. It appears that in the quest for financial success, it pays off to have a breath of fresh air – quite literally.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

Our investigation has unearthed a compelling relationship between the air quality in Harrison, Arkansas and Biogen's stock price, delving into the whimsical realms of statistics and stock market quirks. The initial chuckles we shared over the seemingly absurd connection have now morphed into a genuine appreciation for the unexpected correlations that underpin this engaging scholarly pursuit. Much like a biotechnological experiment gone awry, the fusion of environmental factors and financial indicators has produced results that are nothing short of astonishing.

In line with the playful musings in our literature review, we cant help but marvel at the delightful synergy between our findings and the scholarly exuberance of Lorem and Ipsum (2020). Their likening of the relationship between air quality and stock prices to a delicate chemical equation resonates deeply with our discoveries, reinforcing the notion that the whims of scholarly musings and statistical evidence often dance in harmonious unison. It's as if our research is a delightful concoction in the grand alchemical laboratory of academic inquiry.

Additionally, our findings echo the lively allegories and metaphors peppered throughout our literature review. Just as "The Air Affair" by Jasper Fforde presents a whimsical parallel to our research, our results spin a tale of enchanting correlation between the ethereal air in Harrison and the tantalizing dance of Biogen's stock price. This fanciful journey through the whims of literature and statistical analysis culminates in a revelation that is as refreshing as a breath of clean air.

As we reflect on our statistical marvels, it's evident that our findings not only corroborate prior research but also inject a playful twist into the scholarly narrative surrounding air quality and stock prices. The unexpected bond between these disparate entities is akin to stumbling upon a treasure trove of statistical humor, where the punchline is a resounding correlation coefficient and an r-squared value that dances like a circus performer balancing on a statistical tightrope. Our results are a lighthearted reminder that in the realm of academic pursuit, even the most improbable variables can join hands and sway the stock market in the most unexpected of ways.

Our scholarly escapade, infused with the sprightly whimsy of wordplay and statistical antics, leaves us with a playful nudge to investors: consider the air you breathe alongside the stocks you trade, for this seemingly topsy-turvy connection holds potential for insight and financial gain. After all, in the spirited dance of research and statistical analysis, it's always beneficial to have a breath of fresh air – pun intended.

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 Harrison, Arkansas and Biogen's stock price (BIIB). Make lots of 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]]
"Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price"

[[ABSTRACT]]
The relationship between air quality and stock prices has long been a topic of interest in both environmental and financial domains, but its dynamics continue to elude researchers and investors alike. Our study delves into this conundrum by examining the correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB), a leading biotechnology company. Utilizing data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), we conducted a rigorous analysis spanning the years 2002 to 2023. Surprisingly, our findings reveal a striking correlation coefficient of 0.8657366 and a statistically significant p-value of less than 0.01. While Harrison, Arkansas may be famous for its scenic beauty, the impact of its air quality on the stock market proves to be nothing short of breathtaking. Our study not only sheds light on this unexpected connection but also emphasizes the need for investors to consider the air they breathe alongside the stocks they trade.

[[INTRDUCTION]]
The relationship between environmental factors and financial markets has always piqued the curiosity of researchers and investors alike. While air quality may seem as ethereal as a passing breeze, its impact on stock prices is nothing to sneeze at! In this paper, we embark on a whimsical journey to explore the surprising correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB). As we delve into the depths of statistical analysis, let's don our metaphorical oxygen masks and prepare for an exhilarating ride through the realms of data and finance.

Air quality, a topic that often floats through the corridors of environmental research, takes center stage in our exploration. Harrison, Arkansas, with its charming scenery and picturesque landscapes, sets the backdrop for our investigation. However, beneath the serene façade lays a tale of airborne particles and gaseous compounds that intertwine with the whims of the stock market.
Venturing into the midst of air quality data collected by the Environmental Protection Agency, we traverse through the ozone levels, particulate matter, and volatile organic compounds. As we navigate through the labyrinth of air pollution statistics, the correlation with Biogen's stock price emerges like a beacon of fresh air in a sea of statistical haze.

Enter Biogen, a leading biotechnology company that, much like a strand of DNA, embodies the complex interplay of scientific innovation and stock market valuations. As we scrutinize its stock price through the lens of LSEG Analytics (Refinitiv), we witness a molecular dance of financial fortunes, poised at the intersection of scientific breakthroughs and market dynamics.
Our exploration transcends the traditional boundaries of research, as we juxtapose the arcane world of air quality with the enigmatic domain of stock prices. Through rigorous statistical analysis spanning over two decades, we peel back the layers of uncertainty to unveil a correlation coefficient as robust as a cloned gene - a staggering 0.8657366. Yes, you read that right - air quality in Harrison, Arkansas and Biogen's stock price are not merely acquaintances but statistically significant bedfellows.

As our findings ripple through the waters of academia and finance, it becomes evident that the connection between air quality in Harrison, Arkansas, and Biogen's stock price is more than a mere coincidence. It is a revelation that transcends the boundaries of conventional wisdom and breathes new life into the intricacies of environmental and financial interplay.
In conclusion, our study not only provides a breezy insight into this unexpected correlation but also underscores the need for investors to consider the air they breathe alongside the stocks they trade. So, fasten your statistical seatbelts and prepare for a bumpy yet exhilarating ride through the gusts of empirical evidence and financial foresight.

[[RESULTS]]
The results of our investigation yield a striking correlation between air quality in Harrison, Arkansas, and Biogen's stock price (BIIB) that can only be described as breathtaking. Our statistical analysis reveals a correlation coefficient of 0.8657366, indicating a strong positive relationship between the two variables. This correlation coefficient is accompanied by an r-squared value of 0.7494998, suggesting that approximately 74.95% of the variability in Biogen's stock price can be explained by changes in air quality in Harrison, Arkansas. The p-value of less than 0.01 indicates that this correlation is statistically significant, demonstrating that the relationship between air quality in Harrison, Arkansas and Biogen's stock price is not merely a statistical fluke.
In Fig. 1, we present a scatterplot that vividly illustrates the robust correlation between air quality in Harrison, Arkansas and Biogen's stock price. As we gaze upon this figure, it's as if the data points are whispering to us, revealing the hidden dance between environmental factors and financial markets. The scatterplot serves as a visual testament to the unyielding bond between these seemingly disparate entities, much like the unlikely pairing of peanut butter and jelly.
Our findings not only highlight the unexpected connection between air quality in Harrison, Arkansas, and Biogen's stock price but also serve as a playful nudge to remind investors that even the most unlikely variables can sway the stock market. It appears that in the quest for financial success, it pays off to have a breath of fresh air – quite literally.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our research has blown the lid off the enigmatic relationship between the air quality in Harrison, Arkansas, and Biogen's stock price, revealing a correlation coefficient so strong, it's like they were made for each other – a match made in statistical heaven! Our findings not only give us a breath of fresh air in the world of finance but also serve as a gentle reminder that even the air we breathe can whisper secrets about market movements.

The statistically significant correlation we uncovered is more solid than a petrified fossil, with an r-squared value that explains nearly 75% of the variability in Biogen's stock price. It's as if the air quality in Harrison, Arkansas is casting its influence on the stock market like a silent but powerful force – move over Wall Street, here comes the Harrison breeze!

As we journey through the tantalizing terrain of financial and environmental data, it becomes clear that this correlation is not a statistical wild goose chase, but a bona fide connection that demands attention. The scatterplot, akin to a captivating piece of art, vividly depicts the captivating dance between air quality and stock prices, proving once and for all that in the world of finance, the winds of change may blow from the most unexpected directions!

So, as we close the chapter on this research, we can confidently say that the air in Harrison, Arkansas, and Biogen's stock price are not just passing acquaintances – they are dynamic partners in an intricate statistical ballet that has left us all awe-struck.

In light of these whirlwind findings, we assert that no more research is needed in this area – after all, we've already uncovered enough groundbreaking evidence to last a lifetime. Let's raise a statistical toast to the unexpected, the bizarre, and the correlation coefficient that brought us all together, and bid adieu knowing that the world of research is filled with surprises around every corner!

*Drops the mic*

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 Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental Economics and Stock Market Dynamics

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 Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Atmospheric Anomalies and Economic Indicators

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 Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price with an abstract of The relationship between air quality and stock prices has long been a topic of interest in both environmental and financial domains, but its dynamics continue to elude researchers and investors alike. Our study delves into this conundrum by examining the correlation between the air quality in Harrison, Arkansas, and the stock price of Biogen (BIIB), a leading biotechnology company. Utilizing data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), we conducted a rigorous analysis spanning the years 2002 to 2023. Surprisingly, our findings reveal a striking correlation coefficient of 0.8657366 and a statistically significant p-value of less than 0.01. While Harrison, Arkansas may be famous for its scenic beauty, the impact of its air quality on the stock market proves to be nothing short of breathtaking. Our study not only sheds light on this unexpected connection but also emphasizes the need for investors to consider the air they breathe alongside the stocks they trade.

ChatGPT:

Harrison Arkansas air quality, Biogen stock price, correlation between air quality and stock prices, environmental impact on stock market, air quality impact on investments, Biogen (BIIB) stock analysis, EPA air quality data, LSEG Analytics stock data, air quality research, stock market correlation studies

*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 Harrison, Arkansas
Detailed data title: Percentage of days with good air quality in Harrison, AR
Source: Environmental Protection Agency
See what else correlates with Air quality in Harrison, Arkansas

Biogen's stock price (BIIB)
Detailed data title: Opening price of Biogen (BIIB) on the first trading day of the year
Source: LSEG Analytics (Refinitiv)
Additional Info: ^{See full details} Via Microsoft Excel Stockhistory function

See what else correlates with Biogen's stock price (BIIB)

Correlation r = 0.8657366 (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 = 0.7494998 (Coefficient of determination)
This means 74.9% of the change in the one variable (i.e., Biogen's stock price (BIIB)) is predictable based on the change in the other (i.e., Air quality in Harrison, Arkansas) over the 22 years from 2002 through 2023.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 2.0E-7.^Show 0.0000001951230531844982800000
The p-value is a measure of how probable it is that we would randomly find a result this extreme.^Note More specifically the p-value is a measure of how probable it is that we would randomly find a result this extreme if we had only tested one pair of variables one time.

But I am a p-villain. I absolutely did not test only one pair of variables one time. I correlated hundreds of millions of pairs of variables. I threw boatloads of data into an industrial-sized blender to find this correlation.

Who is going to stop me? p-value reporting doesn't require me to report how many calculations I had to go through in order to find a low p-value!
On average, you will find a correaltion as strong as 0.87 in 2.0E-5% of random cases. Said differently, if you correlated 5,124,971 random variables^Note 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 21 degrees of freedom, ^Note 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.

[ 0.7, 0.94 ] 95% correlation confidence interval (using the Fisher z-transformation)
^{Read more about the confidence interval} The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

This one is a bit more complciated than the other calculations, but I include it because many people have been pushing for confidence intervals instead of p-value calculations (for example: NEJM. However, if you are dredging data, you can reliably find yourself in the 5%. That's my goal!

All values for the years included above: ^Note If I were being very sneaky, I could trim years from the beginning or end of the datasets to increase the correlation on some pairs of variables. I don't do that because there are already plenty of correlations in my database without monkeying with the years.

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.

	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Air quality in Harrison, Arkansas (Good air quality)	0.777159	0.723757	0.788889	0.760989	0.677686	0.752747	0.81044	0.898305	0.79726	0.780822	0.773224	0.873973	0.920548	0.934247	0.956284	0.953425	0.923077	0.950685	0.972527	0.950685	0.939726	0.868132
Biogen's stock price (BIIB) (Stock price)	63.51	30.75	34.03	61.64	42.09	45.39	52.42	43.74	49.71	62.34	102.65	136.99	257.39	315.79	276.64	263.27	321.15	296.84	299.06	245.74	240.15	276.73

Why this works

Data dredging: I have 25,153 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 632,673,409 correlation calculations! This is called “data dredging.” Instead of starting with a hypothesis and testing it, I instead abused the data to see what correlations shake out. It’s a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random.
Lack of causal connection: There is probably^Note Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple^Note Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
p-value calculation does not take this into account, so mathematically it appears less probable than it really is.
Y-axis doesn't start at zero: I truncated the Y-axes of the graph above. I also used a line graph, which makes the visual connection stand out more than it deserves. ^Note Nothing against line graphs. They are great at telling a story when you have linear data! But visually it is deceptive because the only data is at the points on the graph, not the lines on the graph. In between each point, the data could have been doing anything. Like going for a random walk by itself!
Mathematically what I showed is true, but it is intentionally misleading. Below is the same chart but with both Y-axes starting at zero.

Try it yourself

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

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([0.777159,0.723757,0.788889,0.760989,0.677686,0.752747,0.81044,0.898305,0.79726,0.780822,0.773224,0.873973,0.920548,0.934247,0.956284,0.953425,0.923077,0.950685,0.972527,0.950685,0.939726,0.868132,])
array_2 = np.array([63.51,30.75,34.03,61.64,42.09,45.39,52.42,43.74,49.71,62.34,102.65,136.99,257.39,315.79,276.64,263.27,321.15,296.84,299.06,245.74,240.15,276.73,])
array_1_name = "Air quality in Harrison, Arkansas"
array_2_name = "Biogen's stock price (BIIB)"

# Perform the calculation
print(f"Calculating the correlation between {array_1_name} and {array_2_name}...")
correlation, r_squared, p_value = calculate_correlation(array_1, array_2)

# Print the results
print("Correlation Coefficient:", correlation)
print("R-squared:", r_squared)
print("P-value:", p_value)

Reuseable content

You may re-use the images on this page for any purpose, even commercial purposes, without asking for permission. The only requirement is that you attribute Tyler Vigen. ^Note Attribution can take many different forms. If you leave the "tylervigen.com" link in the image, that satisfies it just fine. If you remove it and move it to a footnote, that's fine too. You can also just write "Charts courtesy of Tyler Vigen" at the bottom of an article.

You do not need to attribute "the spurious correlations website," and you don't even need to link here if you don't want to. I don't gain anything from pageviews. There are no ads on this site, there is nothing for sale, and I am not for hire.

For the record, I am just one person. Tyler Vigen, he/him/his. I do have degrees, but they should not go after my name unless you want to annoy my wife. If that is your goal, then go ahead and cite me as "Tyler Vigen, A.A. A.A.S. B.A. J.D." Otherwise it is just "Tyler Vigen."

When spoken, my last name is pronounced "vegan," like I don't eat meat.

Full license details.
For more on re-use permissions, or to get a signed release form, see tylervigen.com/permission.

Download images for these variables:

High resolution line chart ^Note The image linked here is a Scalable Vector Graphic (SVG). It is the highest resolution that is possible to achieve. It scales up beyond the size of the observable universe without pixelating. You do not need to email me asking if I have a higher resolution image. I do not. The physical limitations of our universe prevent me from providing you with an image that is any higher resolution than this one.

If you insert it into a PowerPoint presentation (a tool well-known for managing things that are the scale of the universe), you can right-click > "Ungroup" or "Create Shape" and then edit the lines and text directly. You can also change the colors this way.

Alternatively you can use a tool like Inkscape.
High resolution line chart, optimized for mobile
Alternative high resolution line chart
Scatterplot
Portable line chart (png)
Portable line chart (png), optimized for mobile
Line chart for only Air quality in Harrison, Arkansas
Line chart for only Biogen's stock price (BIIB)
AI-generated correlation image
The spurious research paper: Clearing the Air: Exploring the Gasping Correlation Between Air Quality in Harrison, Arkansas, and Biogen's Stock Price

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Correlation ID: 4275 · Black Variable ID: 21827 · Red Variable ID: 1798


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