Spurious correlation #4,567 · 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 Vallejo, California and the second variable is Applied Materials' stock price (AMAT). The chart goes from 2002 to 2020, and the two variables track closely in value over that time.

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Vallejo, California and the second variable is Applied Materials' stock price (AMAT). The chart goes from 2002 to 2020, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As air pollution in Vallejo, California increased, so did the demand for air purifiers. Applied Materials happens to manufacture cutting-edge air purification technology as a side business, and the sudden surge in orders for their high-tech air filters boosted their overall revenue. This unexpected market for clean air solutions led to a spike in investor interest and a subsequent rise in Applied Materials' stock price. Who knew that smog could indirectly lead to a breath of fresh air for a company's financials!

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a surreal cityscape in Vallejo, California, with skyscrapers obscured by thick, glitchy smog-like patterns that warp the skyline. Amidst the haze, numerous glitched storefronts display exaggerated, larger-than-life air purifiers while glitched stock market charts show Applied Materials' stock price ascending rapidly into the hazy, distorted sky. 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 Vallejo, California and Applied Materials' stock price (AMAT). 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: Cyber folk Glitch art Surrealism Art nouveau Woodblock painting
ChatGPT: Glitch art

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 Vallejo, California and Applied Materials' stock price (AMAT), in the following situation: As air pollution in Vallejo, California increased, so did the demand for air purifiers. Applied Materials happens to manufacture cutting-edge air purification technology as a side business, and the sudden surge in orders for their high-tech air filters boosted their overall revenue. This unexpected market for clean air solutions led to a spike in investor interest and a subsequent rise in Applied Materials' stock price. Who knew that smog could indirectly lead to a breath of fresh air for a company's financials!. Keep the description simple.
ChatGPT: In Vallejo, California, thick smog clouded the sky as pollution levels soared. Amongst this haze, countless air purifiers were in high demand and prominently displayed in store windows. Meanwhile, a stock market chart showed Applied Materials' stock price skyrocketing with an upward trend, reflecting the unexpected surge in investor interest due to the sudden demand for their high-tech air filters.

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: [ Glitch art ] and depicting this scene: In Vallejo, California, thick smog clouded the sky as pollution levels soared. Amongst this haze, countless air purifiers were in high demand and prominently displayed in store windows. Meanwhile, a stock market chart showed Applied Materials' stock price skyrocketing with an upward trend, reflecting the unexpected surge in investor interest due to the sudden demand for their high-tech air filters. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a surreal cityscape in Vallejo, California, with skyscrapers obscured by thick, glitchy smog-like patterns that warp the skyline. Amidst the haze, numerous glitched storefronts display exaggerated, larger-than-life air purifiers while glitched stock market charts show Applied Materials' stock price ascending rapidly into the hazy, distorted sky.

*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 pollution in Vallejo, California caused Applied Materials' stock price (AMAT) to increase.\Make it sound serious until the end.

AI academic paper

(Because p < 0.01)

Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT)

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 dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.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 Vallejo, California and Applied Materials' stock price (AMAT). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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]]
"Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT)"

[[ABSTRACT]]
This study examines the intriguing connection between air pollution levels in the city of Vallejo, California, and the stock price of Applied Materials (AMAT). Drawing on data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), our research team analyzed air quality indicators and stock performance metrics from 2002 to 2020. The findings reveal a substantial correlation coefficient of 0.8046013 and a statistically significant p-value of < 0.01, suggesting a robust relationship between these seemingly unrelated phenomena. Our results indicate that as air pollution levels in Vallejo increased, the stock price of Applied Materials experienced corresponding fluctuations.

The study findings bring to light the unanticipated impact of environmental factors on stock market dynamics, reminding us that even in the world of finance, the air we breathe can have a tangible influence. For those involved in investment decision-making, this research may provide new insight into the environmental factors that can "inflate" or "deflate" stock prices, offering a breath of fresh air in financial analysis. As this unlikely correlation takes center stage, it prompts us to consider the quip, "What do you call a group of stock analysts affected by air pollution? Smog investors!"

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The interplay between environmental factors and financial markets has long been a subject of interest, with researchers continually probing the depths of this complex relationship. In this regard, the unexpected linkage between air pollution levels in Vallejo, California, and the stock price of Applied Materials (AMAT) stands out as a particularly compelling and, dare I say, "air-rising" discovery. As we delve into this gaseous relationship, it brings to mind the age-old question, "What did the air pollution say to the stock price? Let's clear the air and see where this goes!"
The city of Vallejo, located in the San Francisco Bay Area, has grappled with air pollution issues, stemming from both vehicular and industrial sources. Meanwhile, Applied Materials, a prominent player in the semiconductor industry, has witnessed its stock price undergo fluctuations over the years. These seemingly disparate phenomena merge in an unexpected tango, prompting us to ask, "Why did the air pollution invest in the stock market? It wanted to see some green!"
As we set out to explore this intriguing correlation, it is essential to recognize the broader implications of our investigation. The findings derived from this study not only shed light on the influence of air quality on stock prices but also highlight the significance of considering environmental variables within the realm of financial analysis. This investigation serves as a "breath of fresh air" in illuminating the interconnectedness of seemingly unrelated domains. It beckons us to ponder, "Why did the stock price break up with air pollution? It needed some space!"
The gravitational pull between air pollution levels and stock performance metrics in Vallejo and Applied Materials, respectively, reflects a complexity that extends beyond traditional market indicators. It unravels a tale of intertwining destinies, as if to say, "What do you call a semiconductor company's stock price influenced by air pollution? A volatile bond!"
As we navigate through the nuances of this entwined narrative, it becomes evident that this unexpected correlation challenges conventional wisdom, offering a confluence of financial and environmental insights. Our exploration of this uncharted territory not only enriches our understanding of market dynamics but also injects a gust of fresh air into the discourse surrounding the interplay of environmental factors and financial markets.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The connection between air pollution and stock prices has been a subject of interest in the field of environmental economics. Smith et al. (2015) illustrated the potential impact of air quality on financial markets, laying the groundwork for subsequent explorations. Similarly, Doe and Jones (2018) delved into the influence of environmental variables on stock performance, paving the way for a deeper understanding of this intricate relationship.

In "The Economics of Air Pollution" by Anthony J. McMichael, the authors address the far-reaching implications of air pollution on various aspects of society, including its potential effects on financial markets. Moreover, "Capital in the Twenty-First Century" by Thomas Piketty presents an in-depth analysis of wealth and income inequality, indirectly touching on the impacts of environmental factors on economic dynamics.

Turning to fiction, "The Air He Breathes" by Brittainy C. Cherry and "Perfume: The Story of a Murderer" by Patrick Süskind offer imaginative narratives that, although unrelated to finance, symbolically capture the metaphorical essence of air and its influence on human experiences.

Further, one cannot overlook the resonances found in the world of board games. "Fresh Air" by Reiner Knizia and "Smog: The Thirteenth Hour" by Filip Neduk subtly echo the themes of environmental influence and financial interplay, albeit in a playful and lighthearted context.

This juxtaposition of scholarly works and cultural references emphasizes the multifaceted nature of the relationship between air pollution and stock prices. It serves as a reminder that even in the realm of academic research, there is always room for a breath of fresh air and a well-placed dad joke. After all, as the old saying goes, "Why did the stock market like the clean air? It took a breath of fresh share!"

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.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 Vallejo, California and Applied Materials' stock price (AMAT). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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 2020

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]]
"Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT)"

[[ABSTRACT]]
This study examines the intriguing connection between air pollution levels in the city of Vallejo, California, and the stock price of Applied Materials (AMAT). Drawing on data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), our research team analyzed air quality indicators and stock performance metrics from 2002 to 2020. The findings reveal a substantial correlation coefficient of 0.8046013 and a statistically significant p-value of < 0.01, suggesting a robust relationship between these seemingly unrelated phenomena. Our results indicate that as air pollution levels in Vallejo increased, the stock price of Applied Materials experienced corresponding fluctuations.

The study findings bring to light the unanticipated impact of environmental factors on stock market dynamics, reminding us that even in the world of finance, the air we breathe can have a tangible influence. For those involved in investment decision-making, this research may provide new insight into the environmental factors that can "inflate" or "deflate" stock prices, offering a breath of fresh air in financial analysis. As this unlikely correlation takes center stage, it prompts us to consider the quip, "What do you call a group of stock analysts affected by air pollution? Smog investors!"

[[INTRODUCTION]]
The interplay between environmental factors and financial markets has long been a subject of interest, with researchers continually probing the depths of this complex relationship. In this regard, the unexpected linkage between air pollution levels in Vallejo, California, and the stock price of Applied Materials (AMAT) stands out as a particularly compelling and, dare I say, "air-rising" discovery. As we delve into this gaseous relationship, it brings to mind the age-old question, "What did the air pollution say to the stock price? Let's clear the air and see where this goes!"
The city of Vallejo, located in the San Francisco Bay Area, has grappled with air pollution issues, stemming from both vehicular and industrial sources. Meanwhile, Applied Materials, a prominent player in the semiconductor industry, has witnessed its stock price undergo fluctuations over the years. These seemingly disparate phenomena merge in an unexpected tango, prompting us to ask, "Why did the air pollution invest in the stock market? It wanted to see some green!"
As we set out to explore this intriguing correlation, it is essential to recognize the broader implications of our investigation. The findings derived from this study not only shed light on the influence of air quality on stock prices but also highlight the significance of considering environmental variables within the realm of financial analysis. This investigation serves as a "breath of fresh air" in illuminating the interconnectedness of seemingly unrelated domains. It beckons us to ponder, "Why did the stock price break up with air pollution? It needed some space!"
The gravitational pull between air pollution levels and stock performance metrics in Vallejo and Applied Materials, respectively, reflects a complexity that extends beyond traditional market indicators. It unravels a tale of intertwining destinies, as if to say, "What do you call a semiconductor company's stock price influenced by air pollution? A volatile bond!"
As we navigate through the nuances of this entwined narrative, it becomes evident that this unexpected correlation challenges conventional wisdom, offering a confluence of financial and environmental insights. Our exploration of this uncharted territory not only enriches our understanding of market dynamics but also injects a gust of fresh air into the discourse surrounding the interplay of environmental factors and financial markets.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

The primary objective of this research endeavor was to elucidate the potential connection between air pollution in Vallejo, California, and the stock price of Applied Materials (AMAT). To achieve this, a comprehensive methodology encompassing data collection, processing, and analysis was implemented, resembling the intricate dance of air pollutants in the atmosphere and stock prices in the market. This approach aimed to capture the multidimensional nature of the relationship under investigation, akin to untangling a complex knot of interwoven gaseous and financial elements. As we embarked on this endeavor, we couldn't help but ponder, "Why did the air pollution refuse to engage in the stock market? It found the prospect too 'hazy'!"

Data Collection:
The research team diligently scoured various sources, including the Environmental Protection Agency and LSEG Analytics (Refinitiv), to obtain air quality indicators for Vallejo, California, spanning the years 2002 to 2020. Simultaneously, stock performance metrics pertaining to Applied Materials (AMAT) were procured from reputable financial databases. This process involved sifting through a voluminous expanse of information, akin to separating fine particulate matter from a swirling vortex of stock market data. It made us realize that this task was indeed like searching for a needle in a haystack, albeit in a digital landscape filled with numbers and trends, and not actual hay.

Data Processing and Analysis:
The collected data underwent meticulous processing, including cleansing, normalization, and validation, to ensure its suitability for rigorous statistical analysis. Subsequently, the air pollution indicators and stock performance metrics were subjected to a battery of advanced statistical tests, including correlation analysis and regression modeling. These analytical procedures were executed with precision and rigor, resembling the delicate calibration of an air quality sensor and the sophisticated modeling of financial market dynamics. Amidst this meticulous process, we couldn't help but reflect, "Why did the stock price go skydiving with air pollution? It wanted to experience some 'volatile' thrills!"

Correlation Analysis:
The heart of the methodology lay in evaluating the correlation between air pollution levels in Vallejo and the stock price of Applied Materials. This involved calculating correlation coefficients and associated p-values, allowing us to discern the strength and significance of the relationship under scrutiny. The results of these analyses were interpreted with caution and meticulous attention to detail, akin to navigating through a dense smog of statistical outcomes in search of poignant insights. It is worth noting though, that as we delved into this statistical maze, we found ourselves contemplating, "Why was the air pollution hesitant to invest in the stock market? It was concerned about the 'volatile' nature of financial trends!"

It is important to acknowledge the inherent limitations of this study, including the reliance on secondary data sources and the dynamic nature of financial markets. Nevertheless, despite these challenges, the methodology adopted in this research provided a robust framework for exploring the intricate relationship between air pollution in Vallejo, California, and Applied Materials' stock price. It became evident that navigating through this convoluted maze of data and statistical analyses left us pondering, "Why was the statistical model so interested in air pollution? It saw potential for a 'correlation-ship'!"

In summary, the methodology employed in this study was designed to untangle the enigmatic connection between air pollution in Vallejo and the stock price of Applied Materials. It involved a rigorous amalgamation of data collection, processing, and statistical analysis, reminiscent of a whimsical waltz between atmospheric pollutants and financial indicators. As we conclude this section, we cannot help but jest, "What did the statistician say to the air pollution? 'Let's crunch some numbers and clear the air!'"

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.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 Vallejo, California and Applied Materials' stock price (AMAT). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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 2020, you found a correlation 0.8046013, r-squared of 0.6473832, 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]]
"Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT)"

[[ABSTRACT]]
This study examines the intriguing connection between air pollution levels in the city of Vallejo, California, and the stock price of Applied Materials (AMAT). Drawing on data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), our research team analyzed air quality indicators and stock performance metrics from 2002 to 2020. The findings reveal a substantial correlation coefficient of 0.8046013 and a statistically significant p-value of < 0.01, suggesting a robust relationship between these seemingly unrelated phenomena. Our results indicate that as air pollution levels in Vallejo increased, the stock price of Applied Materials experienced corresponding fluctuations.

The study findings bring to light the unanticipated impact of environmental factors on stock market dynamics, reminding us that even in the world of finance, the air we breathe can have a tangible influence. For those involved in investment decision-making, this research may provide new insight into the environmental factors that can "inflate" or "deflate" stock prices, offering a breath of fresh air in financial analysis. As this unlikely correlation takes center stage, it prompts us to consider the quip, "What do you call a group of stock analysts affected by air pollution? Smog investors!"

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The interplay between environmental factors and financial markets has long been a subject of interest, with researchers continually probing the depths of this complex relationship. In this regard, the unexpected linkage between air pollution levels in Vallejo, California, and the stock price of Applied Materials (AMAT) stands out as a particularly compelling and, dare I say, "air-rising" discovery. As we delve into this gaseous relationship, it brings to mind the age-old question, "What did the air pollution say to the stock price? Let's clear the air and see where this goes!"
The city of Vallejo, located in the San Francisco Bay Area, has grappled with air pollution issues, stemming from both vehicular and industrial sources. Meanwhile, Applied Materials, a prominent player in the semiconductor industry, has witnessed its stock price undergo fluctuations over the years. These seemingly disparate phenomena merge in an unexpected tango, prompting us to ask, "Why did the air pollution invest in the stock market? It wanted to see some green!"
As we set out to explore this intriguing correlation, it is essential to recognize the broader implications of our investigation. The findings derived from this study not only shed light on the influence of air quality on stock prices but also highlight the significance of considering environmental variables within the realm of financial analysis. This investigation serves as a "breath of fresh air" in illuminating the interconnectedness of seemingly unrelated domains. It beckons us to ponder, "Why did the stock price break up with air pollution? It needed some space!"
The gravitational pull between air pollution levels and stock performance metrics in Vallejo and Applied Materials, respectively, reflects a complexity that extends beyond traditional market indicators. It unravels a tale of intertwining destinies, as if to say, "What do you call a semiconductor company's stock price influenced by air pollution? A volatile bond!"
As we navigate through the nuances of this entwined narrative, it becomes evident that this unexpected correlation challenges conventional wisdom, offering a confluence of financial and environmental insights. Our exploration of this uncharted territory not only enriches our understanding of market dynamics but also injects a gust of fresh air into the discourse surrounding the interplay of environmental factors and financial markets.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The analysis of the data collected from 2002 to 2020 revealed a substantial correlation coefficient of 0.8046013 between air pollution levels in Vallejo, California, and Applied Materials' stock price (AMAT). The r-squared value of 0.6473832 indicates that approximately 65% of the variability in AMAT stock price can be explained by changes in air pollution levels. The statistically significant p-value of less than 0.01 suggests a robust and reliable relationship between the two variables, providing strong evidence to refute any claims of spurious correlation. This robust correlation prompts us to reconsider the classic question, "What's the best way to invest in air pollution? With a smoggy portfolio, of course!"

The scatterplot (Fig. 1) visually depicts the strong positive correlation between air pollution levels in Vallejo and Applied Materials' stock price, further reinforcing the empirical findings. This correlation, unexpected and yet undeniable, prompts us to ponder, "What did the air pollution investor say to Applied Materials' stock? Let's breathe new life into this partnership!"

These findings highlight the surprising influence of local air quality on the stock market, underscoring the need to incorporate environmental variables into financial models. This unforeseen connection invites us to consider the question, "Why did the air pollution cross the road to affect the stock price? To show that it had a significant impact!"

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.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 Vallejo, California and Applied Materials' stock price (AMAT). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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]]
"Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT)"

[[ABSTRACT]]
This study examines the intriguing connection between air pollution levels in the city of Vallejo, California, and the stock price of Applied Materials (AMAT). Drawing on data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), our research team analyzed air quality indicators and stock performance metrics from 2002 to 2020. The findings reveal a substantial correlation coefficient of 0.8046013 and a statistically significant p-value of < 0.01, suggesting a robust relationship between these seemingly unrelated phenomena. Our results indicate that as air pollution levels in Vallejo increased, the stock price of Applied Materials experienced corresponding fluctuations.

The study findings bring to light the unanticipated impact of environmental factors on stock market dynamics, reminding us that even in the world of finance, the air we breathe can have a tangible influence. For those involved in investment decision-making, this research may provide new insight into the environmental factors that can "inflate" or "deflate" stock prices, offering a breath of fresh air in financial analysis. As this unlikely correlation takes center stage, it prompts us to consider the quip, "What do you call a group of stock analysts affected by air pollution? Smog investors!"

[[LITERATURE REVIEW]]
The connection between air pollution and stock prices has been a subject of interest in the field of environmental economics. Smith et al. (2015) illustrated the potential impact of air quality on financial markets, laying the groundwork for subsequent explorations. Similarly, Doe and Jones (2018) delved into the influence of environmental variables on stock performance, paving the way for a deeper understanding of this intricate relationship.
In "The Economics of Air Pollution" by Anthony J. McMichael, the authors address the far-reaching implications of air pollution on various aspects of society, including its potential effects on financial markets. Moreover, "Capital in the Twenty-First Century" by Thomas Piketty presents an in-depth analysis of wealth and income inequality, indirectly touching on the impacts of environmental factors on economic dynamics.
Turning to fiction, "The Air He Breathes" by Brittainy C. Cherry and "Perfume: The Story of a Murderer" by Patrick Süskind offer imaginative narratives that, although unrelated to finance, symbolically capture the metaphorical essence of air and its influence on human experiences.
Further, one cannot overlook the resonances found in the world of board games. "Fresh Air" by Reiner Knizia and "Smog: The Thirteenth Hour" by Filip Neduk subtly echo the themes of environmental influence and financial interplay, albeit in a playful and lighthearted context.
This juxtaposition of scholarly works and cultural references emphasizes the multifaceted nature of the relationship between air pollution and stock prices. It serves as a reminder that even in the realm of academic research, there is always room for a breath of fresh air and a well-placed dad joke. After all, as the old saying goes, "Why did the stock market like the clean air? It took a breath of fresh share!"

[[RESULTS]]
The analysis of the data collected from 2002 to 2020 revealed a substantial correlation coefficient of 0.8046013 between air pollution levels in Vallejo, California, and Applied Materials' stock price (AMAT). The r-squared value of 0.6473832 indicates that approximately 65% of the variability in AMAT stock price can be explained by changes in air pollution levels. The statistically significant p-value of less than 0.01 suggests a robust and reliable relationship between the two variables, providing strong evidence to refute any claims of spurious correlation. This robust correlation prompts us to reconsider the classic question, "What's the best way to invest in air pollution? With a smoggy portfolio, of course!"
The scatterplot (Fig. 1) visually depicts the strong positive correlation between air pollution levels in Vallejo and Applied Materials' stock price, further reinforcing the empirical findings. This correlation, unexpected and yet undeniable, prompts us to ponder, "What did the air pollution investor say to Applied Materials' stock? Let's breathe new life into this partnership!"
These findings highlight the surprising influence of local air quality on the stock market, underscoring the need to incorporate environmental variables into financial models. This unforeseen connection invites us to consider the question, "Why did the air pollution cross the road to affect the stock price? To show that it had a significant impact!"

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of this study align with prior research on the link between environmental factors and financial markets, providing empirical support for the notion that air pollution can indeed have a tangible impact on stock prices. The notable correlation coefficient of 0.8046013 between air pollution levels in Vallejo, California, and Applied Materials' stock price (AMAT) reaffirms the findings put forth by Smith et al. (2015) and Doe and Jones (2018). It appears that the influence of air quality on stock market dynamics is no mere flight of fancy but rather a substantial and statistically significant relationship. This corroborative evidence invites us to crack a joke, "Why did the stock price go up when the air pollution level increased? It was riding the wave of smog stocks!"

The substantial r-squared value of 0.6473832 indicates that approximately 65% of the variation in AMAT stock price can be attributed to changes in air pollution levels. This outcome underscores the considerable weight of environmental factors in shaping stock price movements, lending credence to the supposition that air pollution is not merely "up in the air" but truly impactful. This solid statistical support prompts us to playfully inquire, "Why did the stock market investor bring a fan to the office? To blow away any uncertainties in air pollution's impact on stock prices!"

Moreover, the visually compelling scatterplot (Fig. 1) vividly demonstrates the strong positive correlation between air pollution levels in Vallejo and AMAT stock price, reinforcing the robustness of the findings. This visual evidence captures the essence of the relationship between these seemingly disparate variables, compelling us to interject with a quip, "What did the stock say to the air pollution? Let's clear the air and see where the market takes us!"

In summary, the present study not only confirms the unexpected alliance between air pollution in Vallejo, California, and Applied Materials' stock price (AMAT) but also underscores the need to account for environmental variables in financial analyses. This intriguing correlation prompts us to humorously muse, "Why did the stock market become friends with the air pollution? They shared a common interest in making a profit, and it was a breath of fresh share for both!"

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.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 Vallejo, California and Applied Materials' stock price (AMAT). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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]]
"Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT)"

[[ABSTRACT]]
This study examines the intriguing connection between air pollution levels in the city of Vallejo, California, and the stock price of Applied Materials (AMAT). Drawing on data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), our research team analyzed air quality indicators and stock performance metrics from 2002 to 2020. The findings reveal a substantial correlation coefficient of 0.8046013 and a statistically significant p-value of < 0.01, suggesting a robust relationship between these seemingly unrelated phenomena. Our results indicate that as air pollution levels in Vallejo increased, the stock price of Applied Materials experienced corresponding fluctuations.

The study findings bring to light the unanticipated impact of environmental factors on stock market dynamics, reminding us that even in the world of finance, the air we breathe can have a tangible influence. For those involved in investment decision-making, this research may provide new insight into the environmental factors that can "inflate" or "deflate" stock prices, offering a breath of fresh air in financial analysis. As this unlikely correlation takes center stage, it prompts us to consider the quip, "What do you call a group of stock analysts affected by air pollution? Smog investors!"

[[INTRDUCTION]]
The interplay between environmental factors and financial markets has long been a subject of interest, with researchers continually probing the depths of this complex relationship. In this regard, the unexpected linkage between air pollution levels in Vallejo, California, and the stock price of Applied Materials (AMAT) stands out as a particularly compelling and, dare I say, "air-rising" discovery. As we delve into this gaseous relationship, it brings to mind the age-old question, "What did the air pollution say to the stock price? Let's clear the air and see where this goes!"
The city of Vallejo, located in the San Francisco Bay Area, has grappled with air pollution issues, stemming from both vehicular and industrial sources. Meanwhile, Applied Materials, a prominent player in the semiconductor industry, has witnessed its stock price undergo fluctuations over the years. These seemingly disparate phenomena merge in an unexpected tango, prompting us to ask, "Why did the air pollution invest in the stock market? It wanted to see some green!"
As we set out to explore this intriguing correlation, it is essential to recognize the broader implications of our investigation. The findings derived from this study not only shed light on the influence of air quality on stock prices but also highlight the significance of considering environmental variables within the realm of financial analysis. This investigation serves as a "breath of fresh air" in illuminating the interconnectedness of seemingly unrelated domains. It beckons us to ponder, "Why did the stock price break up with air pollution? It needed some space!"
The gravitational pull between air pollution levels and stock performance metrics in Vallejo and Applied Materials, respectively, reflects a complexity that extends beyond traditional market indicators. It unravels a tale of intertwining destinies, as if to say, "What do you call a semiconductor company's stock price influenced by air pollution? A volatile bond!"
As we navigate through the nuances of this entwined narrative, it becomes evident that this unexpected correlation challenges conventional wisdom, offering a confluence of financial and environmental insights. Our exploration of this uncharted territory not only enriches our understanding of market dynamics but also injects a gust of fresh air into the discourse surrounding the interplay of environmental factors and financial markets.

[[RESULTS]]
The analysis of the data collected from 2002 to 2020 revealed a substantial correlation coefficient of 0.8046013 between air pollution levels in Vallejo, California, and Applied Materials' stock price (AMAT). The r-squared value of 0.6473832 indicates that approximately 65% of the variability in AMAT stock price can be explained by changes in air pollution levels. The statistically significant p-value of less than 0.01 suggests a robust and reliable relationship between the two variables, providing strong evidence to refute any claims of spurious correlation. This robust correlation prompts us to reconsider the classic question, "What's the best way to invest in air pollution? With a smoggy portfolio, of course!"
The scatterplot (Fig. 1) visually depicts the strong positive correlation between air pollution levels in Vallejo and Applied Materials' stock price, further reinforcing the empirical findings. This correlation, unexpected and yet undeniable, prompts us to ponder, "What did the air pollution investor say to Applied Materials' stock? Let's breathe new life into this partnership!"
These findings highlight the surprising influence of local air quality on the stock market, underscoring the need to incorporate environmental variables into financial models. This unforeseen connection invites us to consider the question, "Why did the air pollution cross the road to affect the stock price? To show that it had a significant impact!"

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Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, the findings of this study illuminate the unexpectedly gaseous relationship between air pollution levels in Vallejo, California, and the stock price of Applied Materials (AMAT). The substantial correlation coefficient and the statistically significant p-value present compelling evidence of a robust connection between these seemingly disparate variables, prompting us to quip, "Why don't stock analysts ever get sick? They have high levels of AMAT in their system!"

These results offer a breath of fresh air in financial analysis, indicating that environmental factors such as air pollution can indeed have a substantial impact on stock market dynamics. The surprising influence of local air quality on stock prices reminds us of the old saying, "Don't hold your breath, but do hold your AMAT stocks!"

Given the unanticipated nature of this correlation, it is clear that the interplay between environmental factors and financial markets is more intricate and far-reaching than previously thought. As we consider the implications of this unlikely pairing, we are reminded of the enduring joke, "Why did the air pollution go to therapy? It had issues that it needed to air out!"

Therefore, based on the robust findings of this study, it can be asserted that no further research in this area is needed. The air has been cleared, and the results have spoken – it's time to let this unlikely association take a 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 Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT). 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 Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT). Respond only with the name of a fictional organization.

ChatGPT:

The Society for Atmospheric Inventory and Market 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 Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT) with an abstract of This study examines the intriguing connection between air pollution levels in the city of Vallejo, California, and the stock price of Applied Materials (AMAT). Drawing on data from the Environmental Protection Agency and LSEG Analytics (Refinitiv), our research team analyzed air quality indicators and stock performance metrics from 2002 to 2020. The findings reveal a substantial correlation coefficient of 0.8046013 and a statistically significant p-value of < 0.01, suggesting a robust relationship between these seemingly unrelated phenomena. Our results indicate that as air pollution levels in Vallejo increased, the stock price of Applied Materials experienced corresponding fluctuations.
The study findings bring to light the unanticipated impact of environmental factors on stock market dynamics, reminding us that even in the world of finance, the air we breathe can have a tangible influence. For those involved in investment decision-making, this research may provide new insight into the environmental factors that can "inflate" or "deflate" stock prices, offering a breath of fresh air in financial analysis. As this unlikely correlation takes center stage, it prompts us to consider the quip, "What do you call a group of stock analysts affected by air pollution? Smog investors!

ChatGPT:

air pollution, Vallejo California, Applied Materials stock price, AMAT, stock market dynamics, environmental factors, investment decision-making, financial analysis, correlation coefficient

*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 Vallejo, California
Detailed data title: Percentage of days 'unhealthy' or worse air quality in Vallejo-Fairfield, CA
Source: Environmental Protection Agency
See what else correlates with Air pollution in Vallejo, California

Applied Materials' stock price (AMAT)
Detailed data title: Opening price of Applied Materials (AMAT) 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 Applied Materials' stock price (AMAT)

Correlation r = 0.8046013 (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 = 0.6473832 (Coefficient of determination)
This means 64.7% of the change in the one variable (i.e., Applied Materials' stock price (AMAT)) is predictable based on the change in the other (i.e., Air pollution in Vallejo, California) over the 19 years from 2002 through 2020.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 3.3E-5.^Show 0.0000327407572187825000000000
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 0.8 in 0.0033% of random cases. Said differently, if you correlated 30,543 random variables^Note You don't actually need 30 thousand variables to find a correlation like this one. 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.

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 18 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 18 because we have two variables measured over a period of 19 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.

[ 0.55, 0.92 ] 95% correlation confidence interval (using the Fisher z-transformation)
^{Read more about the confidence interval} The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

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

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

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

	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
Air pollution in Vallejo, California (Bad air quality days)	0.547945	0	0.273224	0	0.821918	0	1.0929	0	0	0	0	0	0	0	0	1.36986	3.28767	0	1.91257
Applied Materials' stock price (AMAT) (Stock price)	20.43	13.45	22.61	17.2	18.04	18.32	17.73	10.12	14.05	14.13	10.93	11.64	17.69	24.99	18.31	32.36	51.68	32.04	62

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.

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([0.547945,0,0.273224,0,0.821918,0,1.0929,0,0,0,0,0,0,0,0,1.36986,3.28767,0,1.91257,])
array_2 = np.array([20.43,13.45,22.61,17.2,18.04,18.32,17.73,10.12,14.05,14.13,10.93,11.64,17.69,24.99,18.31,32.36,51.68,32.04,62,])
array_1_name = "Air pollution in Vallejo, California"
array_2_name = "Applied Materials' stock price (AMAT)"

# 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
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Line chart for only Air pollution in Vallejo, California
Line chart for only Applied Materials' stock price (AMAT)
AI-generated correlation image
The spurious research paper: Blowing Hot Air: The Gaseous Relationship Between Air Pollution in Vallejo, California and Applied Materials' Stock Price (AMAT)

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Correlation ID: 4567 · Black Variable ID: 21384 · Red Variable ID: 1617


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