Spurious correlation #1,537 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is The number of Breweries in the United States and the second variable is Solar power generated in United States. The chart goes from 1990 to 2021, 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 The number of Breweries in the United States and the second variable is Solar power generated in United States. The chart goes from 1990 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As the number of breweries in the United States increased, so did the demand for craft beer. This led to a nationwide shortage of beer hops, which are crucial for giving beer its distinct flavor. To combat this shortage, hop farmers had to get creative and started planting hops around solar panels in solar farms, utilizing the vertical space to meet the demand. This unexpected dual land usage not only helped in hop production but also provided some much-needed shade for the solar panels, reducing heat stress and increasing their efficiency. So, next time you raise a glass of craft beer, remember that it might just be indirectly powering up those solar panels too! Cheers to renewable energy and hoppy coincidences!

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a high-tech cityscape featuring sleek and futuristic breweries with solar panels covering their rooftops. The roofs of the buildings are lined with rows of glistening solar panels, harnessing the sun's energy. The city streets below are bustling with activity and thick with the buzz of brewery operations, while above, the radiant solar panels symbolize the intersection of brewing and clean, renewable energy in the United States. 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: The number of Breweries in the United States and Solar power generated in United States. 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: An image that looks like it is a scene from a Pixar movie Scalar art Scalar art High-tech Cybernetic art
ChatGPT: High-tech

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both The number of Breweries in the United States and Solar power generated in United States together. Keep the description simple.
ChatGPT: In a bustling city, rows of solar panels stretch across the rooftops of breweries, capturing the bright sunlight and converting it into clean, renewable energy. The breweries below buzz with activity as the sun's rays power their operations, symbolizing the intersection of the number of breweries and solar power generation in the United States.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ High-tech ] and depicting this scene: In a bustling city, rows of solar panels stretch across the rooftops of breweries, capturing the bright sunlight and converting it into clean, renewable energy. The breweries below buzz with activity as the sun's rays power their operations, symbolizing the intersection of the number of breweries and solar power generation in the United States. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a high-tech cityscape featuring sleek and futuristic breweries with solar panels covering their rooftops. The roofs of the buildings are lined with rows of glistening solar panels, harnessing the sun's energy. The city streets below are bustling with activity and thick with the buzz of brewery operations, while above, the radiant solar panels symbolize the intersection of brewing and clean, renewable energy in the United States.

*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 The number of Breweries in the United States caused Solar power generated in United States to increase. Make it feel plausible.

AI academic paper

(Because p < 0.01)

The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection

The Journal of Brewonomics and Renewable Energy

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 The number of Breweries in the United States and Solar power generated in United States. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then cite some social media posts you read that seem to be related.

Here is the title and abstract of the paper:
[[TITLE]]
The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection

[[ABSTRACT]]
This study investigates the intriguing relationship between the number of breweries in the United States and the solar power generated in the country from 1990 to 2021. By utilizing data from the Brewers Association and the Energy Information Administration, we sought to uncover any potential correlation between these seemingly unrelated entities. Our rigorous analysis revealed a remarkably high correlation coefficient of 0.9643500 with a statistically significant p-value of less than 0.01, indicating a robust association between the proliferation of breweries and the solar energy output. These findings prompt a spirited discussion on the interplay of craft beer consumption and solar panel installation, challenging the conventional wisdom that beer and solar power are as related as...well, beer and solar power.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The proliferation of craft breweries in the United States has been a notable phenomenon in recent decades. Concurrently, the adoption of solar power as a renewable energy source has gained increasing attention as a means to mitigate the environmental impact of traditional energy sources. These seemingly disparate trends have captured the curiosity of researchers seeking to understand the underlying factors driving their parallel ascent. Despite their divergent nature, the beer and solar industries may share an unexpected connection, sparking inquiries into the potential relationship between their respective growth patterns.
The interplay between breweries and solar power presents a puzzle that piqued our interest. The perplexing question arose: Could there be an ale-ignment between the flourishing craft beer scene and the burgeoning solar energy sector? Our aim is to unravel this enigma and shed light on the intricate dynamics at play. While the notion of a correlation between beer and solar power may initially seem as far-fetched as finding a hop in a solar panel, our investigation endeavors to explore this curious association with the seriousness it deserves.
In this study, we seek to employ rigorous statistical analysis to illuminate any possible link between the number of breweries and the solar energy generation in the United States. By examining data spanning over three decades, we endeavor to detect underlying patterns and unveil potential insights into the fascinating relationship between these ostensibly unrelated domains. As we unravel this intriguing conundrum, we acknowledge that, much like the perfect brew, a comprehensive understanding of this association necessitates a meticulous blend of data analysis and a dash of whimsy.
This investigation's findings hold the promise of cultivating a deeper understanding of the intersection between the craft beer renaissance and the solar energy revolution, stirring discussions that may quench the thirst for knowledge in unexpected ways. Join us as we set out on a journey to decode the intriguing and intoxicating connection between breweries and solar power. The results are no doubt bound to leave readers with a brew-tiful blend of curiosity and amusement.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The relationship between the number of breweries in the United States and the solar power generated in the country has garnered increasing attention from researchers in recent years. Smith (2017) conducted a comprehensive analysis of the craft beer industry, exploring its exponential growth and cultural impact. Meanwhile, Doe (2019) delved into the complexities of solar energy adoption, elucidating the factors driving its increasing utilization across the nation. Jones (2020) further contributed to this area of inquiry by examining patterns in renewable energy sources and their implications for environmental sustainability.

Turning to non-fiction books, "Brewing Up a Business" by Sam Calagione provides insights into the entrepreneurial journey of craft brewers, offering a nuanced understanding of the industry's evolution. Additionally, "Solar Power Your Home For Dummies" by Rik DeGunther elucidates the intricacies of residential solar panel installation, shedding light on the expanding market for solar energy solutions.

In the realm of fiction, "The Brewmaster's Tale" by Carey Wallace and "The Solar War" by A.G. Riddle engage with themes related to brewing and solar technology, albeit in a more imaginative context. While these works may not be grounded in empirical research, they nonetheless contribute to the broader conversation surrounding the intersection of these two domains.

Furthermore, social media platforms have become avenues for informal discourse on this topic. Anecdotal evidence from posts on platforms such as Reddit and Twitter suggests that individuals have contemplated the potential link between the proliferation of microbreweries and the adoption of solar energy technologies. One user humorously remarked, "Maybe the key to sustainable energy is just a really, really hoppy IPA." While these observations may be light-hearted, they underscore the public's growing curiosity about the fascinating interplay between breweries and solar power.

While the convergence of breweries and solar power may initially appear as incongruous as a stout and a sunbeam, our investigation aims to unravel the enigmatic relationship between these seemingly unrelated entities. Through a synthesis of scholarly research, literary works, and informal discourse, we endeavor to shed light on the captivating association between the craft beer renaissance and the solar energy revolution.

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 The number of Breweries in the United States and Solar power generated in United States. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Brewers Association and Energy Information Administration . You used data from 1990 to 2021

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

Here is the title, abstract, and introduction of the paper:
[[TITLE]]
The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection

[[ABSTRACT]]
This study investigates the intriguing relationship between the number of breweries in the United States and the solar power generated in the country from 1990 to 2021. By utilizing data from the Brewers Association and the Energy Information Administration, we sought to uncover any potential correlation between these seemingly unrelated entities. Our rigorous analysis revealed a remarkably high correlation coefficient of 0.9643500 with a statistically significant p-value of less than 0.01, indicating a robust association between the proliferation of breweries and the solar energy output. These findings prompt a spirited discussion on the interplay of craft beer consumption and solar panel installation, challenging the conventional wisdom that beer and solar power are as related as...well, beer and solar power.

[[INTRODUCTION]]
The proliferation of craft breweries in the United States has been a notable phenomenon in recent decades. Concurrently, the adoption of solar power as a renewable energy source has gained increasing attention as a means to mitigate the environmental impact of traditional energy sources. These seemingly disparate trends have captured the curiosity of researchers seeking to understand the underlying factors driving their parallel ascent. Despite their divergent nature, the beer and solar industries may share an unexpected connection, sparking inquiries into the potential relationship between their respective growth patterns.
The interplay between breweries and solar power presents a puzzle that piqued our interest. The perplexing question arose: Could there be an ale-ignment between the flourishing craft beer scene and the burgeoning solar energy sector? Our aim is to unravel this enigma and shed light on the intricate dynamics at play. While the notion of a correlation between beer and solar power may initially seem as far-fetched as finding a hop in a solar panel, our investigation endeavors to explore this curious association with the seriousness it deserves.
In this study, we seek to employ rigorous statistical analysis to illuminate any possible link between the number of breweries and the solar energy generation in the United States. By examining data spanning over three decades, we endeavor to detect underlying patterns and unveil potential insights into the fascinating relationship between these ostensibly unrelated domains. As we unravel this intriguing conundrum, we acknowledge that, much like the perfect brew, a comprehensive understanding of this association necessitates a meticulous blend of data analysis and a dash of whimsy.
This investigation's findings hold the promise of cultivating a deeper understanding of the intersection between the craft beer renaissance and the solar energy revolution, stirring discussions that may quench the thirst for knowledge in unexpected ways. Join us as we set out on a journey to decode the intriguing and intoxicating connection between breweries and solar power. The results are no doubt bound to leave readers with a brew-tiful blend of curiosity and amusement.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

Data Collection:
The primary data sources for this study were the Brewers Association and the Energy Information Administration, both robust repositories of information on breweries and solar power generation, respectively. Our research team scoured these databases to compile a comprehensive dataset spanning the years 1990 to 2021. The meticulous process of data collection involved sifting through a substantial amount of information, much like sifting through the hops to find the finest ones for a craft beer brew.

Variable Selection:
To assess the relationship between the number of breweries and solar power generated, we identified key variables including the total count of breweries and the solar energy output in the United States. The variables were selected with as much care as a brewmaster selecting the perfect combination of malt and hops for a new ale.

Data Analysis:
The collected data underwent rigorous scrutiny and analysis using advanced statistical methods, akin to the precision employed in the brewing process to ensure the perfect fermentation. We applied correlation analysis to examine the association between the two variables, employing tools that would make even the most discerning beer connoisseur nod in approval.

Model Validation:
To validate our findings, we utilized cross-validation techniques and sensitivity analyses to ensure the robustness and reliability of the observed relationship, reminiscent of the meticulous quality control procedures in a brewery to ensure consistent flavor and aroma in each batch of beer.

Caveats and Considerations:
It is important to note that while every effort was made to ensure the accuracy and reliability of the data, some limitations are inherent in the nature of secondary data sources. However, the potential impact of these limitations was accounted for, much like a brewer adjusting the recipe to compensate for variations in raw materials.

The comprehensive methodology employed in this study aimed to unveil the intriguing connection between breweries and solar power in a manner that is as meticulously crafted as a well-balanced beer, with the hope of quenching the thirst for knowledge and discovery in unexpected ways.

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 The number of Breweries in the United States and Solar power generated in United States. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

For the time period 1990 to 2021, you found a correlation 0.9643500, r-squared of 0.9299710, and p < 0.01.

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

Here is the title and abstract of the paper:
[[TITLE]]
The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection

[[ABSTRACT]]
This study investigates the intriguing relationship between the number of breweries in the United States and the solar power generated in the country from 1990 to 2021. By utilizing data from the Brewers Association and the Energy Information Administration, we sought to uncover any potential correlation between these seemingly unrelated entities. Our rigorous analysis revealed a remarkably high correlation coefficient of 0.9643500 with a statistically significant p-value of less than 0.01, indicating a robust association between the proliferation of breweries and the solar energy output. These findings prompt a spirited discussion on the interplay of craft beer consumption and solar panel installation, challenging the conventional wisdom that beer and solar power are as related as...well, beer and solar power.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The proliferation of craft breweries in the United States has been a notable phenomenon in recent decades. Concurrently, the adoption of solar power as a renewable energy source has gained increasing attention as a means to mitigate the environmental impact of traditional energy sources. These seemingly disparate trends have captured the curiosity of researchers seeking to understand the underlying factors driving their parallel ascent. Despite their divergent nature, the beer and solar industries may share an unexpected connection, sparking inquiries into the potential relationship between their respective growth patterns.
The interplay between breweries and solar power presents a puzzle that piqued our interest. The perplexing question arose: Could there be an ale-ignment between the flourishing craft beer scene and the burgeoning solar energy sector? Our aim is to unravel this enigma and shed light on the intricate dynamics at play. While the notion of a correlation between beer and solar power may initially seem as far-fetched as finding a hop in a solar panel, our investigation endeavors to explore this curious association with the seriousness it deserves.
In this study, we seek to employ rigorous statistical analysis to illuminate any possible link between the number of breweries and the solar energy generation in the United States. By examining data spanning over three decades, we endeavor to detect underlying patterns and unveil potential insights into the fascinating relationship between these ostensibly unrelated domains. As we unravel this intriguing conundrum, we acknowledge that, much like the perfect brew, a comprehensive understanding of this association necessitates a meticulous blend of data analysis and a dash of whimsy.
This investigation's findings hold the promise of cultivating a deeper understanding of the intersection between the craft beer renaissance and the solar energy revolution, stirring discussions that may quench the thirst for knowledge in unexpected ways. Join us as we set out on a journey to decode the intriguing and intoxicating connection between breweries and solar power. The results are no doubt bound to leave readers with a brew-tiful blend of curiosity and amusement.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The analysis of the correlation between the number of breweries in the United States and the solar power generated from 1990 to 2021 revealed a striking association. The correlation coefficient of 0.9643500 suggests a notably robust positive relationship between these seemingly unrelated variables. This remarkable correlation coefficient indicates that as the number of breweries increased, so did the solar power generation, prompting us to ponder whether there may be a "brew-tiful" synergy at play.

Furthermore, the coefficient of determination (R-squared) of 0.9299710 signifies that approximately 93% of the variation in solar power generation can be explained by the proliferation of breweries. This substantial R-squared value underscores the substantial influence of the number of breweries on solar energy production, calling to mind the adage, "where there's hops, there's sunshine."

Notably, the p-value of less than 0.01 provides strong evidence against the null hypothesis, firmly establishing the statistical significance of the observed correlation. This p-value further reinforces the compelling nature of the relationship, compelling us to reimagine the interconnectedness of beer and solar energy in a light that is more - dare I say - illuminating.

In Fig. 1, the scatterplot depicts the undeniable correlation between the number of breweries and the solar power generated, visually capturing the compelling association uncovered by our rigorous analysis.

In summary, our investigation has uncovered a surprising and noteworthy connection between the proliferation of breweries and the solar energy output in the United States, challenging conventional perceptions and toasting to the symbiotic relationship between craft beer and solar power. These findings may spark further exploration into the uncharted terrains of seemingly unrelated industries and inspire a new wave of research in the intersection of beer, sunshine, and statistical revelations.

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 The number of Breweries in the United States and Solar power generated in United States. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Limit your response to 500 tokens.

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

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

[[TITLE]]
The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection

[[ABSTRACT]]
This study investigates the intriguing relationship between the number of breweries in the United States and the solar power generated in the country from 1990 to 2021. By utilizing data from the Brewers Association and the Energy Information Administration, we sought to uncover any potential correlation between these seemingly unrelated entities. Our rigorous analysis revealed a remarkably high correlation coefficient of 0.9643500 with a statistically significant p-value of less than 0.01, indicating a robust association between the proliferation of breweries and the solar energy output. These findings prompt a spirited discussion on the interplay of craft beer consumption and solar panel installation, challenging the conventional wisdom that beer and solar power are as related as...well, beer and solar power.

[[LITERATURE REVIEW]]
The relationship between the number of breweries in the United States and the solar power generated in the country has garnered increasing attention from researchers in recent years. Smith (2017) conducted a comprehensive analysis of the craft beer industry, exploring its exponential growth and cultural impact. Meanwhile, Doe (2019) delved into the complexities of solar energy adoption, elucidating the factors driving its increasing utilization across the nation. Jones (2020) further contributed to this area of inquiry by examining patterns in renewable energy sources and their implications for environmental sustainability.
Turning to non-fiction books, "Brewing Up a Business" by Sam Calagione provides insights into the entrepreneurial journey of craft brewers, offering a nuanced understanding of the industry's evolution. Additionally, "Solar Power Your Home For Dummies" by Rik DeGunther elucidates the intricacies of residential solar panel installation, shedding light on the expanding market for solar energy solutions.
In the realm of fiction, "The Brewmaster's Tale" by Carey Wallace and "The Solar War" by A.G. Riddle engage with themes related to brewing and solar technology, albeit in a more imaginative context. While these works may not be grounded in empirical research, they nonetheless contribute to the broader conversation surrounding the intersection of these two domains.
Furthermore, social media platforms have become avenues for informal discourse on this topic. Anecdotal evidence from posts on platforms such as Reddit and Twitter suggests that individuals have contemplated the potential link between the proliferation of microbreweries and the adoption of solar energy technologies. One user humorously remarked, "Maybe the key to sustainable energy is just a really, really hoppy IPA." While these observations may be light-hearted, they underscore the public's growing curiosity about the fascinating interplay between breweries and solar power.
While the convergence of breweries and solar power may initially appear as incongruous as a stout and a sunbeam, our investigation aims to unravel the enigmatic relationship between these seemingly unrelated entities. Through a synthesis of scholarly research, literary works, and informal discourse, we endeavor to shed light on the captivating association between the craft beer renaissance and the solar energy revolution.

[[RESULTS]]
The analysis of the correlation between the number of breweries in the United States and the solar power generated from 1990 to 2021 revealed a striking association. The correlation coefficient of 0.9643500 suggests a notably robust positive relationship between these seemingly unrelated variables. This remarkable correlation coefficient indicates that as the number of breweries increased, so did the solar power generation, prompting us to ponder whether there may be a "brew-tiful" synergy at play.
Furthermore, the coefficient of determination (R-squared) of 0.9299710 signifies that approximately 93% of the variation in solar power generation can be explained by the proliferation of breweries. This substantial R-squared value underscores the substantial influence of the number of breweries on solar energy production, calling to mind the adage, "where there's hops, there's sunshine."
Notably, the p-value of less than 0.01 provides strong evidence against the null hypothesis, firmly establishing the statistical significance of the observed correlation. This p-value further reinforces the compelling nature of the relationship, compelling us to reimagine the interconnectedness of beer and solar energy in a light that is more - dare I say - illuminating.
In Fig. 1, the scatterplot depicts the undeniable correlation between the number of breweries and the solar power generated, visually capturing the compelling association uncovered by our rigorous analysis.
In summary, our investigation has uncovered a surprising and noteworthy connection between the proliferation of breweries and the solar energy output in the United States, challenging conventional perceptions and toasting to the symbiotic relationship between craft beer and solar power. These findings may spark further exploration into the uncharted terrains of seemingly unrelated industries and inspire a new wave of research in the intersection of beer, sunshine, and statistical revelations.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of this study support and extend prior research findings on the relationship between the number of breweries in the United States and the solar power generated in the country. Our findings align with Smith's (2017) work on the exponential growth of the craft beer industry, as well as Doe's (2019) exploration of the factors driving the increasing utilization of solar energy. The remarkably high correlation coefficient of 0.9643500 lends empirical support to the growing anecdotal evidence from social media, as alluded to in the literature review. This empirical evidence has further validated the informal discourse surrounding the potential link between microbreweries and solar energy technologies - a topic that is now illuminated by statistically significant findings.

The significant relationship between the proliferation of breweries and the solar energy output challenges conventional wisdom. The substantial R-squared value of 0.9299710 emphasizes the considerable influence of the number of breweries on solar energy production, highlighting the potent role of craft beer in facilitating solar power generation. By providing strong evidence against the null hypothesis, the p-value of less than 0.01 firmly establishes the statistical significance of the observed correlation, underscoring the robustness of our findings and the compelling nature of the relationship.

Our investigation has unveiled the unexpectedly "brew-tiful" synergy between the craft beer renaissance and the solar energy revolution. These results not only contribute to the literature on seemingly unrelated industries but also invite a lighthearted recognition of the interconnectedness of beer and solar energy. The proliferation of breweries may indeed be a harbinger of sunlight, as suggested by the undeniable correlation captured in the scatterplot (Fig. 1). This visual representation encapsulates the intoxicating relationship between breweries and solar power, prompting us to raise a "glass" to the symbiotic alliance between craft beer and sustainable energy.

In conclusion, the findings of this study encourage a reimagining of the interplay between breweries and solar power and spotlight the potential for further examination of the uncharted terrains of seemingly unrelated industries. As the sun sets on this phase of our research, we are left pondering the enigmatic connection between the proliferation of breweries and the generation of solar power, drawing inspiration from the unexpected unity of beer, sunshine, and statistical revelations.

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 The number of Breweries in the United States and Solar power generated in United States. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection

[[ABSTRACT]]
This study investigates the intriguing relationship between the number of breweries in the United States and the solar power generated in the country from 1990 to 2021. By utilizing data from the Brewers Association and the Energy Information Administration, we sought to uncover any potential correlation between these seemingly unrelated entities. Our rigorous analysis revealed a remarkably high correlation coefficient of 0.9643500 with a statistically significant p-value of less than 0.01, indicating a robust association between the proliferation of breweries and the solar energy output. These findings prompt a spirited discussion on the interplay of craft beer consumption and solar panel installation, challenging the conventional wisdom that beer and solar power are as related as...well, beer and solar power.

[[INTRDUCTION]]
The proliferation of craft breweries in the United States has been a notable phenomenon in recent decades. Concurrently, the adoption of solar power as a renewable energy source has gained increasing attention as a means to mitigate the environmental impact of traditional energy sources. These seemingly disparate trends have captured the curiosity of researchers seeking to understand the underlying factors driving their parallel ascent. Despite their divergent nature, the beer and solar industries may share an unexpected connection, sparking inquiries into the potential relationship between their respective growth patterns.
The interplay between breweries and solar power presents a puzzle that piqued our interest. The perplexing question arose: Could there be an ale-ignment between the flourishing craft beer scene and the burgeoning solar energy sector? Our aim is to unravel this enigma and shed light on the intricate dynamics at play. While the notion of a correlation between beer and solar power may initially seem as far-fetched as finding a hop in a solar panel, our investigation endeavors to explore this curious association with the seriousness it deserves.
In this study, we seek to employ rigorous statistical analysis to illuminate any possible link between the number of breweries and the solar energy generation in the United States. By examining data spanning over three decades, we endeavor to detect underlying patterns and unveil potential insights into the fascinating relationship between these ostensibly unrelated domains. As we unravel this intriguing conundrum, we acknowledge that, much like the perfect brew, a comprehensive understanding of this association necessitates a meticulous blend of data analysis and a dash of whimsy.
This investigation's findings hold the promise of cultivating a deeper understanding of the intersection between the craft beer renaissance and the solar energy revolution, stirring discussions that may quench the thirst for knowledge in unexpected ways. Join us as we set out on a journey to decode the intriguing and intoxicating connection between breweries and solar power. The results are no doubt bound to leave readers with a brew-tiful blend of curiosity and amusement.

[[RESULTS]]
The analysis of the correlation between the number of breweries in the United States and the solar power generated from 1990 to 2021 revealed a striking association. The correlation coefficient of 0.9643500 suggests a notably robust positive relationship between these seemingly unrelated variables. This remarkable correlation coefficient indicates that as the number of breweries increased, so did the solar power generation, prompting us to ponder whether there may be a "brew-tiful" synergy at play.
Furthermore, the coefficient of determination (R-squared) of 0.9299710 signifies that approximately 93% of the variation in solar power generation can be explained by the proliferation of breweries. This substantial R-squared value underscores the substantial influence of the number of breweries on solar energy production, calling to mind the adage, "where there's hops, there's sunshine."
Notably, the p-value of less than 0.01 provides strong evidence against the null hypothesis, firmly establishing the statistical significance of the observed correlation. This p-value further reinforces the compelling nature of the relationship, compelling us to reimagine the interconnectedness of beer and solar energy in a light that is more - dare I say - illuminating.
In Fig. 1, the scatterplot depicts the undeniable correlation between the number of breweries and the solar power generated, visually capturing the compelling association uncovered by our rigorous analysis.
In summary, our investigation has uncovered a surprising and noteworthy connection between the proliferation of breweries and the solar energy output in the United States, challenging conventional perceptions and toasting to the symbiotic relationship between craft beer and solar power. These findings may spark further exploration into the uncharted terrains of seemingly unrelated industries and inspire a new wave of research in the intersection of beer, sunshine, and statistical revelations.

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Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our study has unraveled an unexpected and intoxicating connection between the proliferation of breweries and the solar energy output in the United States. The high correlation coefficient and statistically significant p-value convincingly indicate a robust association between these seemingly disparate domains. These findings challenge conventional wisdom and invite a lighthearted consideration of the interplay between craft beer consumption and solar panel installation. Our investigation has shed light on the intricate dynamics at play, and the link between beer and solar power may very well be brewing up more than just a storm in a pint glass.

The substantial R-squared value suggests that the variation in solar power generation can be hop-ily explained by the proliferation of breweries, underscoring the potential influence of the number of breweries on solar energy production. The statistically significant p-value encourages a reimagining of the interconnectedness of beer and solar energy, illuminating a path for future research that may quench the thirst for knowledge in unexpected ways.

In Fig. 1, the scatterplot visually captures the compelling association between the number of breweries and the solar power generated, providing a "brew-tiful" illustration of the correlation uncovered by our rigorous analysis.

In the spirit of a well-crafted brew, this investigation has crafted a nuanced understanding of the peculiar association between breweries and solar power. The findings are bound to leave readers with a brew-tiful blend of curiosity and amusement, sparking discussions that may lead to further exploration and elating revelations. Therefore, we assert that no further research is needed in this area, as we have indeed brewed up a satisfyingly robust understanding of the intriguing and intoxicating connection between breweries and solar power.

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of academic journals. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding research, scientific, or academic journal that would publish a paper entited The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Brewonomics and Renewable Energy

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of nonprofit research organizations and associations. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding nonprofit, academic, or scientific association or organization that would sponsor research that resulted in a paper entited The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection. Respond only with the name of a fictional organization.

ChatGPT:

The Thirsty Photon Foundation

Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection with an abstract of This study investigates the intriguing relationship between the number of breweries in the United States and the solar power generated in the country from 1990 to 2021. By utilizing data from the Brewers Association and the Energy Information Administration, we sought to uncover any potential correlation between these seemingly unrelated entities. Our rigorous analysis revealed a remarkably high correlation coefficient of 0.9643500 with a statistically significant p-value of less than 0.01, indicating a robust association between the proliferation of breweries and the solar energy output. These findings prompt a spirited discussion on the interplay of craft beer consumption and solar panel installation, challenging the conventional wisdom that beer and solar power are as related as...well, beer and solar power.

ChatGPT:

breweries, solar power, United States, craft beer, solar panel installation, correlation coefficient, energy production, Brewers Association, Energy Information Administration

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

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Data details

The number of Breweries in the United States
Detailed data title: Number of Breweries in the United States
Source: Brewers Association
See what else correlates with The number of Breweries in the United States

Solar power generated in United States
Detailed data title: Total solar power generated in United States in billion kWh
Source: Energy Information Administration
See what else correlates with Solar power generated in United States

Correlation r = 0.9643500 (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 = 0.9299710 (Coefficient of determination)
This means 93% of the change in the one variable (i.e., Solar power generated in United States) is predictable based on the change in the other (i.e., The number of Breweries in the United States) over the 32 years from 1990 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 7.1E-19.^Show 0.0000000000000000007139706545
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 0.96 in 7.1E-17% of random cases. Said differently, if you correlated 1,400,617,789,676,956,416 random variables^Note You don't actually need 1 quintillion 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 31 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 31 because we have two variables measured over a period of 32 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.

[ 0.93, 0.98 ] 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.

	1990	1991	1992	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021
The number of Breweries in the United States (Number of breweries)	298	350	405	490	634	1006	1305	1475	1651	1577	1493	1499	1575	1629	1635	1612	1741	1805	1896	1933	2131	2525	2670	3162	4014	4847	5780	6767	7722	8557	9092	9384
Solar power generated in United States (Billion kWh)	0.402291	0.51107	0.44286	0.509843	0.539697	0.5575	0.59092	0.58923	0.590776	0.59781	0.609905	0.683644	0.721829	0.728998	0.816721	0.912741	1.0363	1.3581	2.06365	2.50321	3.75044	5.85127	10.8231	17.2168	28.9237	39.0322	54.8665	77.2771	93.3646	106.894	130.721	163.703

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.
Confounding variable: 2020 is particularly different from the other years on this graph. Confounding variables (like global pandemics) will cause two variables to look connected when in fact a "sneaky third" variable is influencing both of them behind the scenes.
Outlandish outliers: There are "outliers" in this data.^Note In concept, "outlier" just means "way different than the rest of your dataset." When calculating a correlation like this, they are particularly impactful because a single outlier can substantially increase your correlation.

For the purposes of this project, I counted a point as an outlier if it the residual was two standard deviations from the mean.

(This bullet point only shows up in the details page on charts that do, in fact, have outliers.)
They stand out on the scatterplot above: notice the dots that are far away from any other dots. I intentionally mishandeled outliers, which makes the correlation look extra strong.

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([298,350,405,490,634,1006,1305,1475,1651,1577,1493,1499,1575,1629,1635,1612,1741,1805,1896,1933,2131,2525,2670,3162,4014,4847,5780,6767,7722,8557,9092,9384,])
array_2 = np.array([0.402291,0.51107,0.44286,0.509843,0.539697,0.5575,0.59092,0.58923,0.590776,0.59781,0.609905,0.683644,0.721829,0.728998,0.816721,0.912741,1.0363,1.3581,2.06365,2.50321,3.75044,5.85127,10.8231,17.2168,28.9237,39.0322,54.8665,77.2771,93.3646,106.894,130.721,163.703,])
array_1_name = "The number of Breweries in the United States"
array_2_name = "Solar power generated in United States"

# 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 The number of Breweries in the United States
Line chart for only Solar power generated in United States
AI-generated correlation image
The spurious research paper: The Ale-Ignment of Breweries and Solar Power: An Intoxicating Connection

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Correlation ID: 1537 · Black Variable ID: 34 · Red Variable ID: 24078


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