Spurious correlation #1,350 · 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 Total wind power generated globally. 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 Total wind power generated globally. 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 amount of hot air being produced about new craft beer releases. This led to a surge in local wind currents, ultimately contributing to an increase in total wind power generated globally. It's a beery gusty situation!

^{Show image generation prompt} Model: dalle-3
Prompt: Generate a 3D Pixar style scene of a lively United States cityscape, with diverse and vibrant breweries lining the streets, each featuring unique architecture and neon-lit signs showcasing their specialties. In the backdrop, towering wind turbines spin gracefully, symbolizing the harmonious coexistence of traditional brewing culture and sustainable energy. The streets are bustling with activity, as people move between the breweries and revel in the energetic atmosphere. The cityscape radiates a sense of dynamic growth, blending the traditional charm of breweries with the progressive embrace of clean energy. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.

This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the situation described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here is a situation: Because as the number of breweries in the United States increases, so does the amount of hot air being released, fueling the turbines and propelling wind power generation globally. It's a brew-tiful cycle of ale-lectricity production! Plus, the hops and barley fields are providing extra air circulation, giving a whole new meaning to "beer-powered energy." Cheers to renewable wind power, brought to you by the booming brewery business!. Given that situation, which of the following image descriptions seems most appropriate? Pick the one that seems to be related to one of the variables at hand and the tone of the explanation. Please respond with only one of the following potential descriptions: Art nouveau Oragami Glitch art Realistic 3D Pixar Style
ChatGPT: 3D Pixar Style

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated and the explanation described. Do not reference graphs or charts; describe physical objects.
User prompt: Please describe a visual scene that prominently depicts both The number of Breweries in the United States and Total wind power generated globally Keep the description simple.
ChatGPT: Picture a bustling cityscape in the United States with numerous vibrant breweries lining the streets, each with its unique architecture and signs displaying their specialties. In the distance, tall wind turbines dot the horizon, spinning leisurely and generating clean energy to power the city. The coexistence of the breweries and the wind turbines represents the simultaneous growth in the number of breweries in the U.S. and the increasing utilization of wind power worldwide.

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: [ 3D Pixar Style ] and depicting this scene: Picture a bustling cityscape in the United States with numerous vibrant breweries lining the streets, each with its unique architecture and signs displaying their specialties. In the distance, tall wind turbines dot the horizon, spinning leisurely and generating clean energy to power the city. The coexistence of the breweries and the wind turbines represents the simultaneous growth in the number of breweries in the U.S. and the increasing utilization of wind power worldwide. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate a 3D Pixar style scene of a lively United States cityscape, with diverse and vibrant breweries lining the streets, each featuring unique architecture and neon-lit signs showcasing their specialties. In the backdrop, towering wind turbines spin gracefully, symbolizing the harmonious coexistence of traditional brewing culture and sustainable energy. The streets are bustling with activity, as people move between the breweries and revel in the energetic atmosphere. The cityscape radiates a sense of dynamic growth, blending the traditional charm of breweries with the progressive embrace of clean energy.

*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 Total wind power generated globally to increase.

AI academic paper

(Because p < 0.01)

Brews and Breezes: Exploring the Link Between US Breweries and Global Wind Power

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

Please make up the discussion section of an academic research paper presenting the findings of the connection between The number of Breweries in the United States and Total wind power generated globally. Make lots of jokes, goofy observations, and puns.

Limit your response to 500 tokens.

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

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

[[TITLE]]
Brews and Breezes: Exploring the Link Between US Breweries and Global Wind Power

[[ABSTRACT]]
In the quest to brew up some enlightening insights, this study delves into the unconventional connection between the proliferation of breweries in the United States and the generation of wind power across the globe. With a dash of frothy humor and a pinch of windy whimsy, our research team extracted data from the Brewers Association and the Energy Information Administration to satiate our curiosity. Lo and behold, we unearthed a surprisingly strong correlation with a coefficient of 0.9842458 and a p-value less than 0.01 for the years 1990 to 2021.

As the plot thickens, let's tap into the frothy findings and breeze through the nuances of this unexpected relationship. We'll ferment our discussions with some hop-infused humor and perhaps some corny jokes, while we blow past the norms of conventional research. So, cheers to unconventional connections and may the wind power of our research blow you away!

[[LITERATURE REVIEW]]
In "Smith and Doe," the authors find that the number of breweries in the United States has been on the rise over the past few decades, reflecting a burgeoning craft beer industry. Meanwhile, "Jones" investigates the global trends in wind power generation, highlighting the shift towards renewable energy sources. The connection between these seemingly unrelated phenomena piques our curiosity and leads us to explore further.
Turning to non-fiction literature, "Craft Beer Revolution" by Steve Hindy and "Wind Power for Dummies" by Ian Woofenden provide valuable insights into the respective industries. These works offer a serious and detailed examination of the individual developments in brewing and wind power but leave the intertwined relationship unexplored.
On the fictional front, "A Storm of Swords" by George R.R. Martin and "The Wind-Up Bird Chronicle" by Haruki Murakami symbolically evoke the themes of turbulent energy and unseen connections, serving as metaphorical inspiration for our investigation into the intersection of brews and breezes.
As we venture into more unconventional sources, our research takes a whimsical turn. The back labels of shampoo bottles – yes, shampoo bottles – surprisingly offer an unexpected yet poignant commentary on the frothy bubbles of atmospheric interaction and the effervescence of renewable energy possibilities. The unorthodox nature of these sources mirrors the unorthodox nature of our inquiry, as we aim to inject an element of levity into the otherwise staid world of academic research.
In this madcap quest for knowledge, we delve into the brew-tiful and wind-swept realms of possibility, where the unexpected connections between suds and zephyrs emerge like a refreshing breeze on a scorching day. So, grab a pint, let the wind tousle your hair, and join us on this unconventional romp through the literature – it promises to be a frolicsome and gusty adventure!

[[RESULTS]]
The results of our analysis revealed an astonishingly strong correlation between the number of breweries in the United States and the total wind power generated globally. The correlation coefficient of 0.9842458 suggests a relationship that is not just statistically significant, but also brew-tifully robust. The r-squared value of 0.9687397 further confirms that the proliferation of breweries can be closely associated with the generation of wind power, blowing away any doubts about the strength of this unexpected connection.
Our findings point to a truly brew-tastic relationship that defies conventional wisdom. It's as if the craft beer industry and the wind energy sector have been in cahoots all along, blending their influences to create a gusty partnership. Those who thought that wind power was just a breezy concept and that breweries were only about satisfying our thirst – well, prepare to be pleasantly surprised.
The p-value of less than 0.01 illuminates the significance of our discovery, providing resounding evidence that the relationship between breweries in the US and global wind power generation is more than just a frothy coincidence. It's a marriage of malt and momentum, an unexpected union of hops and high winds that leaves us with a taste of intrigue and a whiff of wonder.
To visually capture the essence of this unexpectedly interconnected dance of brews and breezes, we present Figure 1, a scatterplot that unapologetically flaunts the strong correlation between these seemingly disparate variables. Behold the synergy, the interplay, and the fermenting force that transcends boundaries and tickles our intellectual taste buds.
In summary, our results unveil a captivating tale of seemingly unrelated elements coming together in a spirited union. The implications of this brew-blowing discovery ripple through the domains of economics, environmental studies, and perhaps even philosophy. So, raise a pint to the power of unexpected connections, and let the winds of curiosity carry you into uncharted territories. Cheers to the blend of brews and breezes – a match made in statistical heaven!

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

Well, well, well, hopheads and wind worshippers, it looks like we've stumbled upon a revelation that's not just blowing in the wind but also brewing up some serious excitement! Our findings not only support prior research but add a frothy layer of validation to the bizarre but bewitching relationship between breweries in the US and global wind power generation.

First off, let's tip our hats to "Smith and Doe" for uncovering the surge in breweries across the United States. It seems that the craft beer revolution isn't just about pleasing palates but also stirring up some serious atmospheric energy. Now, isn't that a hoppy coincidence? Their work lays the foamy foundation for our exploration, and our results echo their enthusiastic findings by revealing a robust connection between breweries and wind power – it's like a perfect beer pairing with a gusty twist.

And how can we forget about "Jones" and their examination of global wind power trends? Their work led us into the whirlwind of renewable energy sources, and our findings breeze in to solidify the importance of this sustainable shift. Indeed, it's like the windmills of our mind are churning out an epic saga of brews and breezes, much like a craft beer rendition of "Don Quixote."

But hey, let's not overlook the fictional inspirations from George R.R. Martin and Haruki Murakami. Their metaphorical gusts of symbolism are akin to a creative leap into the whirligig of interconnectedness, reminding us that the seemingly unrelated can dance together in an intellectual waltz. It's like a literary symphony, with the unexpected harmony of suds and zephyrs ringing in our ears.

Now, let's get serious for a moment – our correlation coefficient of 0.9842458 is no laughing matter. It's a solid testament to the fact that the number of breweries in the US and global wind power generation are not just casually associated but deeply entwined, like the malt in a finely brewed ale. And that p-value less than 0.01? Cha-ching! It's like hitting the jackpot in a game of statistical roulette, confirming that our findings are not just a random fluctuation but a significant revelation.

As our results pull back the curtain on this incredible interplay between brews and breezes, it's as if we've stumbled upon the ale of unexpected correlations – refreshing, intoxicating, and leaving us thirsting for more. Our scatterplot, akin to a Mona Lisa of statistical revelry, proudly showcases the powerful synergy between these unlikely partners. It's a visual testament to the fact that when it comes to statistical seduction, breweries and wind power are a match made in a data-driven paradise.

In closing this discussion (for now, at least), let's raise a virtual pint to the fusion of brews and breezes – a symbiotic relationship that's not just about numbers and trends, but about the tantalizing dance of interconnectivity in the most unlikely of places. We invite our fellow researchers to join us at the crossroads of ale and air, where statistical gravity meets gusty greatness. Here's to the power of unexpected connections, and may the winds of curiosity carry us ever onward! Cheers to the blend of brews and breezes – a match made in statistical heaven!

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

Please make up a short conclusion of an academic research paper presenting the findings of the connection between The number of Breweries in the United States and Total wind power generated globally. Make lots of jokes, goofy observations, and puns.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
Brews and Breezes: Exploring the Link Between US Breweries and Global Wind Power

[[ABSTRACT]]
In the quest to brew up some enlightening insights, this study delves into the unconventional connection between the proliferation of breweries in the United States and the generation of wind power across the globe. With a dash of frothy humor and a pinch of windy whimsy, our research team extracted data from the Brewers Association and the Energy Information Administration to satiate our curiosity. Lo and behold, we unearthed a surprisingly strong correlation with a coefficient of 0.9842458 and a p-value less than 0.01 for the years 1990 to 2021.

As the plot thickens, let's tap into the frothy findings and breeze through the nuances of this unexpected relationship. We'll ferment our discussions with some hop-infused humor and perhaps some corny jokes, while we blow past the norms of conventional research. So, cheers to unconventional connections and may the wind power of our research blow you away!

[[INTRDUCTION]]
A casual observer might not see much in common between the rise of breweries in the United States and the global generation of wind power. After all, one seems to be about sipping on refreshing libations while the other is all about harnessing the power of the air currents. However, as we embark on this ale-mentary exploration, we'll find that there's more than meets the eye – and definitely more than meets the lips.
The age-old question of "What's on tap?" is about to take on a whole new meaning as we uncork the data and let it breathe. In this study, we're not just serving up statistics – we're brewing up a storm of insights and fermenting some unconventional connections.
As we embark on this journey, we'll encounter a heady mix of hops and turbines, a blend of grains and gusts. It's a bit like pairing a strong IPA with a light breeze – unexpected, but surprisingly satisfying.
So, take a deep breath, sip on your favorite brew, and get ready to be whisked away by the frothy findings and breezy revelations that await. This is not your typical research journey, but then again, we're not your typical researchers. Here's to swirling winds and hops that have the power to intoxicate – figuratively speaking, of course!

[[RESULTS]]
The results of our analysis revealed an astonishingly strong correlation between the number of breweries in the United States and the total wind power generated globally. The correlation coefficient of 0.9842458 suggests a relationship that is not just statistically significant, but also brew-tifully robust. The r-squared value of 0.9687397 further confirms that the proliferation of breweries can be closely associated with the generation of wind power, blowing away any doubts about the strength of this unexpected connection.
Our findings point to a truly brew-tastic relationship that defies conventional wisdom. It's as if the craft beer industry and the wind energy sector have been in cahoots all along, blending their influences to create a gusty partnership. Those who thought that wind power was just a breezy concept and that breweries were only about satisfying our thirst – well, prepare to be pleasantly surprised.
The p-value of less than 0.01 illuminates the significance of our discovery, providing resounding evidence that the relationship between breweries in the US and global wind power generation is more than just a frothy coincidence. It's a marriage of malt and momentum, an unexpected union of hops and high winds that leaves us with a taste of intrigue and a whiff of wonder.
To visually capture the essence of this unexpectedly interconnected dance of brews and breezes, we present Figure 1, a scatterplot that unapologetically flaunts the strong correlation between these seemingly disparate variables. Behold the synergy, the interplay, and the fermenting force that transcends boundaries and tickles our intellectual taste buds.
In summary, our results unveil a captivating tale of seemingly unrelated elements coming together in a spirited union. The implications of this brew-blowing discovery ripple through the domains of economics, environmental studies, and perhaps even philosophy. So, raise a pint to the power of unexpected connections, and let the winds of curiosity carry you into uncharted territories. Cheers to the blend of brews and breezes – a match made in statistical heaven!

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, we've successfully uncorked the frothy findings and blown through the winds of statistical significance to reveal an unexpectedly robust relationship between the number of breweries in the United States and the total wind power generated globally. With a correlation coefficient that's stronger than a double IPA and a p-value lower than the spirits at a craft beer festival, our results have left us feeling hop-pily satisfied.

The implications of our brew-tiful discovery are as refreshing as a cool breeze on a sunny day. It's not just about the numbers – it's about the spirited union of seemingly unrelated forces, the hoppy harmony of malt and momentum. Our scatterplot, lovingly dubbed "The Brews and Breezes Tango," captures this dance of data in all its quirky glory, proving that when it comes to unexpected connections, statistics can be quite the party-crasher.

As we raise a toast to this revelation, it's clear that no more research is needed in this area. The link between breweries and wind power is as clear as a perfectly poured pint of lager. So, let's bask in the frothy glow of this discovery, savor the zesty zing of statistical significance, and bid adieu to this unconventional, yet thoroughly intoxicating, academic journey. Cheers, and may the winds of curiosity continue to blow in delightfully unexpected directions!

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 Brews and Breezes: Exploring the Link Between US Breweries and Global Wind Power. Respond only with the name of a fictional academic journal.

ChatGPT:

Journal of Fermentation 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 Brews and Breezes: Exploring the Link Between US Breweries and Global Wind Power. Respond only with the name of a fictional organization.

ChatGPT:

The International Institute for Beer and Sustainable Energy

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 Brews and Breezes: Exploring the Link Between US Breweries and Global Wind Power with an abstract of In the quest to brew up some enlightening insights, this study delves into the unconventional connection between the proliferation of breweries in the United States and the generation of wind power across the globe. With a dash of frothy humor and a pinch of windy whimsy, our research team extracted data from the Brewers Association and the Energy Information Administration to satiate our curiosity. Lo and behold, we unearthed a surprisingly strong correlation with a coefficient of 0.9842458 and a p-value less than 0.01 for the years 1990 to 2021.
As the plot thickens, let's tap into the frothy findings and breeze through the nuances of this unexpected relationship. We'll ferment our discussions with some hop-infused humor and perhaps some corny jokes, while we blow past the norms of conventional research. So, cheers to unconventional connections and may the wind power of our research blow you away!

ChatGPT:

US breweries, global wind power, correlation, wind energy generation, wind power data, Brewers Association, Energy Information Administration, unconventional connections, correlation coefficient, p-value, 1990-2021, beer production, renewable energy, wind power industry

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

Random correlation

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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

Total wind power generated globally
Detailed data title: Total wind power generated globally in billion kWh
Source: Energy Information Administration
See what else correlates with Total wind power generated globally

Correlation r = 0.9842458 (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 = 0.9687397 (Coefficient of determination)
This means 96.9% of the change in the one variable (i.e., Total wind power generated globally) 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 3.9E-24.^Show 0.0000000000000000000000039004
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 0.98 in 3.9E-22% of random cases. Said differently, if you correlated 256,383,960,619,423,623,020,544 random variables^Note You don't actually need 256 sextillion 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.

[ 0.97, 0.99 ] 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
Total wind power generated globally (Billion kWh)	3.6036	4.09695	4.61206	5.55793	7.28441	7.93552	9.28889	12.134	16.1075	21.2765	31.3317	38.3652	52.7331	64.5029	84.6314	104.241	133.42	171.303	221.363	277.775	339.401	435.106	521.503	645.078	717.25	827.435	957.251	1127.11	1263.52	1399.1	1590.47	1807.8

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.

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([3.6036,4.09695,4.61206,5.55793,7.28441,7.93552,9.28889,12.134,16.1075,21.2765,31.3317,38.3652,52.7331,64.5029,84.6314,104.241,133.42,171.303,221.363,277.775,339.401,435.106,521.503,645.078,717.25,827.435,957.251,1127.11,1263.52,1399.1,1590.47,1807.8,])
array_1_name = "The number of Breweries in the United States"
array_2_name = "Total wind power generated globally"

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

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

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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 Total wind power generated globally
The spurious research paper: Brews and Breezes: Exploring the Link Between US Breweries and Global Wind Power

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Correlation ID: 1350 · Black Variable ID: 34 · Red Variable ID: 23443


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