Spurious correlation #3,602 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Solar power generated in Mozambique and the second variable is Lululemon's stock price (LULU). The chart goes from 2012 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 Solar power generated in Mozambique and the second variable is Lululemon's stock price (LULU). The chart goes from 2012 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The boost in solar power led to a surge in positive energy, creating a widespread demand for Lululemon's activewear to harness and contain all that newfound sunny optimism. Looks like Mozambique's solar flair is really illuminating the stock market!

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a futuristic scene in Mozambique where sleek solar panels glisten under the bright sun, generating clean energy. People in stylish Lululemon yoga pants are basking in the sunlight, creating a dazzling reflection that illuminates the stock ticker for Lululemon (LULU), while its value surges. 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: Solar power generated in Mozambique and Lululemon's stock price (LULU). 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: Cyberpunk Data cyber art Cute 2D animation Futuristic An image that looks like it is a scene from A Disney Movie
ChatGPT: Futuristic

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 Solar power generated in Mozambique and Lululemon's stock price (LULU), in the following situation: Because as solar power surged in Mozambique, the sun started reflecting off Lululemon's sleek yoga pants, causing a blinding glow of admiration that boosted their stock price.. Keep the description simple.
ChatGPT: The bright sun shines down on solar panels in Mozambique, generating abundant clean energy. Nearby, people wearing Lululemon's sleek yoga pants bask in the sunlight, causing a dazzling reflection that illuminates the stock ticker for Lululemon (LULU), as its value surges.

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: [ Futuristic ] and depicting this scene: The bright sun shines down on solar panels in Mozambique, generating abundant clean energy. Nearby, people wearing Lululemon's sleek yoga pants bask in the sunlight, causing a dazzling reflection that illuminates the stock ticker for Lululemon (LULU), as its value surges. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a futuristic scene in Mozambique where sleek solar panels glisten under the bright sun, generating clean energy. People in stylish Lululemon yoga pants are basking in the sunlight, creating a dazzling reflection that illuminates the stock ticker for Lululemon (LULU), while its value surges.

*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 Solar power generated in Mozambique caused Lululemon's stock price (LULU) to increase. Add a funny one-liner at the end.

AI academic paper

(Because p < 0.01)

Solar Power from Sub-Saharan Africa to Stock Surges: The Lululemon Link

The Journal of Renewable Energy Economics and Fashion Trends

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 Solar power generated in Mozambique and Lululemon's stock price (LULU). 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]]
Solar Power from Sub-Saharan Africa to Stock Surges: The Lululemon Link

[[ABSTRACT]]
This study explores the perplexing correlation between solar power generation in Mozambique and Lululemon Athletica's (LULU) stock price. While this inquiry may seem as incongruous as a pickle in a parfait, we employed empirical data from the Energy Information Administration and LSEG Analytics (Refinitiv) to conduct our analysis. Our findings revealed a surprising correlation coefficient of 0.9731367 with a statistical significance of p < 0.01, for the period of 2012 to 2021. This correlation stands out as vividly as a neon leotard against a backdrop of gray sweatpants. Our research raises questions as to what celestial forces or cosmic currents may be underpinning the seemingly covariant trajectories of solar power production in Mozambique and Lululemon's stock performance. Despite the unexpected connection, we caution against investing solely based on solar luminosity and Lululemon's stock movements, as correlations can often be deceiving, like a pair of yoga pants that seem to fit perfectly in the store but then ride up uncomfortably during a workout.

[[LITERATURE REVIEW]]
The perplexing correlation between solar power generation in Mozambique and the stock price of Lululemon Athletica (LULU) has sparked curiosity and skepticism akin to finding a penguin at a tropical beach. The quest to understand this unlikely connection led us to explore a wide array of literature and research findings, much like navigating through a maze of yoga mats in search of inner peace.
In "The Journal of Solar Energy" by Smith et al., the authors find a robust relationship between solar power output in sub-Saharan Africa and the region's potential for sustainable energy development. This serves as the foundation of our investigation, much like how sun salutations serve as the cornerstone of many yoga practices.
Moving beyond the realm of sober scientific inquiry, "The Economics of Athleisure" by Doe delves into the market dynamics and consumer behavior shaping the lucrative athleisure industry. Little did we know that our exploration of solar power and stock prices would lead us to this intersection of fashion and finance, much like stumbling upon a hidden treasure in a labyrinth.
Expanding our horizons, "The Power of Positive Energy" by Jones examines the psychological effects of renewable energy on human well-being. While seemingly unrelated to stock prices, the book's insights on the influence of solar energy on individual moods gave us a moment of enlightenment, much like the unexpected burst of energy that comes from sipping on a green smoothie during a mid-afternoon slump.
Venturing into non-fiction titles, we also considered "The Big Pivot" by Andrew S. Winston, which explores the potential for global business to profit from environmental sustainability efforts. Little did we expect that our investigation of solar power and stock performance would lead us to contemplate the business implications of sustainable energy practices, much like stumbling upon a pair of running shoes in a department store while looking for a new briefcase.
Turning to fiction, the enigmatic allure of solar power and stock prices drew us to "The Sun Also Rises" by Ernest Hemingway and "The Yoga of Max's Discontent" by Karan Bajaj. While the former transports readers to the sun-soaked landscapes of Spain, the latter takes us on a journey of self-discovery through yoga and meditation in India. These literary works offered a whimsical escape from the rigorous analysis of data, much like imagining ourselves doing a downward dog on a remote Mozambican beach while monitoring stock prices on a smartphone.
In a similar spirit of unexpected connections, our research prompted us to revisit cinematic marvels such as "The Secret Life of Walter Mitty" and "Eat Pray Love." While these films may not offer direct insights into solar power or stock market movements, their themes of self-discovery and unconventional journeys resonated with the unconventional nature of our investigation, much like stumbling upon a hidden oasis while wandering through a desert of financial reports.
As we sifted through this eclectic mix of literature and cultural references, we found ourselves entertained by the unexpected synchronicity of seemingly disparate topics. Much like finding humor in a yoga class when the instructor unexpectedly breaks into a dance, our literature review journey has been filled with moments of delight and amusement.

[[RESULTS]]
The results of our analysis unveiled a remarkably strong correlation between solar power generation in Mozambique and the stock price of Lululemon Athletica (LULU) over the period of 2012 to 2021. The correlation coefficient of 0.9731367 is as eye-catching as a pair of neon yoga pants in a sea of black leggings, demonstrating a nearly perfect positive relationship between these seemingly unrelated variables. In simpler terms, it's as if the sun in Mozambique decided to do some sun salutations and Lululemon's stock price decided to stretch to new heights in unison.
Furthermore, the r-squared value of 0.9469950 indicates that a whopping 94.7% of the variability in Lululemon's stock price can be explained by the solar power generated in Mozambique. This finding is as surprising as discovering that the real source of flexibility in Lululemon's clothing line is not just the fabric, but rather the solar-powered energy emanating from the southern hemisphere.
The p-value of less than 0.01 adds yet another layer of significance to our results, indicating that the likelihood of this strong correlation occurring by chance is about as rare as finding a four-leaf clover in a field of dandelions. It's safe to say that this correlation is about as statistically robust as Lululemon's core workout leggings.
Fig. 1 provides a visual representation of this striking correlation, perfectly encapsulating the strong relationship between solar power generation in Mozambique and Lululemon's stock price. It's a sight to behold, much like witnessing a synchronized swimming routine between the African sun and a well-performing athleisure stock.
In summary, our findings highlight a surprising and robust association between solar power in Mozambique and Lululemon's stock price, raising questions about the celestial or market mechanisms at play. While this correlation may be as mystifying as figuring out how Lululemon manages to make leggings both stretchy and squat-proof, investors should approach it with caution and refrain from basing their financial decisions solely on the luminosity of the sun and Lululemon’s stock movements. After all, just as in yoga, balance is key, and a holistic view of investment strategies is essential to avoid getting tangled in a web of misleading correlations.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of our analysis have unveiled a connection between solar power generation in Mozambique and the stock price of Lululemon Athletica (LULU) that is as surprising as finding a yoga studio in the middle of a desert – it's unexpected, but oh so intriguing. Our findings support the existing literature, much like a supportive sports bra, and shed light on the entwined dance of solar energy and stock market performance.

In line with Smith et al.'s work in "The Journal of Solar Energy," which highlighted the potential for sustainable energy development in sub-Saharan Africa, our research confirmed the significant relationship between solar power output in the region and Lululemon's stock price. This correlation is as robust as the core stability required for a perfect tree pose – the kind that makes you wonder if Lululemon's designers have been taking cues from the power of the African sun.

Additionally, our investigation aligns with the insights of Doe's "The Economics of Athleisure," as we unexpectedly found ourselves delving into the market dynamics of the athleisure industry while exploring the connection between solar power and stock prices. This connection is as seamless as a well-designed seamless yoga set from Lululemon – it may not seem obvious at first, but it's there, supporting the intertwining of two distinct worlds.

Just as Jones' "The Power of Positive Energy" explored the psychological effects of renewable energy, our study unexpectedly brought us to consider the influence of solar power generation on Lululemon's stock movements. Our findings resonate with Jones' emphasis on the positive impact of renewable energy, suggesting a positive upsurge in Lululemon's stock price with increased solar power generation, as if the stock itself were on a powerful, sun-drenched mountain hike.

Furthermore, our research delved into the business implications of sustainable energy practices, mirroring the insights in "The Big Pivot" by Andrew S. Winston. While our primary focus was on solar power and stock performance, the unforeseen connection with the business impacts of environmental sustainability efforts adds another layer to the unexpected harmony between the two seemingly disparate realms – much like discovering that the best yoga inversions are often born out of unlikely transitions.

In essence, our results not only substantiate the previously explored connections but also add a layer of complexity, much like discovering intricate patterns in a meticulously designed yoga mat. The unexpected correlation between solar power in Mozambique and Lululemon's stock price may seem as enigmatic as the tranquility achieved in a serene meditation session, yet it offers a refreshing perspective on the potential interplay between renewable energy and financial indicators.

In navigating the uncharted territory of solar power and stock prices, we stumbled upon unexpected synchronicities and surprising alignments, much like finding humor in an academic discussion on solar power and athleisure. Our study contributes to the expanding landscape of interdisciplinary research, uncovering the intriguing parallels between elements as unrelated as a sunny African landscape and a booming athleisure stock.

As we continue to ponder the inexplicable ties between solar power in Mozambique and Lululemon's stock performance, we are reminded that beneath the mysteries of statistical correlations lie realms of untold possibilities and unexpected associations. Much like in the practice of yoga, where each asana holds the promise of new revelations, our exploration has opened doors to uncover the unexpected harmony between the celestial forces of solar power and the dynamic movements of the stock market.

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 Solar power generated in Mozambique and Lululemon's stock price (LULU). 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]]
Solar Power from Sub-Saharan Africa to Stock Surges: The Lululemon Link

[[ABSTRACT]]
This study explores the perplexing correlation between solar power generation in Mozambique and Lululemon Athletica's (LULU) stock price. While this inquiry may seem as incongruous as a pickle in a parfait, we employed empirical data from the Energy Information Administration and LSEG Analytics (Refinitiv) to conduct our analysis. Our findings revealed a surprising correlation coefficient of 0.9731367 with a statistical significance of p < 0.01, for the period of 2012 to 2021. This correlation stands out as vividly as a neon leotard against a backdrop of gray sweatpants. Our research raises questions as to what celestial forces or cosmic currents may be underpinning the seemingly covariant trajectories of solar power production in Mozambique and Lululemon's stock performance. Despite the unexpected connection, we caution against investing solely based on solar luminosity and Lululemon's stock movements, as correlations can often be deceiving, like a pair of yoga pants that seem to fit perfectly in the store but then ride up uncomfortably during a workout.

[[INTRDUCTION]]
INTRODUCTION
In the world of finance and energy, one would hardly expect to find a connection between the solar-drenched plains of Mozambique and the stock price of a prominent athleisure brand, as unlikely as stumbling upon a unicorn in a cornfield. However, the enigmatic correlation between solar power generation in Sub-Saharan Africa and the ebbs and flows of Lululemon's (LULU) stock price has piqued both curiosity and skepticism in the research community and financial markets alike.
While most would assume that the only thing connecting solar panels and Lululemon leggings is the occasional yoga session, our investigation delved into the unexplored territory where energy production meets retail flair. Drawing on empirical data from the Energy Information Administration and LSEG Analytics (Refinitiv), we embarked on a quest to unravel this baffling correlation, akin to untangling a stretchy resistance band after an intense workout.
The revelation of a striking correlation coefficient of 0.9731367, coupled with a statistical significance of p < 0.01, during the period of 2012 to 2021, left us as shocked as finding out that avocados and coconuts are actually classified as berries. This correlation stood out as conspicuously as a pair of neon-colored leggings at a conservative business meeting, prompting us to dig deeper into the celestial or market forces involved.
While our findings raise eyebrows and evoke intrigue, we advise caution against making investment decisions based solely on the luminosity of the sun and Lululemon's stock antics, as correlation does not always imply causation. As tantalizing as it may be to think that harnessing solar power in Mozambique could forecast the rise and fall of Lululemon's stock like a solar-powered pendulum, investment strategies are best formulated with a broader perspective, much like choosing the right balance between downward dog and warrior poses in a yoga class.

[[RESULTS]]
The results of our analysis unveiled a remarkably strong correlation between solar power generation in Mozambique and the stock price of Lululemon Athletica (LULU) over the period of 2012 to 2021. The correlation coefficient of 0.9731367 is as eye-catching as a pair of neon yoga pants in a sea of black leggings, demonstrating a nearly perfect positive relationship between these seemingly unrelated variables. In simpler terms, it's as if the sun in Mozambique decided to do some sun salutations and Lululemon's stock price decided to stretch to new heights in unison.
Furthermore, the r-squared value of 0.9469950 indicates that a whopping 94.7% of the variability in Lululemon's stock price can be explained by the solar power generated in Mozambique. This finding is as surprising as discovering that the real source of flexibility in Lululemon's clothing line is not just the fabric, but rather the solar-powered energy emanating from the southern hemisphere.
The p-value of less than 0.01 adds yet another layer of significance to our results, indicating that the likelihood of this strong correlation occurring by chance is about as rare as finding a four-leaf clover in a field of dandelions. It's safe to say that this correlation is about as statistically robust as Lululemon's core workout leggings.
Fig. 1 provides a visual representation of this striking correlation, perfectly encapsulating the strong relationship between solar power generation in Mozambique and Lululemon's stock price. It's a sight to behold, much like witnessing a synchronized swimming routine between the African sun and a well-performing athleisure stock.
In summary, our findings highlight a surprising and robust association between solar power in Mozambique and Lululemon's stock price, raising questions about the celestial or market mechanisms at play. While this correlation may be as mystifying as figuring out how Lululemon manages to make leggings both stretchy and squat-proof, investors should approach it with caution and refrain from basing their financial decisions solely on the luminosity of the sun and Lululemon’s stock movements. After all, just as in yoga, balance is key, and a holistic view of investment strategies is essential to avoid getting tangled in a web of misleading correlations.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our investigation has illuminated a truly unexpected and seemingly cosmic connection between solar power generation in Mozambique and the performance of Lululemon's stock, leaving us as incredulous as a squirrel realizing it has stashed its nuts in a vegan cafe. Our findings are as clear as a downward dog pose in a yoga class, demonstrating a correlation as strong as a triple-shot espresso in a sleep-deprived office.

While the correlation coefficient of 0.9731367 and the astonishing r-squared value of 0.9469950 speak volumes about the relationship between these seemingly disparate variables, we must approach this discovery with cautious optimism. Just as one might hesitate before doing a headstand without proper alignment, investors should be wary of leaping to conclusions based solely on this correlation.

As tempting as it may be to base financial decisions on solar luminosity and Lululemon's stock gyrations, correlations can be as misleading as trying to find the end of a rainbow. Just as Lululemon advises against wearing yoga pants for high-impact activities, we urge investors to consider a more comprehensive approach to their investment strategy.

In the grand scheme of financial and cosmic mysteries, this correlation between solar power in Mozambique and Lululemon's stock appears to be an enigma as confounding as realizing that avocados are, in fact, berries. As such, while this research has shed light on this perplexing correlation, we assert that no further research in this area is needed, just as no more research is needed to determine that a cat's distaste for water is as universal as, well, anything universally despised.

So, let us bid adieu to this quirky correlation and divert our attention to more conventional financial indicators, as advisable as wearing appropriate footwear for a hike in the mountains.

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 Solar Power from Sub-Saharan Africa to Stock Surges: The Lululemon Link. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Renewable Energy Economics and Fashion Trends

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 Solar Power from Sub-Saharan Africa to Stock Surges: The Lululemon Link. Respond only with the name of a fictional organization.

ChatGPT:

The Global Institute for Renewable Energy Studies and Sustainable Development

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 Solar Power from Sub-Saharan Africa to Stock Surges: The Lululemon Link with an abstract of This study explores the perplexing correlation between solar power generation in Mozambique and Lululemon Athletica's (LULU) stock price. While this inquiry may seem as incongruous as a pickle in a parfait, we employed empirical data from the Energy Information Administration and LSEG Analytics (Refinitiv) to conduct our analysis. Our findings revealed a surprising correlation coefficient of 0.9731367 with a statistical significance of p < 0.01, for the period of 2012 to 2021. This correlation stands out as vividly as a neon leotard against a backdrop of gray sweatpants. Our research raises questions as to what celestial forces or cosmic currents may be underpinning the seemingly covariant trajectories of solar power production in Mozambique and Lululemon's stock performance. Despite the unexpected connection, we caution against investing solely based on solar luminosity and Lululemon's stock movements, as correlations can often be deceiving, like a pair of yoga pants that seem to fit perfectly in the store but then ride up uncomfortably during a workout.

ChatGPT:

solar power Sub-Saharan Africa, solar power generation Mozambique, Lululemon stock price correlation, solar power production data, Energy Information Administration, LSEG Analytics, Refinitiv, solar power stock correlation, solar power and stock market, Mozambique solar energy, Lululemon Athletica stock performance, cosmic forces stock market correlation

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

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Data details

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

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

See what else correlates with Lululemon's stock price (LULU)

Correlation r = 0.9731367 (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 = 0.9469950 (Coefficient of determination)
This means 94.7% of the change in the one variable (i.e., Lululemon's stock price (LULU)) is predictable based on the change in the other (i.e., Solar power generated in Mozambique) over the 10 years from 2012 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 2.21E-6.^Show 0.0000022057047832886450000000
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 0.97 in 0.000221% of random cases. Said differently, if you correlated 453,370 random variables^Note You don't actually need 453 thousand 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 9 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 9 because we have two variables measured over a period of 10 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.

[ 0.89, 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.

	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021
Solar power generated in Mozambique (Billion kWh)	0.0001	0.0004	0.001	0.002	0.002	0.002	0.002	0.002	0.031	0.07
Lululemon's stock price (LULU) (Stock price)	47.5	77.73	59.08	56.01	53.71	65.94	77.31	118.89	232.9	351.67

Why this works

Data dredging: I have 25,153 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 632,673,409 correlation calculations! This is called “data dredging.” Instead of starting with a hypothesis and testing it, I instead abused the data to see what correlations shake out. It’s a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random.
Lack of causal connection: There is probably^Note Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple^Note Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
p-value calculation does not take this into account, so mathematically it appears less probable than it really is.

Try it yourself

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

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([0.0001,0.0004,0.001,0.002,0.002,0.002,0.002,0.002,0.031,0.07,])
array_2 = np.array([47.5,77.73,59.08,56.01,53.71,65.94,77.31,118.89,232.9,351.67,])
array_1_name = "Solar power generated in Mozambique"
array_2_name = "Lululemon's stock price (LULU)"

# 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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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.

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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 Solar power generated in Mozambique
Line chart for only Lululemon's stock price (LULU)
AI-generated correlation image
The spurious research paper: Solar Power from Sub-Saharan Africa to Stock Surges: The Lululemon Link

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Correlation ID: 3602 · Black Variable ID: 23834 · Red Variable ID: 1735


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