Spurious correlation #3,752 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Number of public school students in 3rd grade and the second variable is Hydopower energy generated in Paraguay. 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 Number of public school students in 3rd grade and the second variable is Hydopower energy generated in Paraguay. The chart goes from 1990 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The influx of 3rd graders brought an unexpected surge in enthusiasm for science, leading to a groundbreaking class project on renewable energy. As the students delved into hydropower, they inadvertently sparked a competition to design more efficient water wheels, creating a mini boom in hydro innovation. The Paraguayan government, astounded by the 8-year-old prodigies' achievements, implemented their designs in major hydroelectric plants, ultimately revolutionizing the hydro industry. The pint-sized pioneers not only elevated the nation's energy output but also left a lasting ripple in the world of green technology. Who knew that a few extra 3rd graders could power up Paraguay's hydroelectricity in such a shocking manner!

^{Show image generation prompt} Model: dalle-3
Prompt: An image that looks like it is a scene from a Pixar movie, depicting a bustling classroom in Paraguay. Inside the lively classroom, 3rd graders are diligently using colorful crayons to bring their drawings to life. Sunlight streams in through the windows, illuminating the scene and powering the solar panels on the roof. Meanwhile, outside, the rushing waters of the Itaipu Dam churn away, supplying hydroelectricity to fuel the crayon factories and meet the heightened demand caused by the larger number of students. 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: Number of public school students in 3rd grade and Hydopower energy generated in Paraguay. 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: Data cyber art Oragami Charcoal An image that looks like it is a scene from a Pixar movie Whimsical illustration
ChatGPT: An image that looks like it is a scene from a Pixar movie

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 Number of public school students in 3rd grade and Hydopower energy generated in Paraguay, in the following situation: Because as the number of 3rd graders increases, more crayons are used, leading to increased demand for hydroelectricity to power the crayon factories in Paraguay.. Keep the description simple.
ChatGPT: In a bustling classroom in Paraguay, lots of 3rd graders are hard at work, using colorful crayons to bring their drawings to life. Sunlight streams in through the windows, powering the solar panels on the roof, while outside, the rushing waters of the Itaipu Dam churn away, generating hydroelectricity to fuel the crayon factories and meet the heightened demand caused by the larger number of students.

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: [ An image that looks like it is a scene from a Pixar movie ] and depicting this scene: In a bustling classroom in Paraguay, lots of 3rd graders are hard at work, using colorful crayons to bring their drawings to life. Sunlight streams in through the windows, powering the solar panels on the roof, while outside, the rushing waters of the Itaipu Dam churn away, generating hydroelectricity to fuel the crayon factories and meet the heightened demand caused by the larger number of students. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: An image that looks like it is a scene from a Pixar movie, depicting a bustling classroom in Paraguay. Inside the lively classroom, 3rd graders are diligently using colorful crayons to bring their drawings to life. Sunlight streams in through the windows, illuminating the scene and powering the solar panels on the roof. Meanwhile, outside, the rushing waters of the Itaipu Dam churn away, supplying hydroelectricity to fuel the crayon factories and meet the heightened demand caused by the larger number of students.

*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 Number of public school students in 3rd grade caused Hydopower energy generated in Paraguay to increase.\Make it sound serious until the end.

AI academic paper

(Because p < 0.01)

Perplexing Parallels: Pupils and Power in Paraguay

The Journal of Comparative Ophthalmological and Political Studies

Jan 2024

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

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

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

Please make up a literature review section of an academic research paper presenting the findings of the connection between Number of public school students in 3rd grade and Hydopower energy generated in Paraguay. 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 name a few real TV shows that sound like they might be relevant to the topic that you watched as research.

Here is the title and abstract of the paper:
[[TITLE]]
Perplexing Parallels: Pupils and Power in Paraguay

[[ABSTRACT]]
In this research paper, we delve into the delightful dance between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Our team extracted data from the National Center for Education Statistics and the Energy Information Administration to embark on this captivating quest. Employing statistical analysis, we uncovered a striking correlation coefficient of 0.9213313 and a significant p-value of less than 0.01 for the period spanning from 1990 to 2021. Our findings not only raise eyebrows but also prompt further investigation into the quirky, yet captivating, relationship between education and energy in the land of stunning waterfalls and power plants.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The interplay between education and energy production has long been a topic of intrigue and speculation. In the pursuit of unearthing connections that defy conventional wisdom, we set out to explore the relationship between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Much like the intricate web of neurotransmitters firing in the brain, we sought to unravel the enigmatic correlation between these seemingly disparate variables.
As researchers, we are accustomed to embracing the unexpected, much like navigating a labyrinth of data to discern patterns and relationships. Our pursuit of knowledge often leads us down uncharted paths, akin to boldly venturing into the wilderness armed with nothing but a compass and a keen sense of curiosity, but with fewer mosquitoes and more spreadsheets.
Paraguay, known for its breathtaking natural landscape and abundant hydropower potential, provided an enticing backdrop for our investigation. Like a scientist approaching a bubbling beaker with cautious optimism, we approached the intersection of education and hydroelectricity with both excitement and an unwavering commitment to scientific rigor.
Our quest began by gathering data from the National Center for Education Statistics and the Energy Information Administration – a process that involved sifting through countless rows and columns, not unlike searching for a single needle in an unforgiving haystack of digits. Armed with an arsenal of statistical tools and a healthy dose of curiosity, we delved into the numbers with a fervor reminiscent of a sleuth hot on the trail of a mystery, albeit with more software programs and fewer trench coats.
The period from 1990 to 2021 served as our temporal canvas, where we painted a landscape of figures and trends, much like a group of statisticians armed with a palette of data points and an assortment of brushes. Our analysis unveiled a remarkable correlation coefficient of 0.9213313, which beckoned to us like a glimmering scientific unicorn prancing through the statistical forest. Coupled with a p-value of less than 0.01, the significance of our findings was akin to stumbling upon a rare gem in a vast expanse of numerical gravel.
These findings not only piqued our interest but also compelled us to contemplate the profound implications of the intricate connection between education and energy production in Paraguay. The implications are as profound as an over-inflated balloon in a room filled with curious cats, leading us to question, with a mix of awe and amusement, the underlying mechanisms at play.
As we embark on this academic odyssey, we invite readers to join us in this delightful dance of data and discovery, where the lines between education and energy blur and merge like two disparate puzzle pieces finally finding their rightful place. As we unravel the complexities of this charming correlation, we stand poised on the precipice of newfound knowledge, eager to share our illuminating insights and unveil the whimsical wonders that lie hidden within the seemingly mundane world of educational statistics and energy production.
Stay tuned for the illuminating ride that lies ahead – it’s bound to be more thrilling than a roller coaster of regression analyses.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

As we delve into the realm of literature concerning the captivating correlation between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay, we encounter a myriad of studies and publications that offer valuable insights. Smith et al. (2015) explored the nexus between primary education and renewable energy production, shedding light on the potential synergies that exist between these seemingly unrelated domains. Their rigorous analysis paved the way for further research, much like a trusty guide illuminating a dimly lit path in the wilderness of academia.

Building upon this foundation, Doe and colleagues (2018) investigated the impact of educational attainment on sustainable energy practices in South America. Their comprehensive study highlighted the importance of early education in shaping attitudes towards renewable energy, serving as a beacon of knowledge amidst the turbulent seas of academic inquiry.

Jones (2020) delved into the societal implications of hydropower development, offering a panoramic view of the interconnectedness between education and energy in the Paraguayan context. Their work, much like a masterfully crafted tapestry, intricately weaved together the threads of education and hydropower, unveiling a rich tapestry of correlations and causations.

Transitioning from scholarly works to the realm of non-fiction books, "The Water Will Come: Rising Seas, Sinking Cities, and the Remaking of the Civilized World" by Jeff Goodell provides a thought-provoking exploration of the interplay between water, energy, and civilization, painting a vivid portrait of the intricate dance between natural resources and human society.

On a more fictional note, "The Power" by Naomi Alderman presents a gripping narrative that imaginatively weaves together themes of power, societal dynamics, and unexpected transformations, offering a tantalizing glimpse into the realm of power - both electric and otherwise.

Adding a touch of lightheartedness, popular television shows such as "The Powerpuff Girls" and "Stranger Things" inadvertently offer glimpses into the themes of power, energy, and the enigmatic capabilities of young individuals, serving as anecdotal artifacts in our quest to understand the underlying currents of the Paraguayan education and energy landscape.

These disparate sources, while diverging in scope and genre, collectively contribute to our understanding of the intricate web that connects education and hydropower generation in Paraguay. As we step into the interdisciplinary arena of education, power, and literature, we invite readers to join us on this delightful journey of discovery and whimsy, where the serious and the serendipitous converge in an intellectual pas de deux.

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

Please make up the methodology section of an academic research paper presenting the findings of the connection between Number of public school students in 3rd grade and Hydopower energy generated in Paraguay. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from National Center for Education Statistics 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]]
Perplexing Parallels: Pupils and Power in Paraguay

[[ABSTRACT]]
In this research paper, we delve into the delightful dance between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Our team extracted data from the National Center for Education Statistics and the Energy Information Administration to embark on this captivating quest. Employing statistical analysis, we uncovered a striking correlation coefficient of 0.9213313 and a significant p-value of less than 0.01 for the period spanning from 1990 to 2021. Our findings not only raise eyebrows but also prompt further investigation into the quirky, yet captivating, relationship between education and energy in the land of stunning waterfalls and power plants.

[[INTRODUCTION]]
The interplay between education and energy production has long been a topic of intrigue and speculation. In the pursuit of unearthing connections that defy conventional wisdom, we set out to explore the relationship between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Much like the intricate web of neurotransmitters firing in the brain, we sought to unravel the enigmatic correlation between these seemingly disparate variables.
As researchers, we are accustomed to embracing the unexpected, much like navigating a labyrinth of data to discern patterns and relationships. Our pursuit of knowledge often leads us down uncharted paths, akin to boldly venturing into the wilderness armed with nothing but a compass and a keen sense of curiosity, but with fewer mosquitoes and more spreadsheets.
Paraguay, known for its breathtaking natural landscape and abundant hydropower potential, provided an enticing backdrop for our investigation. Like a scientist approaching a bubbling beaker with cautious optimism, we approached the intersection of education and hydroelectricity with both excitement and an unwavering commitment to scientific rigor.
Our quest began by gathering data from the National Center for Education Statistics and the Energy Information Administration – a process that involved sifting through countless rows and columns, not unlike searching for a single needle in an unforgiving haystack of digits. Armed with an arsenal of statistical tools and a healthy dose of curiosity, we delved into the numbers with a fervor reminiscent of a sleuth hot on the trail of a mystery, albeit with more software programs and fewer trench coats.
The period from 1990 to 2021 served as our temporal canvas, where we painted a landscape of figures and trends, much like a group of statisticians armed with a palette of data points and an assortment of brushes. Our analysis unveiled a remarkable correlation coefficient of 0.9213313, which beckoned to us like a glimmering scientific unicorn prancing through the statistical forest. Coupled with a p-value of less than 0.01, the significance of our findings was akin to stumbling upon a rare gem in a vast expanse of numerical gravel.
These findings not only piqued our interest but also compelled us to contemplate the profound implications of the intricate connection between education and energy production in Paraguay. The implications are as profound as an over-inflated balloon in a room filled with curious cats, leading us to question, with a mix of awe and amusement, the underlying mechanisms at play.
As we embark on this academic odyssey, we invite readers to join us in this delightful dance of data and discovery, where the lines between education and energy blur and merge like two disparate puzzle pieces finally finding their rightful place. As we unravel the complexities of this charming correlation, we stand poised on the precipice of newfound knowledge, eager to share our illuminating insights and unveil the whimsical wonders that lie hidden within the seemingly mundane world of educational statistics and energy production.
Stay tuned for the illuminating ride that lies ahead – it’s bound to be more thrilling than a roller coaster of regression analyses.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

As with any scientific endeavor, our methodology was characterized by a careful balance of precision and the occasional suspiciously spontaneous coffee break. The collection and analysis of data proceeded with the methodical diligence of a squirrel hoarding acorns for the winter, albeit with less fur and more statistical software.

Data Collection:
To assemble the necessary inputs for our analysis, we scoured the virtual nooks and crannies of the internet, mining data from sources such as the National Center for Education Statistics and the Energy Information Administration. This process involved navigating through a digital labyrinth of spreadsheets and databases, akin to a determined spelunker seeking hidden treasures amidst the dark recesses of cyberspace.

The number of public school students in 3rd grade in Paraguay was obtained from the National Center for Education Statistics, utilizing records spanning the years 1990 to 2021. This exhaustive collection process required the strategic deployment of keyword searches and an iron will in the face of seemingly endless rows and columns of data – not unlike searching for a needle in a haystack, if the hay were made entirely of ones and zeroes.

Similarly, data on hydropower energy generation in Paraguay was extracted from the Energy Information Administration, reflecting the same 1990 to 2021 timeframe. This endeavor called for an astute attention to detail, akin to a detective meticulously piecing together clues from a crime scene, albeit with more spreadsheets and fewer dramatic interrogations.

Data Analysis:
With our data in hand, we set about analyzing the relationship between the number of 3rd-grade public school students and hydropower energy generation in Paraguay. Armed with statistical software and a predisposition for perusing p-values, we delved into the realm of correlation analysis with the enthusiasm of a child in a candy store – if the candy were statistical concepts and the store was a meticulously organized spreadsheet.

To quantify the connection between these variables, we calculated the correlation coefficient using robust statistical methods. The correlation analysis involved techniques that embodied the essence of mathematical finesse and empirical rigor, much like a graceful dance between two partners in perfect statistical harmony – albeit with more numbers and fewer dance shoes.

Furthermore, the estimation of the p-value allowed us to ascertain the significance of the observed correlation, delving into the realm of statistical confidence and probability with a fervor typically reserved for solving cryptic crossword puzzles. The statistical analyses danced across the screen like joyous pixels in a digital ballet, revealing patterns and connections that surpassed mere numerical coincidence.

It is important to note that our approach to data analysis upheld the sacred principles of objectivity and scientific integrity, much like a vigilant guardian of scholarly truth amidst the ever-shifting tides of data interpretation. We navigated the murky waters of statistical inference with caution and precision, ensuring that our findings stood as steadfast beacons of empirical insight in the tempest of scholarly inquiry.

In summary, our methodology balanced the meticulous collection of data with the rigorous application of statistical techniques, culminating in a comprehensive analysis of the relationship between the number of public school students in 3rd grade and hydropower energy generation in Paraguay. This process embraced the boundless spirit of scientific discovery, punctuated by the occasional nod to caffeinated inspiration and the timeless allure of uncovering hidden correlations amidst the bustling landscape of empirical inquiry.

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

Please make up the results section of an academic research paper presenting the findings of the connection between Number of public school students in 3rd grade and Hydopower energy generated in Paraguay. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from National Center for Education Statistics and Energy Information Administration .

For the time period 1990 to 2021, you found a correlation 0.9213313, r-squared of 0.8488514, 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]]
Perplexing Parallels: Pupils and Power in Paraguay

[[ABSTRACT]]
In this research paper, we delve into the delightful dance between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Our team extracted data from the National Center for Education Statistics and the Energy Information Administration to embark on this captivating quest. Employing statistical analysis, we uncovered a striking correlation coefficient of 0.9213313 and a significant p-value of less than 0.01 for the period spanning from 1990 to 2021. Our findings not only raise eyebrows but also prompt further investigation into the quirky, yet captivating, relationship between education and energy in the land of stunning waterfalls and power plants.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The interplay between education and energy production has long been a topic of intrigue and speculation. In the pursuit of unearthing connections that defy conventional wisdom, we set out to explore the relationship between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Much like the intricate web of neurotransmitters firing in the brain, we sought to unravel the enigmatic correlation between these seemingly disparate variables.
As researchers, we are accustomed to embracing the unexpected, much like navigating a labyrinth of data to discern patterns and relationships. Our pursuit of knowledge often leads us down uncharted paths, akin to boldly venturing into the wilderness armed with nothing but a compass and a keen sense of curiosity, but with fewer mosquitoes and more spreadsheets.
Paraguay, known for its breathtaking natural landscape and abundant hydropower potential, provided an enticing backdrop for our investigation. Like a scientist approaching a bubbling beaker with cautious optimism, we approached the intersection of education and hydroelectricity with both excitement and an unwavering commitment to scientific rigor.
Our quest began by gathering data from the National Center for Education Statistics and the Energy Information Administration – a process that involved sifting through countless rows and columns, not unlike searching for a single needle in an unforgiving haystack of digits. Armed with an arsenal of statistical tools and a healthy dose of curiosity, we delved into the numbers with a fervor reminiscent of a sleuth hot on the trail of a mystery, albeit with more software programs and fewer trench coats.
The period from 1990 to 2021 served as our temporal canvas, where we painted a landscape of figures and trends, much like a group of statisticians armed with a palette of data points and an assortment of brushes. Our analysis unveiled a remarkable correlation coefficient of 0.9213313, which beckoned to us like a glimmering scientific unicorn prancing through the statistical forest. Coupled with a p-value of less than 0.01, the significance of our findings was akin to stumbling upon a rare gem in a vast expanse of numerical gravel.
These findings not only piqued our interest but also compelled us to contemplate the profound implications of the intricate connection between education and energy production in Paraguay. The implications are as profound as an over-inflated balloon in a room filled with curious cats, leading us to question, with a mix of awe and amusement, the underlying mechanisms at play.
As we embark on this academic odyssey, we invite readers to join us in this delightful dance of data and discovery, where the lines between education and energy blur and merge like two disparate puzzle pieces finally finding their rightful place. As we unravel the complexities of this charming correlation, we stand poised on the precipice of newfound knowledge, eager to share our illuminating insights and unveil the whimsical wonders that lie hidden within the seemingly mundane world of educational statistics and energy production.
Stay tuned for the illuminating ride that lies ahead – it’s bound to be more thrilling than a roller coaster of regression analyses.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

Our intrepid journey into the correlation between the number of public school students in 3rd grade and hydropower energy generated in Paraguay yielded some intriguing results that are as captivating as a magic show at a statistics conference.

First and foremost, our analysis revealed a robust correlation coefficient of 0.9213313 between the two variables. This correlation coefficient is as strong as the gravitational pull of a massive statistical discovery, drawing our attention like moths to a scientific flame.

Furthermore, the calculated r-squared value of 0.8488514 indicated that approximately 84.89% of the variability in hydropower energy generated in Paraguay could be explained by the number of public school students in 3rd grade. It's as if the tiny hula hoop of 3rd-grade student numbers was able to capture the attention of a large and energetic hydropower generator, drawing it into an elaborate dance of statistical significance.

In addition, the p-value of less than 0.01 that emerged from our analysis decisively rejected the null hypothesis, providing compelling evidence of a significant relationship between these two seemingly unrelated variables. It's as if the p-value waved a giant foam finger, cheerfully proclaiming, "We've got ourselves a statistically significant result, folks!"

The scatterplot in Figure 1 illustrates the striking correlation between the number of public school students in 3rd grade and hydropower energy generated in Paraguay, resembling a beautiful symphony where each data point plays its own harmonious note in the grand composition of statistical exploration. Like a perfectly executed magic trick, this scatterplot reveals the captivating connection that exists between education and energy in the mesmerizing land of Paraguay.

In summary, our findings not only establish a compelling relationship between the number of public school students in 3rd grade and hydropower energy generated in Paraguay but also stimulate further curiosity and probing into this peculiar pairing that transcends traditional scientific boundaries. This correlation is more elusive than a statistical unicorn, but our study has managed to capture its essence in a delightful waltz of data analysis and scientific exploration. As we bask in the glow of these captivating results, we eagerly anticipate the next act in this captivating saga of statistical serendipity.

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 Number of public school students in 3rd grade and Hydopower energy generated in Paraguay. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Limit your response to 500 tokens.

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

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

[[TITLE]]
Perplexing Parallels: Pupils and Power in Paraguay

[[ABSTRACT]]
In this research paper, we delve into the delightful dance between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Our team extracted data from the National Center for Education Statistics and the Energy Information Administration to embark on this captivating quest. Employing statistical analysis, we uncovered a striking correlation coefficient of 0.9213313 and a significant p-value of less than 0.01 for the period spanning from 1990 to 2021. Our findings not only raise eyebrows but also prompt further investigation into the quirky, yet captivating, relationship between education and energy in the land of stunning waterfalls and power plants.

[[LITERATURE REVIEW]]
As we delve into the realm of literature concerning the captivating correlation between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay, we encounter a myriad of studies and publications that offer valuable insights. Smith et al. (2015) explored the nexus between primary education and renewable energy production, shedding light on the potential synergies that exist between these seemingly unrelated domains. Their rigorous analysis paved the way for further research, much like a trusty guide illuminating a dimly lit path in the wilderness of academia.
Building upon this foundation, Doe and colleagues (2018) investigated the impact of educational attainment on sustainable energy practices in South America. Their comprehensive study highlighted the importance of early education in shaping attitudes towards renewable energy, serving as a beacon of knowledge amidst the turbulent seas of academic inquiry.
Jones (2020) delved into the societal implications of hydropower development, offering a panoramic view of the interconnectedness between education and energy in the Paraguayan context. Their work, much like a masterfully crafted tapestry, intricately weaved together the threads of education and hydropower, unveiling a rich tapestry of correlations and causations.
Transitioning from scholarly works to the realm of non-fiction books, "The Water Will Come: Rising Seas, Sinking Cities, and the Remaking of the Civilized World" by Jeff Goodell provides a thought-provoking exploration of the interplay between water, energy, and civilization, painting a vivid portrait of the intricate dance between natural resources and human society.
On a more fictional note, "The Power" by Naomi Alderman presents a gripping narrative that imaginatively weaves together themes of power, societal dynamics, and unexpected transformations, offering a tantalizing glimpse into the realm of power - both electric and otherwise.
Adding a touch of lightheartedness, popular television shows such as "The Powerpuff Girls" and "Stranger Things" inadvertently offer glimpses into the themes of power, energy, and the enigmatic capabilities of young individuals, serving as anecdotal artifacts in our quest to understand the underlying currents of the Paraguayan education and energy landscape.
These disparate sources, while diverging in scope and genre, collectively contribute to our understanding of the intricate web that connects education and hydropower generation in Paraguay. As we step into the interdisciplinary arena of education, power, and literature, we invite readers to join us on this delightful journey of discovery and whimsy, where the serious and the serendipitous converge in an intellectual pas de deux.

[[RESULTS]]
Our intrepid journey into the correlation between the number of public school students in 3rd grade and hydropower energy generated in Paraguay yielded some intriguing results that are as captivating as a magic show at a statistics conference.
First and foremost, our analysis revealed a robust correlation coefficient of 0.9213313 between the two variables. This correlation coefficient is as strong as the gravitational pull of a massive statistical discovery, drawing our attention like moths to a scientific flame.
Furthermore, the calculated r-squared value of 0.8488514 indicated that approximately 84.89% of the variability in hydropower energy generated in Paraguay could be explained by the number of public school students in 3rd grade. It's as if the tiny hula hoop of 3rd-grade student numbers was able to capture the attention of a large and energetic hydropower generator, drawing it into an elaborate dance of statistical significance.
In addition, the p-value of less than 0.01 that emerged from our analysis decisively rejected the null hypothesis, providing compelling evidence of a significant relationship between these two seemingly unrelated variables. It's as if the p-value waved a giant foam finger, cheerfully proclaiming, "We've got ourselves a statistically significant result, folks!"
The scatterplot in Figure 1 illustrates the striking correlation between the number of public school students in 3rd grade and hydropower energy generated in Paraguay, resembling a beautiful symphony where each data point plays its own harmonious note in the grand composition of statistical exploration. Like a perfectly executed magic trick, this scatterplot reveals the captivating connection that exists between education and energy in the mesmerizing land of Paraguay.
In summary, our findings not only establish a compelling relationship between the number of public school students in 3rd grade and hydropower energy generated in Paraguay but also stimulate further curiosity and probing into this peculiar pairing that transcends traditional scientific boundaries. This correlation is more elusive than a statistical unicorn, but our study has managed to capture its essence in a delightful waltz of data analysis and scientific exploration. As we bask in the glow of these captivating results, we eagerly anticipate the next act in this captivating saga of statistical serendipity.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The robust correlation coefficient and substantial r-squared value derived from our analysis provide compelling evidence of the captivating relationship between the number of public school students in 3rd grade and hydropower energy generated in Paraguay. These results not only align with prior research but also amplify the resonance of the enthralling nexus between education and energy in this South American nation.

Building on the groundwork laid by Smith et al. (2015), our findings corroborate the potential synergy between primary education and renewable energy production, unraveling a tapestry of statistical intrigue that is as rich and vibrant as a Paraguayan sunset. Likewise, the work of Doe and colleagues (2018) receives a resounding encore as our study echoes the resounding importance of early education in shaping attitudes towards sustainable energy practices. The societal implications illuminated by Jones (2020) come to life as our analysis spotlights the interconnectedness between education and hydropower development, much like the vivid imagery in "The Water Will Come" by Jeff Goodell. In a delightful twist, our research lends credence to the notion that power – both electric and otherwise – permeates the fabric of society, akin to the themes woven through "The Power" by Naomi Alderman and the adventures of "The Powerpuff Girls" and "Stranger Things."

This study leaps beyond the traditional confines of academic inquiry, bridging the realms of statistical precision and scientific whimsy, in a dance as intricate and captivating as a well-executed statistical unicorn and capturing its essence in an enchanting waltz of data analysis and scholarly exploration. As we ponder the implications of our findings, we are reminded of the words of Albert Einstein, who once remarked, "The most beautiful thing we can experience is the mysterious. It is the source of all true art and science." In this spirit, we invite fellow researchers to join us in unraveling the enigmatic web that binds education and energy in the captivating landscape of Paraguay.

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 Number of public school students in 3rd grade and Hydopower energy generated in Paraguay. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
Perplexing Parallels: Pupils and Power in Paraguay

[[ABSTRACT]]
In this research paper, we delve into the delightful dance between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Our team extracted data from the National Center for Education Statistics and the Energy Information Administration to embark on this captivating quest. Employing statistical analysis, we uncovered a striking correlation coefficient of 0.9213313 and a significant p-value of less than 0.01 for the period spanning from 1990 to 2021. Our findings not only raise eyebrows but also prompt further investigation into the quirky, yet captivating, relationship between education and energy in the land of stunning waterfalls and power plants.

[[INTRDUCTION]]
The interplay between education and energy production has long been a topic of intrigue and speculation. In the pursuit of unearthing connections that defy conventional wisdom, we set out to explore the relationship between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Much like the intricate web of neurotransmitters firing in the brain, we sought to unravel the enigmatic correlation between these seemingly disparate variables.
As researchers, we are accustomed to embracing the unexpected, much like navigating a labyrinth of data to discern patterns and relationships. Our pursuit of knowledge often leads us down uncharted paths, akin to boldly venturing into the wilderness armed with nothing but a compass and a keen sense of curiosity, but with fewer mosquitoes and more spreadsheets.
Paraguay, known for its breathtaking natural landscape and abundant hydropower potential, provided an enticing backdrop for our investigation. Like a scientist approaching a bubbling beaker with cautious optimism, we approached the intersection of education and hydroelectricity with both excitement and an unwavering commitment to scientific rigor.
Our quest began by gathering data from the National Center for Education Statistics and the Energy Information Administration – a process that involved sifting through countless rows and columns, not unlike searching for a single needle in an unforgiving haystack of digits. Armed with an arsenal of statistical tools and a healthy dose of curiosity, we delved into the numbers with a fervor reminiscent of a sleuth hot on the trail of a mystery, albeit with more software programs and fewer trench coats.
The period from 1990 to 2021 served as our temporal canvas, where we painted a landscape of figures and trends, much like a group of statisticians armed with a palette of data points and an assortment of brushes. Our analysis unveiled a remarkable correlation coefficient of 0.9213313, which beckoned to us like a glimmering scientific unicorn prancing through the statistical forest. Coupled with a p-value of less than 0.01, the significance of our findings was akin to stumbling upon a rare gem in a vast expanse of numerical gravel.
These findings not only piqued our interest but also compelled us to contemplate the profound implications of the intricate connection between education and energy production in Paraguay. The implications are as profound as an over-inflated balloon in a room filled with curious cats, leading us to question, with a mix of awe and amusement, the underlying mechanisms at play.
As we embark on this academic odyssey, we invite readers to join us in this delightful dance of data and discovery, where the lines between education and energy blur and merge like two disparate puzzle pieces finally finding their rightful place. As we unravel the complexities of this charming correlation, we stand poised on the precipice of newfound knowledge, eager to share our illuminating insights and unveil the whimsical wonders that lie hidden within the seemingly mundane world of educational statistics and energy production.
Stay tuned for the illuminating ride that lies ahead – it’s bound to be more thrilling than a roller coaster of regression analyses.

[[RESULTS]]
Our intrepid journey into the correlation between the number of public school students in 3rd grade and hydropower energy generated in Paraguay yielded some intriguing results that are as captivating as a magic show at a statistics conference.
First and foremost, our analysis revealed a robust correlation coefficient of 0.9213313 between the two variables. This correlation coefficient is as strong as the gravitational pull of a massive statistical discovery, drawing our attention like moths to a scientific flame.
Furthermore, the calculated r-squared value of 0.8488514 indicated that approximately 84.89% of the variability in hydropower energy generated in Paraguay could be explained by the number of public school students in 3rd grade. It's as if the tiny hula hoop of 3rd-grade student numbers was able to capture the attention of a large and energetic hydropower generator, drawing it into an elaborate dance of statistical significance.
In addition, the p-value of less than 0.01 that emerged from our analysis decisively rejected the null hypothesis, providing compelling evidence of a significant relationship between these two seemingly unrelated variables. It's as if the p-value waved a giant foam finger, cheerfully proclaiming, "We've got ourselves a statistically significant result, folks!"
The scatterplot in Figure 1 illustrates the striking correlation between the number of public school students in 3rd grade and hydropower energy generated in Paraguay, resembling a beautiful symphony where each data point plays its own harmonious note in the grand composition of statistical exploration. Like a perfectly executed magic trick, this scatterplot reveals the captivating connection that exists between education and energy in the mesmerizing land of Paraguay.
In summary, our findings not only establish a compelling relationship between the number of public school students in 3rd grade and hydropower energy generated in Paraguay but also stimulate further curiosity and probing into this peculiar pairing that transcends traditional scientific boundaries. This correlation is more elusive than a statistical unicorn, but our study has managed to capture its essence in a delightful waltz of data analysis and scientific exploration. As we bask in the glow of these captivating results, we eagerly anticipate the next act in this captivating saga of statistical serendipity.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our research has illuminated a remarkable correlation between the number of public school students in 3rd grade and hydropower energy generated in Paraguay. The findings are more intriguing than a surprise birthday party for a data set. The robust correlation coefficient of 0.9213313 and the substantial r-squared value of 0.8488514 dance together like two partners in a well-choreographed statistical tango. The p-value, a staunch advocate for statistical significance, emphatically proclaims the existence of a profound relationship between these seemingly disparate variables, akin to an enthusiastic tour guide leading us through the land of statistical wonders.

The scatterplot, resembling a dazzling fireworks display of data points, visually captures the enthralling connection between education and energy in Paraguay. As we wrap up this enthralling expedition into the intersection of pedagogy and power production, we cannot help but be reminded of the captivating marvels that await those willing to tread the uncharted territories of statistical exploration.

In light of these compelling findings, we assert with utmost confidence that no further research is required in this area. The correlation between the number of public school students in 3rd grade and hydropower energy generated in Paraguay is as clear as a crystal ball in the hand of a smiling statistician, and has been unmasked in all its delightful glory.

Now, onto the next captivating statistical adventure!

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 Perplexing Parallels: Pupils and Power in Paraguay. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Comparative Ophthalmological and Political Studies

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 Perplexing Parallels: Pupils and Power in Paraguay. Respond only with the name of a fictional organization.

ChatGPT:

The International Institute for Intercultural Inquiry

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 Perplexing Parallels: Pupils and Power in Paraguay with an abstract of In this research paper, we delve into the delightful dance between the number of public school students in 3rd grade and the hydropower energy generated in Paraguay. Our team extracted data from the National Center for Education Statistics and the Energy Information Administration to embark on this captivating quest. Employing statistical analysis, we uncovered a striking correlation coefficient of 0.9213313 and a significant p-value of less than 0.01 for the period spanning from 1990 to 2021. Our findings not only raise eyebrows but also prompt further investigation into the quirky, yet captivating, relationship between education and energy in the land of stunning waterfalls and power plants.

ChatGPT:

Paraguay, public school students, 3rd grade, hydropower energy, correlation coefficient, statistical analysis, National Center for Education Statistics, Energy Information Administration, education and energy relationship, waterfalls, power plants

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

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Data details

Number of public school students in 3rd grade
Detailed data title: 3rd grade enrollment in public elementary and secondary schools
Source: National Center for Education Statistics
See what else correlates with Number of public school students in 3rd grade

Hydopower energy generated in Paraguay
Detailed data title: Total hydopower energy generated in Paraguay in billion kWh
Source: Energy Information Administration
See what else correlates with Hydopower energy generated in Paraguay

Correlation r = 0.9213313 (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 = 0.8488514 (Coefficient of determination)
This means 84.9% of the change in the one variable (i.e., Hydopower energy generated in Paraguay) is predictable based on the change in the other (i.e., Number of public school students in 3rd grade) over the 32 years from 1990 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 7.7E-14.^Show 0.0000000000000765633946103722
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 0.92 in 7.7E-12% of random cases. Said differently, if you correlated 13,061,071,874,999 random variables^Note You don't actually need 13 trillion 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.

[ 0.84, 0.96 ] 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
Number of public school students in 3rd grade (Students)	3296720	3333960	3361360	3436980	3439040	3444740	3523760	3596890	3695640	3690650	3675800	3653310	3622790	3611040	3580460	3586110	3627490	3658860	3707770	3707040	3685830	3703310	3719140	3737690	3806160	3868950	3874020	3787970	3708630	3686360	3551530	3541690
Hydopower energy generated in Paraguay (Billion kWh)	27.185	29.351	27.141	31.097	36.032	41.671	44.828	50.309	50.328	51.4	52.957	44.864	47.73	51.253	51.412	50.654	53.246	53.188	54.909	54.409	53.524	57.049	59.63	59.774	54.723	55.186	63.132	59.087	58.6189	48.9347	46.371	39.8852

Why this works

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

Try it yourself

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

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([3296720,3333960,3361360,3436980,3439040,3444740,3523760,3596890,3695640,3690650,3675800,3653310,3622790,3611040,3580460,3586110,3627490,3658860,3707770,3707040,3685830,3703310,3719140,3737690,3806160,3868950,3874020,3787970,3708630,3686360,3551530,3541690,])
array_2 = np.array([27.185,29.351,27.141,31.097,36.032,41.671,44.828,50.309,50.328,51.4,52.957,44.864,47.73,51.253,51.412,50.654,53.246,53.188,54.909,54.409,53.524,57.049,59.63,59.774,54.723,55.186,63.132,59.087,58.6189,48.9347,46.371,39.8852,])
array_1_name = "Number of public school students in 3rd grade"
array_2_name = "Hydopower energy generated in Paraguay"

# 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 Number of public school students in 3rd grade
Line chart for only Hydopower energy generated in Paraguay
AI-generated correlation image
The spurious research paper: Perplexing Parallels: Pupils and Power in Paraguay

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Correlation ID: 3752 · Black Variable ID: 1300 · Red Variable ID: 23893


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