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Spurious correlation #3,496 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Ithaca and the second variable is Remaining Forest Cover in the Brazilian Amazon.  The chart goes from 1990 to 2022, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

As the air in Ithaca became cleaner, it created a stronger urge for locals to take up competitive houseplant growing. This led to a surge in demand for exotic plants, prompting an unforeseen deforestation epidemic in the Brazilian Amazon as Ithacans sought the perfect ferns and palms. Remember, cleaner air in one place could leaf to unforested territories elsewhere!

Model: dalle-3
Prompt: Prompt: Create a reddit-worthy image of tourists amazed by the lush greenery of the Brazilian Amazon, juxtaposed with the devastation of trees being felled for development. The image should evoke a sense of wonder and concern, as travelers take in the beauty of the rainforest while also witnessing the impact of deforestation. Capture the contrast between the vibrant, untouched forest and the stark evidence of human intervention. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.
This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: Air pollution in Ithaca and Remaining Forest Cover in the Brazilian Amazon. 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: Cubism a funny image you would see on reddit An image that looks like it is a scene from A Disney Movie Cubism Cutsy graphics
ChatGPT: a funny image you would see on reddit

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Air pollution in Ithaca and Remaining Forest Cover in the Brazilian Amazon, in the following situation: As air pollution decreased in Ithaca, people were able to breathe easier and decided to take more exotic vacations to the Amazon. The influx of tourists led to increased deforestation as they couldn't "leaf" the rainforest alone.. Keep the description simple.
ChatGPT: As the air cleared in Ithaca, people joyfully took deep breaths in the fresh, revitalized atmosphere. Excited travelers from Ithaca set off on exotic vacations to the Brazilian Amazon. Amid the lush greenery, tourists marveled at the vibrant forest cover before sadly witnessing the increase in deforestation, with trees being felled to make way for development.

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: [ a funny image you would see on reddit ] and depicting this scene: As the air cleared in Ithaca, people joyfully took deep breaths in the fresh, revitalized atmosphere. Excited travelers from Ithaca set off on exotic vacations to the Brazilian Amazon. Amid the lush greenery, tourists marveled at the vibrant forest cover before sadly witnessing the increase in deforestation, with trees being felled to make way for development. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Prompt: Create a reddit-worthy image of tourists amazed by the lush greenery of the Brazilian Amazon, juxtaposed with the devastation of trees being felled for development. The image should evoke a sense of wonder and concern, as travelers take in the beauty of the rainforest while also witnessing the impact of deforestation. Capture the contrast between the vibrant, untouched forest and the stark evidence of human intervention.

*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.

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 a decrease in Air pollution in Ithaca caused Remaining Forest Cover in the Brazilian Amazon to decrease. Add a funny one-liner at the end.

AI academic paper

(Because p < 0.01)
Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon

The Journal of Environmental Enigmas

Jan 2024

Reminder: This paper is AI-generated. Not real!
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 witty academic researcher. Your writing sounds like it belongs in a statistics journal.You write titles and abstracts of goofy academic research papers.
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, and add unexpected twists in your writing.

Please draft the title and abstract of an academic research paper presenting the findings of the connection between Air pollution in Ithaca and Remaining Forest Cover in the Brazilian Amazon. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

Make the title punny if you can come up with clever pun. If not, make it sound serious.

Your research team used data from Environmental Protection Agency and Mongabay to assess this nagging question. You found a correlation coefficient of 0.8700489 and p < 0.01 for 1990 to 2022.

Please respond in this format (replace "Lorem ipsum dolor sit" with your title and abstract)

[[TITLE]]
Lorem ipsum dolor sit

[[ABSTRACT]]
Lorem ipsum dolor sit



ChatGPT:
[[TITLE]]
"Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon"

[[ABSTRACT]]
The environmental relationship between air pollution in distant Ithaca and the remaining forest cover in the Brazilian Amazon has long captivated researchers. In this study, we delved into this intriguing nexus using data from the Environmental Protection Agency and Mongabay. Our findings revealed a robust correlation coefficient of 0.8700489 and a p-value less than 0.01 for the period spanning 1990 to 2022.

Our analyses pointed to a significant linkage between air quality in Ithaca and the remaining forest cover in the Brazilian Amazon, much like how trees seem to root for cleaner air. The association we uncovered was as clear as the sky on a sunny day, sprinkled with a few particulates, of course.

This study not only sheds light on this quirky connection but also manages to put the "fun" in "fundamental research." After all, forest-air relationships shouldn't be taken for granted - they're nothing to leaf aside.


Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.You draft the introduction 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 introduction section of an academic research paper presenting the findings of the connection between Air pollution in Ithaca and Remaining Forest Cover in the Brazilian Amazon. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

Here is the title and abstract of the paper:
[[TITLE]]
"Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon"

[[ABSTRACT]]
The environmental relationship between air pollution in distant Ithaca and the remaining forest cover in the Brazilian Amazon has long captivated researchers. In this study, we delved into this intriguing nexus using data from the Environmental Protection Agency and Mongabay. Our findings revealed a robust correlation coefficient of 0.8700489 and a p-value less than 0.01 for the period spanning 1990 to 2022.

Our analyses pointed to a significant linkage between air quality in Ithaca and the remaining forest cover in the Brazilian Amazon, much like how trees seem to root for cleaner air. The association we uncovered was as clear as the sky on a sunny day, sprinkled with a few particulates, of course.

This study not only sheds light on this quirky connection but also manages to put the "fun" in "fundamental research." After all, forest-air relationships shouldn't be taken for granted - they're nothing to leaf aside.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
[[INTRODUCTION]]

The interplay between distant environmental phenomena has always intrigued researchers, much like how a good mystery novel keeps readers guessing until the very end. In our case, we set out to unravel the connection between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. This relationship, as elusive as a chameleon in a rainforest, raises important questions about global environmental dynamics and the interconnectedness of ecosystems.

It's not every day that you come across a research topic that ties together a picturesque college town like Ithaca with the majestic rainforests of the Amazon. It's almost like discovering that the roots of a problem are far-reaching, much like the roots of a tree searching for nutrients. Ah, the wonders of cross-continental environmental correlations – they sure make for interesting dinner table conversations.

Previous studies have often focused on local or regional air pollution impacts, but this study aims to elevate our gaze towards a more global perspective. Our findings promise to shed light on the intricate dance between seemingly disparate ecosystems, much like how two dance partners find unexpected harmony on the floor. Can't you just imagine the atmospheric tango between the forests of the Amazon and the air quality in Ithaca?

With this research, we hope to branch out from the typical scope of environmental studies and delve into unexplored connections. Who would have thought that the path to understanding the world's forests could wind its way through a small town famous for its gorges and waterfalls? It's almost as surprising as finding a pine tree in the middle of a bustling city – I guess you could call it an urban "conifer"-ence.


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

Please make up a literature review section of an academic research paper presenting the findings of the connection between Air pollution in Ithaca and Remaining Forest Cover in the Brazilian Amazon. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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

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

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

Here is the title and abstract of the paper:
[[TITLE]]
"Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon"

[[ABSTRACT]]
The environmental relationship between air pollution in distant Ithaca and the remaining forest cover in the Brazilian Amazon has long captivated researchers. In this study, we delved into this intriguing nexus using data from the Environmental Protection Agency and Mongabay. Our findings revealed a robust correlation coefficient of 0.8700489 and a p-value less than 0.01 for the period spanning 1990 to 2022.

Our analyses pointed to a significant linkage between air quality in Ithaca and the remaining forest cover in the Brazilian Amazon, much like how trees seem to root for cleaner air. The association we uncovered was as clear as the sky on a sunny day, sprinkled with a few particulates, of course.

This study not only sheds light on this quirky connection but also manages to put the "fun" in "fundamental research." After all, forest-air relationships shouldn't be taken for granted - they're nothing to leaf aside.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The interplay between distant environmental phenomena has always intrigued researchers, much like how a good mystery novel keeps readers guessing until the very end. In our case, we set out to unravel the connection between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. This relationship, as elusive as a chameleon in a rainforest, raises important questions about global environmental dynamics and the interconnectedness of ecosystems.
It's not every day that you come across a research topic that ties together a picturesque college town like Ithaca with the majestic rainforests of the Amazon. It's almost like discovering that the roots of a problem are far-reaching, much like the roots of a tree searching for nutrients. Ah, the wonders of cross-continental environmental correlations – they sure make for interesting dinner table conversations.
Previous studies have often focused on local or regional air pollution impacts, but this study aims to elevate our gaze towards a more global perspective. Our findings promise to shed light on the intricate dance between seemingly disparate ecosystems, much like how two dance partners find unexpected harmony on the floor. Can't you just imagine the atmospheric tango between the forests of the Amazon and the air quality in Ithaca?
With this research, we hope to branch out from the typical scope of environmental studies and delve into unexplored connections. Who would have thought that the path to understanding the world's forests could wind its way through a small town famous for its gorges and waterfalls? It's almost as surprising as finding a pine tree in the middle of a bustling city – I guess you could call it an urban "conifer"-ence.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

Previous studies have elucidated the complex relationship between air pollution and forest cover, but few have ventured into the idiosyncratic realm of investigating the potential link between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon. Smith et al. (2017) thoroughly examined the impact of air pollution on urban and rural landscapes, while Doe and Jones (2019) delved into the interplay between deforestation and regional air quality. However, our study seeks to untangle the enigmatic bond between the misty hills of Ithaca and the verdant expanses of the Amazon rainforest.

"In 'Air Pollution and Its Global Implications,' Smith et al. (2017) noted the far-reaching effects of air pollution on various ecological systems. Similarly, Doe and Jones (2019) underscored the intricate relationship between deforestation and air quality, showcasing the domino effect of environmental degradation."

Now, shifting away from the academic sphere, it's essential to highlight the wealth of literature that indirectly addresses the whimsical connection we are exploring. The book "The Hidden Life of Trees" by Peter Wohlleben offers a fascinating glimpse into the intricate communication network within forests, which could potentially be affected by air pollution from distant lands. Moreover, "The Great Derangement" by Amitav Ghosh tantalizingly delves into the interconnectedness of global environmental phenomena, making us ponder if the fog in Ithaca and the forests of the Amazon are engaged in an elaborate pas de deux.

And speaking of interconnectedness, in a rather surprising turn of events, "The Hitchhiker's Guide to the Galaxy" by Douglas Adams unexpectedly sheds light on the intergalactic parallels to our research. While not directly related to our study, the book's exploration of interconnectedness, in a whimsical and farcical manner, resonates with the underlying theme of our research. It's almost as if the infinite improbability drive landed us in the midst of this peculiar nexus between air pollution and Amazonian forests.

Now, turning to sources of a more informal nature, social media platforms have proven to be surprisingly fertile ground for insightful musings on environmental correlations. A compelling tweet by @EnviroEnigma exclaimed, "Is the smog in Ithaca secretly whispering to the trees in the Amazon? #enviroconnections #mysteryoftheages." This seemingly lighthearted remark, while posted in jest, resonates with the essence of our research – unraveling the mysterious and often inexplicable bond between two seemingly distinct ecological entities.

With a substantial foundation laid by previous research and a sprinkle of unexpected literary parallels, we embark on our investigation into the quirky nexus of air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. After all, who said research couldn't take a leaf out of the book of humor and whimsy?


Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.You draft the methodology section of an academic research paper.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the methodology section of an academic research paper presenting the findings of the connection between Air pollution in Ithaca and Remaining Forest Cover in the Brazilian Amazon. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Mongabay . You used data from 1990 to 2022

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]]
"Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon"

[[ABSTRACT]]
The environmental relationship between air pollution in distant Ithaca and the remaining forest cover in the Brazilian Amazon has long captivated researchers. In this study, we delved into this intriguing nexus using data from the Environmental Protection Agency and Mongabay. Our findings revealed a robust correlation coefficient of 0.8700489 and a p-value less than 0.01 for the period spanning 1990 to 2022.

Our analyses pointed to a significant linkage between air quality in Ithaca and the remaining forest cover in the Brazilian Amazon, much like how trees seem to root for cleaner air. The association we uncovered was as clear as the sky on a sunny day, sprinkled with a few particulates, of course.

This study not only sheds light on this quirky connection but also manages to put the "fun" in "fundamental research." After all, forest-air relationships shouldn't be taken for granted - they're nothing to leaf aside.

[[INTRODUCTION]]
The interplay between distant environmental phenomena has always intrigued researchers, much like how a good mystery novel keeps readers guessing until the very end. In our case, we set out to unravel the connection between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. This relationship, as elusive as a chameleon in a rainforest, raises important questions about global environmental dynamics and the interconnectedness of ecosystems.
It's not every day that you come across a research topic that ties together a picturesque college town like Ithaca with the majestic rainforests of the Amazon. It's almost like discovering that the roots of a problem are far-reaching, much like the roots of a tree searching for nutrients. Ah, the wonders of cross-continental environmental correlations – they sure make for interesting dinner table conversations.
Previous studies have often focused on local or regional air pollution impacts, but this study aims to elevate our gaze towards a more global perspective. Our findings promise to shed light on the intricate dance between seemingly disparate ecosystems, much like how two dance partners find unexpected harmony on the floor. Can't you just imagine the atmospheric tango between the forests of the Amazon and the air quality in Ithaca?
With this research, we hope to branch out from the typical scope of environmental studies and delve into unexplored connections. Who would have thought that the path to understanding the world's forests could wind its way through a small town famous for its gorges and waterfalls? It's almost as surprising as finding a pine tree in the middle of a bustling city – I guess you could call it an urban "conifer"-ence.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

To unearth the tango between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon, we embarked on a data safari through the vast savannah of information. Our expedition was guided by the Environmental Protection Agency's Air Quality System and Mongabay's comprehensive forest cover datasets. We rustled up data from 1990 to 2022, casting a wide net to capture the environmental rhythms of these distant yet interconnected regions.

In this cross-continental quest, our research team meticulously curated air quality data from Ithaca, NY, like a sommelier selecting the finest wines. Our data expedition traversed through the digital wilderness, navigating through the EPA's troves of air quality index readings, atmospheric composition metrics, and other air pollution descriptors.
Why don't air molecules date? They've got too many issues!

Similarly, our foraging for forest cover data in the Brazilian Amazon led us to Mongabay's rich tapestry of satellite imagery and ground truth data. With the precision of an artisanal chef, we carefully gathered information on forest extent, deforestation rates, and ecological dynamics in the Amazon basin. We were so immersed in this data collection process that we nearly turned into virtual lumberjacks.

Armed with these two comprehensive sets of data, we employed a statistical approach as meticulous as a weaver bird crafting its intricate nest. First, we unleashed the power of correlation analysis to tease out the relationship between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. Like a detective connecting the dots in a criminal case, we meticulously examined the co-movement of these two environmental variables. The correlation coefficient emerged as the Sherlock Holmes of our investigation, revealing the strength and direction of the association between air quality in Ithaca and the Amazon's verdant canopy.
Why did the statistician go to art school? To learn how to draw a conclusion!

Next, we subjected our data to a rigorous regression analysis that was as robust as a medieval fortress. This allowed us to disentangle the nuances of the relationship and discern how changes in air pollution levels in Ithaca may influence the remaining forest cover in the Brazilian Amazon. The regression model danced through the data like a samba, unraveling the potential impacts of air quality on the Amazonian rainforest. As we untangled the statistical threads, it became clear that the relationship was not just a casual fling, but rather a long-term commitment between the two distant ecosystems.
Why was the statistician always calm? They had a mean demeanor!

Lastly, to account for any potential confounding variables that could muddy the waters of our analysis, we conducted a sensitivity analysis akin to a taste test for statistical robustness. This allowed us to gauge the resilience of our findings to external influences, ensuring that our results were as sturdy as an ancient redwood tree.
What do statisticians do when they're constipated? They work it out with a pooper-scooper!

In summary, our methodology combined the rigor of statistical analyses with the finesse of data collection to unravel the fascinating interplay between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. Our approach was as methodical as a symphony conductor, orchestrating a harmonious blend of data-driven insights and environmental intrigue.



Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.You draft the results section of an academic research paper. You speak in the past tense (you found...).
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the results section of an academic research paper presenting the findings of the connection between Air pollution in Ithaca and Remaining Forest Cover in the Brazilian Amazon. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Mongabay .

For the time period 1990 to 2022, you found a correlation 0.8700489, r-squared of 0.7569851, 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]]
"Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon"

[[ABSTRACT]]
The environmental relationship between air pollution in distant Ithaca and the remaining forest cover in the Brazilian Amazon has long captivated researchers. In this study, we delved into this intriguing nexus using data from the Environmental Protection Agency and Mongabay. Our findings revealed a robust correlation coefficient of 0.8700489 and a p-value less than 0.01 for the period spanning 1990 to 2022.

Our analyses pointed to a significant linkage between air quality in Ithaca and the remaining forest cover in the Brazilian Amazon, much like how trees seem to root for cleaner air. The association we uncovered was as clear as the sky on a sunny day, sprinkled with a few particulates, of course.

This study not only sheds light on this quirky connection but also manages to put the "fun" in "fundamental research." After all, forest-air relationships shouldn't be taken for granted - they're nothing to leaf aside.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The interplay between distant environmental phenomena has always intrigued researchers, much like how a good mystery novel keeps readers guessing until the very end. In our case, we set out to unravel the connection between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. This relationship, as elusive as a chameleon in a rainforest, raises important questions about global environmental dynamics and the interconnectedness of ecosystems.
It's not every day that you come across a research topic that ties together a picturesque college town like Ithaca with the majestic rainforests of the Amazon. It's almost like discovering that the roots of a problem are far-reaching, much like the roots of a tree searching for nutrients. Ah, the wonders of cross-continental environmental correlations – they sure make for interesting dinner table conversations.
Previous studies have often focused on local or regional air pollution impacts, but this study aims to elevate our gaze towards a more global perspective. Our findings promise to shed light on the intricate dance between seemingly disparate ecosystems, much like how two dance partners find unexpected harmony on the floor. Can't you just imagine the atmospheric tango between the forests of the Amazon and the air quality in Ithaca?
With this research, we hope to branch out from the typical scope of environmental studies and delve into unexplored connections. Who would have thought that the path to understanding the world's forests could wind its way through a small town famous for its gorges and waterfalls? It's almost as surprising as finding a pine tree in the middle of a bustling city – I guess you could call it an urban "conifer"-ence.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

The results of our analysis revealed a strong and statistically significant correlation between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. The correlation coefficient of 0.8700489 indicates a robust relationship between these two seemingly unrelated environmental factors, akin to the unexpected bond between peanut butter and pickles - it may sound strange, but it's truly a match made in statistical heaven.

Furthermore, the r-squared value of 0.7569851 demonstrates that a substantial proportion of the variation in remaining forest cover in the Brazilian Amazon can be explained by the levels of air pollution in Ithaca. It's as if the forest cover is responding to the air pollution levels like a conscientious student heeding the instructions of a strict teacher.

Importantly, the p-value of less than 0.01 provides strong evidence against the null hypothesis of no relationship between these variables, much like a detective presenting compelling evidence that leaves no room for doubt - except in this case, the culprits are air pollutants and their impact on the Amazon rainforest.

Fig. 1 illustrates the strong correlation between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon. The scatterplot visually encapsulates the magnitude of the relationship, painting a clear picture of the intricate interaction between seemingly distant environmental phenomena, much like a symphony conductor orchestrating a harmonious performance between musicians from different corners of the world. It truly is a sight to behold, like finding the missing piece to an environmental puzzle.

In summary, our findings not only confirm the existence of a significant association between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon but also emphasize the need to consider the far-reaching impacts of local environmental factors. This study not only contributes to the expanding body of knowledge on environmental interconnections but also serves as a reminder of the unexpected and often entangled nature of ecological dynamics. After all, who would have thought that the air in a small town in New York could be leaving its mark on the rainforests of Brazil? It's a reminder that in the intricate web of environmental relationships, every breath we take matters.


Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.You draft the discussion section of an academic research paper.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the discussion section of an academic research paper presenting the findings of the connection between Air pollution in Ithaca and Remaining Forest Cover in the Brazilian Amazon. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

Limit your response to 500 tokens.

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

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

[[TITLE]]
"Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon"

[[ABSTRACT]]
The environmental relationship between air pollution in distant Ithaca and the remaining forest cover in the Brazilian Amazon has long captivated researchers. In this study, we delved into this intriguing nexus using data from the Environmental Protection Agency and Mongabay. Our findings revealed a robust correlation coefficient of 0.8700489 and a p-value less than 0.01 for the period spanning 1990 to 2022.

Our analyses pointed to a significant linkage between air quality in Ithaca and the remaining forest cover in the Brazilian Amazon, much like how trees seem to root for cleaner air. The association we uncovered was as clear as the sky on a sunny day, sprinkled with a few particulates, of course.

This study not only sheds light on this quirky connection but also manages to put the "fun" in "fundamental research." After all, forest-air relationships shouldn't be taken for granted - they're nothing to leaf aside.

[[LITERATURE REVIEW]]
Previous studies have elucidated the complex relationship between air pollution and forest cover, but few have ventured into the idiosyncratic realm of investigating the potential link between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon. Smith et al. (2017) thoroughly examined the impact of air pollution on urban and rural landscapes, while Doe and Jones (2019) delved into the interplay between deforestation and regional air quality. However, our study seeks to untangle the enigmatic bond between the misty hills of Ithaca and the verdant expanses of the Amazon rainforest.
"In 'Air Pollution and Its Global Implications,' Smith et al. (2017) noted the far-reaching effects of air pollution on various ecological systems. Similarly, Doe and Jones (2019) underscored the intricate relationship between deforestation and air quality, showcasing the domino effect of environmental degradation."
Now, shifting away from the academic sphere, it's essential to highlight the wealth of literature that indirectly addresses the whimsical connection we are exploring. The book "The Hidden Life of Trees" by Peter Wohlleben offers a fascinating glimpse into the intricate communication network within forests, which could potentially be affected by air pollution from distant lands. Moreover, "The Great Derangement" by Amitav Ghosh tantalizingly delves into the interconnectedness of global environmental phenomena, making us ponder if the fog in Ithaca and the forests of the Amazon are engaged in an elaborate pas de deux.
And speaking of interconnectedness, in a rather surprising turn of events, "The Hitchhiker's Guide to the Galaxy" by Douglas Adams unexpectedly sheds light on the intergalactic parallels to our research. While not directly related to our study, the book's exploration of interconnectedness, in a whimsical and farcical manner, resonates with the underlying theme of our research. It's almost as if the infinite improbability drive landed us in the midst of this peculiar nexus between air pollution and Amazonian forests.
Now, turning to sources of a more informal nature, social media platforms have proven to be surprisingly fertile ground for insightful musings on environmental correlations. A compelling tweet by @EnviroEnigma exclaimed, "Is the smog in Ithaca secretly whispering to the trees in the Amazon? #enviroconnections #mysteryoftheages." This seemingly lighthearted remark, while posted in jest, resonates with the essence of our research – unraveling the mysterious and often inexplicable bond between two seemingly distinct ecological entities.
With a substantial foundation laid by previous research and a sprinkle of unexpected literary parallels, we embark on our investigation into the quirky nexus of air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. After all, who said research couldn't take a leaf out of the book of humor and whimsy?

[[RESULTS]]
The results of our analysis revealed a strong and statistically significant correlation between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. The correlation coefficient of 0.8700489 indicates a robust relationship between these two seemingly unrelated environmental factors, akin to the unexpected bond between peanut butter and pickles - it may sound strange, but it's truly a match made in statistical heaven.
Furthermore, the r-squared value of 0.7569851 demonstrates that a substantial proportion of the variation in remaining forest cover in the Brazilian Amazon can be explained by the levels of air pollution in Ithaca. It's as if the forest cover is responding to the air pollution levels like a conscientious student heeding the instructions of a strict teacher.
Importantly, the p-value of less than 0.01 provides strong evidence against the null hypothesis of no relationship between these variables, much like a detective presenting compelling evidence that leaves no room for doubt - except in this case, the culprits are air pollutants and their impact on the Amazon rainforest.
Fig. 1 illustrates the strong correlation between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon. The scatterplot visually encapsulates the magnitude of the relationship, painting a clear picture of the intricate interaction between seemingly distant environmental phenomena, much like a symphony conductor orchestrating a harmonious performance between musicians from different corners of the world. It truly is a sight to behold, like finding the missing piece to an environmental puzzle.
In summary, our findings not only confirm the existence of a significant association between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon but also emphasize the need to consider the far-reaching impacts of local environmental factors. This study not only contributes to the expanding body of knowledge on environmental interconnections but also serves as a reminder of the unexpected and often entangled nature of ecological dynamics. After all, who would have thought that the air in a small town in New York could be leaving its mark on the rainforests of Brazil? It's a reminder that in the intricate web of environmental relationships, every breath we take matters.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

The results of our study unequivocally supported the prior research that indirectly hinted at the whimsical connection between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon. Building on the literature review's discussion of the intricacies of the misty hills of Ithaca and the verdant expanses of the Amazon rainforest, our findings confirm a robust correlation between these seemingly disparate environmental phenomena. It's almost as if the air pollution in Ithaca and the Amazonian forest cover have a long-distance relationship that defies traditional geographic and ecological boundaries - talk about an eco-mance!

The substantial correlation coefficient of 0.8700489 aligns seamlessly with the previous studies that delved into the impact of air pollution on ecological systems. This statistically significant relationship underscores the poignant connection between air quality in Ithaca and the remaining forest cover in the Brazilian Amazon, shedding light on an unexpected bond that's as surprising as finding a tree in a forest. This correlation is rooted in data that unequivocally showcases the far-reaching impacts of local environmental factors on a global scale, much like a tree's airborne whispers being carried off by the wind to the distant lands of the Amazon - it's a tree-mendous tale of environmental interconnectedness.

Moreover, the r-squared value of 0.7569851, which demonstrates a substantial proportion of the variation in remaining forest cover in the Brazilian Amazon can be explained by the levels of air pollution in Ithaca, accentuates the profound impact of air quality on the Amazonian ecosystem. Our findings fortify the previous research that emphasized the intricate and domino effect-like relationship between deforestation and air quality. It's as if the forest cover is not only responding to but also swaying to the tune of air pollution levels in Ithaca, akin to a dance where the steps are dictated by an invisible partner – the Earth's atmospheric conditions.

The visually captivating scatterplot in Fig. 1 paints a compelling picture of this intricate interaction, akin to witnessing a captivating symphony where the melodic notes of air pollution in Ithaca and the choreographed movements of forest cover in the Brazilian Amazon create an environmental masterpiece. This evidence lends weight to the argument that the air in a small town like Ithaca could significantly influence the well-being of the distant Amazon rainforest. It's as if the environmental puzzle has finally revealed its missing piece, much like finding Waldo in a forest of statistical data.

In conclusion, our study adds a whimsical yet substantial contribution to the expanding body of knowledge on environmental interconnections. The unexpected nexus between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon serves as a poignant reminder of the intricate web of environmental relationships. As researchers, it's crucial for us to continue unraveling these mysterious and often inexplicable connections, because in the intricate dance of ecology, every breath we take matters – even the ones hidden in the fog of Ithaca or among the towering trees of the Amazon.


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

Please make up a short conclusion of an academic research paper presenting the findings of the connection between Air pollution in Ithaca and Remaining Forest Cover in the Brazilian Amazon. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
"Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon"

[[ABSTRACT]]
The environmental relationship between air pollution in distant Ithaca and the remaining forest cover in the Brazilian Amazon has long captivated researchers. In this study, we delved into this intriguing nexus using data from the Environmental Protection Agency and Mongabay. Our findings revealed a robust correlation coefficient of 0.8700489 and a p-value less than 0.01 for the period spanning 1990 to 2022.

Our analyses pointed to a significant linkage between air quality in Ithaca and the remaining forest cover in the Brazilian Amazon, much like how trees seem to root for cleaner air. The association we uncovered was as clear as the sky on a sunny day, sprinkled with a few particulates, of course.

This study not only sheds light on this quirky connection but also manages to put the "fun" in "fundamental research." After all, forest-air relationships shouldn't be taken for granted - they're nothing to leaf aside.

[[INTRDUCTION]]
The interplay between distant environmental phenomena has always intrigued researchers, much like how a good mystery novel keeps readers guessing until the very end. In our case, we set out to unravel the connection between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. This relationship, as elusive as a chameleon in a rainforest, raises important questions about global environmental dynamics and the interconnectedness of ecosystems.
It's not every day that you come across a research topic that ties together a picturesque college town like Ithaca with the majestic rainforests of the Amazon. It's almost like discovering that the roots of a problem are far-reaching, much like the roots of a tree searching for nutrients. Ah, the wonders of cross-continental environmental correlations – they sure make for interesting dinner table conversations.
Previous studies have often focused on local or regional air pollution impacts, but this study aims to elevate our gaze towards a more global perspective. Our findings promise to shed light on the intricate dance between seemingly disparate ecosystems, much like how two dance partners find unexpected harmony on the floor. Can't you just imagine the atmospheric tango between the forests of the Amazon and the air quality in Ithaca?
With this research, we hope to branch out from the typical scope of environmental studies and delve into unexplored connections. Who would have thought that the path to understanding the world's forests could wind its way through a small town famous for its gorges and waterfalls? It's almost as surprising as finding a pine tree in the middle of a bustling city – I guess you could call it an urban "conifer"-ence.

[[RESULTS]]
The results of our analysis revealed a strong and statistically significant correlation between air pollution in Ithaca and the remaining forest cover in the Brazilian Amazon. The correlation coefficient of 0.8700489 indicates a robust relationship between these two seemingly unrelated environmental factors, akin to the unexpected bond between peanut butter and pickles - it may sound strange, but it's truly a match made in statistical heaven.
Furthermore, the r-squared value of 0.7569851 demonstrates that a substantial proportion of the variation in remaining forest cover in the Brazilian Amazon can be explained by the levels of air pollution in Ithaca. It's as if the forest cover is responding to the air pollution levels like a conscientious student heeding the instructions of a strict teacher.
Importantly, the p-value of less than 0.01 provides strong evidence against the null hypothesis of no relationship between these variables, much like a detective presenting compelling evidence that leaves no room for doubt - except in this case, the culprits are air pollutants and their impact on the Amazon rainforest.
Fig. 1 illustrates the strong correlation between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon. The scatterplot visually encapsulates the magnitude of the relationship, painting a clear picture of the intricate interaction between seemingly distant environmental phenomena, much like a symphony conductor orchestrating a harmonious performance between musicians from different corners of the world. It truly is a sight to behold, like finding the missing piece to an environmental puzzle.
In summary, our findings not only confirm the existence of a significant association between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon but also emphasize the need to consider the far-reaching impacts of local environmental factors. This study not only contributes to the expanding body of knowledge on environmental interconnections but also serves as a reminder of the unexpected and often entangled nature of ecological dynamics. After all, who would have thought that the air in a small town in New York could be leaving its mark on the rainforests of Brazil? It's a reminder that in the intricate web of environmental relationships, every breath we take matters.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In conclusion, our study has peeled back the layers of environmental interconnectedness, revealing a robust correlation between air pollution in Ithaca and remaining forest cover in the Brazilian Amazon. It's like finding a needle in a haystack, except in this case, the needle is a correlation coefficient and the haystack is the vast expanse of environmental data.

Our research has not only deepened our understanding of global environmental dynamics but has also sparked ecological revelations that are as refreshing as a walk in the woods. Our findings underscore the importance of considering the far-reaching impacts of seemingly localized environmental factors, much like how a small ripple in a pond can create waves on the other side.

Our results provide compelling evidence of a significant association between air pollution and forest cover, much like how a good punchline ties together a long-winded joke. It's clear that the air in Ithaca is not just blowing in the wind; it's leaving its mark on the distant forests of the Amazon, reminding us that environmental influences know no boundaries.

Therefore, we firmly assert that no more research is needed in this area – we've already cleared the air on this topic, and any further investigation would be like beating a dead horse – unnecessary, and it might just make the air quality worse!

So, let's take a deep breath, inhale the sweet scent of scientific discovery, and exhale with the satisfaction of having cracked this environmental conundrum wide open. After all, in the forest of academic inquiry, we've found the statistical trees that really make the correlation forest-"grove."

And remember, when it comes to environmental research, the stakes are high, the bar is set, and the air is cleaner when we all do our part.


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 Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental Enigmas


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 Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon. Respond only with the name of a fictional organization.

ChatGPT:

The Institute for Bucolic Ecology and Atmospheric Studies


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 Forest Fumes & Fabled Fog: Unraveling the Nexus of Air Pollution in Ithaca and Remaining Rainforest in the Brazilian Amazon with an abstract of The environmental relationship between air pollution in distant Ithaca and the remaining forest cover in the Brazilian Amazon has long captivated researchers. In this study, we delved into this intriguing nexus using data from the Environmental Protection Agency and Mongabay. Our findings revealed a robust correlation coefficient of 0.8700489 and a p-value less than 0.01 for the period spanning 1990 to 2022.
Our analyses pointed to a significant linkage between air quality in Ithaca and the remaining forest cover in the Brazilian Amazon, much like how trees seem to root for cleaner air. The association we uncovered was as clear as the sky on a sunny day, sprinkled with a few particulates, of course.
This study not only sheds light on this quirky connection but also manages to put the "fun" in "fundamental research." After all, forest-air relationships shouldn't be taken for granted - they're nothing to leaf aside.

ChatGPT:

air pollution, forest cover, environmental relationship, nexus, Ithaca, Brazilian Amazon, correlation coefficient, p-value, EPA data, Mongabay data, air quality, forest-air relationship

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



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Data details

Air pollution in Ithaca
Detailed data title: Percentage of days with moderate or worse air quality in Ithaca, NY
Source: Environmental Protection Agency
See what else correlates with Air pollution in Ithaca

Remaining Forest Cover in the Brazilian Amazon
Detailed data title: Estimated Remaining Forest Cover in the Brazilian Amazon
Source: Mongabay
See what else correlates with Remaining Forest Cover in the Brazilian Amazon

Correlation r = 0.8700489 (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 = 0.7569851 (Coefficient of determination)
This means 75.7% of the change in the one variable (i.e., Remaining Forest Cover in the Brazilian Amazon) is predictable based on the change in the other (i.e., Air pollution in Ithaca) over the 33 years from 1990 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 4.9E-11. 0.0000000000485725911717962000
The p-value is a measure of how probable it is that we would randomly find a result this extreme. 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 0.87 in 4.9E-9% of random cases. Said differently, if you correlated 20,587,742,508 random variables You don't actually need 20 billion 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 32 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 32 because we have two variables measured over a period of 33 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.

[ 0.75, 0.93 ] 95% correlation confidence interval (using the Fisher z-transformation)
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: 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.
199019911992199319941995199619971998199920002001200220032004200520062007200820092010201120122013201420152016201720182019202020212022
Air pollution in Ithaca (Bad air quality days)0.2212640.2734810.1456040.2945210.2909840.2602230.2341460.2361110.2777780.2586210.1465520.2256270.2299170.1863350.1420450.2148760.1149430.1516850.08587260.0547550.1362320.06920420.1285710.06837610.05382440.05413110.08310250.03966010.07777780.01966290.01373630.07222220.033241
Remaining Forest Cover in the Brazilian Amazon (Sq. KM)369202036809903667200365231036374103608350359019035769603559580354232035241003505930348428034588803431110341210033978103386160337325033657903358790335237033478003341910333690033306903322800331585033083103298550329012032796503268050




Why this works

  1. 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.
  2. Lack of causal connection: There is probably 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.
  3. 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 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.
  4. 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. 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.
  5. Outlandish outliers: There are "outliers" in this data. In concept, "outlier" just means "way different than the rest of your dataset." When calculating a correlation like this, they are particularly impactful because a single outlier can substantially increase your correlation.

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

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




Try it yourself

You can calculate the values on this page on your own! Try running the Python code to see the calculation results. 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([0.221264,0.273481,0.145604,0.294521,0.290984,0.260223,0.234146,0.236111,0.277778,0.258621,0.146552,0.225627,0.229917,0.186335,0.142045,0.214876,0.114943,0.151685,0.0858726,0.054755,0.136232,0.0692042,0.128571,0.0683761,0.0538244,0.0541311,0.0831025,0.0396601,0.0777778,0.0196629,0.0137363,0.0722222,0.033241,])
array_2 = np.array([3692020,3680990,3667200,3652310,3637410,3608350,3590190,3576960,3559580,3542320,3524100,3505930,3484280,3458880,3431110,3412100,3397810,3386160,3373250,3365790,3358790,3352370,3347800,3341910,3336900,3330690,3322800,3315850,3308310,3298550,3290120,3279650,3268050,])
array_1_name = "Air pollution in Ithaca"
array_2_name = "Remaining Forest Cover in the Brazilian Amazon"

# 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. 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.

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Correlation ID: 3496 · Black Variable ID: 22195 · Red Variable ID: 372
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