Spurious correlation #1,942 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air quality in Phoenix and the second variable is Remaining Forest Cover in the Brazilian Amazon. The chart goes from 1987 to 2022, 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 Air quality in Phoenix and the second variable is Remaining Forest Cover in the Brazilian Amazon. The chart goes from 1987 to 2022, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As air quality in Phoenix decreased, more people decided to ditch the desert for the lush greenery of the Amazon. This led to an unexpected influx of Phoenix residents partaking in urban Amazon adventuring. And as they say, where there's smog, there's a rainforest romp - talk about a breath of fresh Amazonian air!

^{Show image generation prompt} Model: dalle-3
Prompt: An image that looks like it is a scene from A Disney Movie: Create a breathtaking landscape where the air in Phoenix is crisp and clear, featuring a bright blue sky and puffy white clouds. Below, capture the lush, vibrant trees of the Brazilian Amazon, creating a rich and healthy forest canopy. Ensure the scene feels magical and awe-inspiring, evoking the spirit of a Disney movie. 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: Good air quality in Phoenix 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: A comic-book-style illustration with muted colors and a dotted halftone pattern from the 1960s Photorealism An image that looks like it is a scene from A Disney Movie Hyper-realistic Parallax art
ChatGPT: An image that looks like it is a scene from A Disney 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 Good air quality in Phoenix and Remaining Forest Cover in the Brazilian Amazon together. Keep the description simple.
ChatGPT: In the scene, the air in Phoenix is crisp and clear, with blue skies and white fluffy clouds overhead. Meanwhile, lush and vibrant trees cover the expansive landscape of the Brazilian Amazon, creating a rich and healthy forest canopy.

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 Disney Movie ] and depicting this scene: In the scene, the air in Phoenix is crisp and clear, with blue skies and white fluffy clouds overhead. Meanwhile, lush and vibrant trees cover the expansive landscape of the Brazilian Amazon, creating a rich and healthy forest canopy. 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 Disney Movie: Create a breathtaking landscape where the air in Phoenix is crisp and clear, featuring a bright blue sky and puffy white clouds. Below, capture the lush, vibrant trees of the Brazilian Amazon, creating a rich and healthy forest canopy. Ensure the scene feels magical and awe-inspiring, evoking the spirit of a Disney movie.

*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 a decrease in Air quality in Phoenix caused Remaining Forest Cover in the Brazilian Amazon to decrease. Include one good pun.

AI academic paper

(Because p < 0.01)

A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green

The Journal of Ecological Engineering and Sustainable Solutions

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 Air quality in Phoenix 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 name some movies that you watched that are tangentially related to the topic.

Here is the title and abstract of the paper:
[[TITLE]]
A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green

[[ABSTRACT]]
In this study, we examine the unlikely connection between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. Our research aimed to shed light on whether the air in the desert oasis of Phoenix could have any influence, direct or indirect, on the lush green canopy of the Amazon. We dived into the data with an eagerness reminiscent of a dad eagerly awaiting the punchline to a joke, and the findings were both insightful and humorous.

Utilizing data from the Environmental Protection Agency and Mongabay, we set out on a mission to unravel this mystery. The correlation coefficient of 0.7052788 and p < 0.01 for the period from 1987 to 2022 emerged as a beacon of statistical significance, shining through the clouds of uncertainty like the sun through the leaves of the rainforest. It was as though we stumbled upon a hidden punchline, much like a dad finding a stray sock at the back of the laundry cabinet - unexpected but undeniably impactful.

Our results suggest a noteworthy association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if a breath taken in one part of the world can influence the well-being of trees in another – the kind of interconnectedness that even a dad joke enthusiast can appreciate. This link emphasizes the importance of global environmental consciousness and the impact of seemingly unrelated phenomena on a broader scale.

In conclusion, we hope this study contributes to a deeper understanding of the intricate and quirky connections that exist in our global ecosystem. Let's remember, sometimes the punchline to a good dad joke is as unexpected and far-reaching as the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The world of environmental science has long been a treasure trove of surprises, much like finding a hidden stash of chocolate in the pantry after a long day. In this vein, our study sets out to unravel a conundrum that is as unexpected as it is compelling: the potential relationship between air quality in the desert metropolis of Phoenix and the remaining forest cover in the luscious expanse of the Brazilian Amazon. It's like discovering a dad joke in a scientific journal – surprising, yet oddly fitting.
Now, you might be wondering – what does the dry, arid climate of Phoenix have to do with the verdant, rain-drenched Amazon? Well, hold onto your hats (and maybe your lab coats too) – because the results of our research may just leave you as wide-eyed as a dad who just realized he's been wearing mismatched socks all day.
Armed with data from the Environmental Protection Agency and Mongabay, we embarked on this scientific expedition with the same gusto as a dad armed with a barbecue on a sunny holiday weekend. We dove headfirst into the numbers, the statistics, and the graphs, and what we found was nothing short of astonishing, like finally understanding a complicated dad joke that's been eluding you for years.
The statistical analysis revealed a correlation coefficient of 0.7052788 and a p-value of less than 0.01 for the period from 1987 to 2022. This may sound like a string of random numbers to the uninitiated, but to us, it was as thrilling as deciphering the punchline of a particularly cunning dad joke – unexpected, but undeniably significant.
Our findings suggest a tangible association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if the winds of Phoenix carry with them the subtle whispers of influence that dance through the amplitudes of the Amazonian rainforest – a notion that tickles the imagination much like a well-crafted dad joke.
In closing, we hope our study not only sheds light on this extraordinary connection but also underscores the importance of recognizing the unexpected ways in which our world is interconnected. Just like a dad joke that transcends generations, the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon is a testament to the wondrous and often whimsical nature of our planet's ecosystems.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
**LITERATURE REVIEW**

The connection between air quality in urban areas and its impact on global environmental phenomena has been a topic of growing interest in recent years. Smith et al. (2018) conducted a comprehensive study on the influence of urban air pollution on distant ecosystems, highlighting the unforeseen ripple effects of human activity on the natural world. Similarly, Doe and Jones (2017) explored the relationship between atmospheric conditions in densely populated areas and their potential repercussions on remote ecological systems. These studies, much like a dad's one-liner, shed light on the unexpected connections that underpin the complex web of our planet's environmental dynamics.

But now, let's take a detour from the serious to the surreal. In "The Hidden Life of Trees" by Peter Wohlleben, the author uncovers the fascinating and often surprising ways in which trees communicate and interact with their surroundings, almost as if they're sharing the best dad jokes of the forest. Meanwhile, "The Lorax" by Dr. Seuss is a whimsical yet poignant tale that implores us to consider the far-reaching consequences of environmental degradation, albeit without the inclusion of any actual dad jokes.

On a cinematic note, "FernGully: The Last Rainforest" offers a visually captivating portrayal of a lush and vibrant Amazonian setting, prompting viewers to marvel at the awe-inspiring beauty of nature in a manner that is both engaging and informative. Much like a well-timed dad joke, this film strikes a balance between levity and solemnity, merging entertainment with a profound message about the fragility of our planet's ecosystems.

As we venture into the realm of literature and film, it becomes evident that the interconnectedness of seemingly disparate elements forms the crux of our understanding of environmental phenomena. Well, much like a punchline delivered by a dad, the unexpected ironies of our world continue to reveal themselves, reminding us of the delightful absurdity and complexity of existence. So, let's embrace these quirks and dive deeper into the link between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon with a sense of curiosity and, of course, humor.

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 Air quality in Phoenix 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. 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 Environmental Protection Agency and Mongabay . You used data from 1987 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]]
A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green

[[ABSTRACT]]
In this study, we examine the unlikely connection between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. Our research aimed to shed light on whether the air in the desert oasis of Phoenix could have any influence, direct or indirect, on the lush green canopy of the Amazon. We dived into the data with an eagerness reminiscent of a dad eagerly awaiting the punchline to a joke, and the findings were both insightful and humorous.

Utilizing data from the Environmental Protection Agency and Mongabay, we set out on a mission to unravel this mystery. The correlation coefficient of 0.7052788 and p < 0.01 for the period from 1987 to 2022 emerged as a beacon of statistical significance, shining through the clouds of uncertainty like the sun through the leaves of the rainforest. It was as though we stumbled upon a hidden punchline, much like a dad finding a stray sock at the back of the laundry cabinet - unexpected but undeniably impactful.

Our results suggest a noteworthy association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if a breath taken in one part of the world can influence the well-being of trees in another – the kind of interconnectedness that even a dad joke enthusiast can appreciate. This link emphasizes the importance of global environmental consciousness and the impact of seemingly unrelated phenomena on a broader scale.

In conclusion, we hope this study contributes to a deeper understanding of the intricate and quirky connections that exist in our global ecosystem. Let's remember, sometimes the punchline to a good dad joke is as unexpected and far-reaching as the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon.

[[INTRODUCTION]]
The world of environmental science has long been a treasure trove of surprises, much like finding a hidden stash of chocolate in the pantry after a long day. In this vein, our study sets out to unravel a conundrum that is as unexpected as it is compelling: the potential relationship between air quality in the desert metropolis of Phoenix and the remaining forest cover in the luscious expanse of the Brazilian Amazon. It's like discovering a dad joke in a scientific journal – surprising, yet oddly fitting.
Now, you might be wondering – what does the dry, arid climate of Phoenix have to do with the verdant, rain-drenched Amazon? Well, hold onto your hats (and maybe your lab coats too) – because the results of our research may just leave you as wide-eyed as a dad who just realized he's been wearing mismatched socks all day.
Armed with data from the Environmental Protection Agency and Mongabay, we embarked on this scientific expedition with the same gusto as a dad armed with a barbecue on a sunny holiday weekend. We dove headfirst into the numbers, the statistics, and the graphs, and what we found was nothing short of astonishing, like finally understanding a complicated dad joke that's been eluding you for years.
The statistical analysis revealed a correlation coefficient of 0.7052788 and a p-value of less than 0.01 for the period from 1987 to 2022. This may sound like a string of random numbers to the uninitiated, but to us, it was as thrilling as deciphering the punchline of a particularly cunning dad joke – unexpected, but undeniably significant.
Our findings suggest a tangible association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if the winds of Phoenix carry with them the subtle whispers of influence that dance through the amplitudes of the Amazonian rainforest – a notion that tickles the imagination much like a well-crafted dad joke.
In closing, we hope our study not only sheds light on this extraordinary connection but also underscores the importance of recognizing the unexpected ways in which our world is interconnected. Just like a dad joke that transcends generations, the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon is a testament to the wondrous and often whimsical nature of our planet's ecosystems.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

To investigate the potential connection between air quality in Phoenix and remaining forest cover in the Brazilian Amazon, we employed a methodology as precise as a meticulously timed dad joke. Our data collection journey took us through the expansive realms of the Environmental Protection Agency and Mongabay, akin to a dad meticulously combing through his collection of puns and witty one-liners.

We considered various factors such as particulate matter levels, carbon monoxide emissions, and nitrogen dioxide concentrations in the air quality of Phoenix, all the while keeping in mind the delicate balance of comedy and science, not unlike the delicate balance of a dad trying to keep a straight face while slipping in a pun during a serious conversation.

Simultaneously, we delved into the intricate details of forest cover in the Brazilian Amazon, scrutinizing deforestation rates, reforestation efforts, and habitat destruction with an intensity comparable to a dad scouring the local newspaper for the perfect joke to slip into the family dinner conversation.

Our approach incorporated a time-series analysis, allowing us to capture changes over the years and unveil patterns that might have otherwise evaded our keen scientific eye. Imagine this as akin to a dad meticulously honing his craft of comedy over the years, perfecting the art of timing and delivery to elicit the most laughter from his audience.

Using statistical software, we conducted correlation and regression analyses, treating our data with the same care and precision as a dad crafting the punchline to a well-timed joke, ensuring that every variable was accounted for and every relationship explored thoroughly – just like meticulously setting up a dad joke, ensuring that the setup is just as crucial as the punchline itself.

In addition to statistical analyses, we employed geographic information systems (GIS) to map the spatial distribution of air quality in Phoenix and forest cover in the Brazilian Amazon, providing us with a visual representation of the potential interplay between these seemingly distant phenomena. It was as if we were creating a comedic map of the environmental landscape, locating the hidden humor in the unexpected relationship between these two disparate regions.

Furthermore, we conducted a comprehensive literature review, engaging with existing research and scientific discourse, ensuring that our study was not only novel but also grounded in the existing body of knowledge – much like a dad who carefully studies classic jokes before adding his own twist to the punchline.

Overall, our methodology was as robust as a well-constructed dad joke, blending the precision of scientific inquiry with the lightheartedness of a clever pun, to unravel the unlikely bond between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon.

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 Air quality in Phoenix 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. 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 Environmental Protection Agency and Mongabay .

For the time period 1987 to 2022, you found a correlation 0.7052788, r-squared of 0.4974182, 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]]
A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green

[[ABSTRACT]]
In this study, we examine the unlikely connection between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. Our research aimed to shed light on whether the air in the desert oasis of Phoenix could have any influence, direct or indirect, on the lush green canopy of the Amazon. We dived into the data with an eagerness reminiscent of a dad eagerly awaiting the punchline to a joke, and the findings were both insightful and humorous.

Utilizing data from the Environmental Protection Agency and Mongabay, we set out on a mission to unravel this mystery. The correlation coefficient of 0.7052788 and p < 0.01 for the period from 1987 to 2022 emerged as a beacon of statistical significance, shining through the clouds of uncertainty like the sun through the leaves of the rainforest. It was as though we stumbled upon a hidden punchline, much like a dad finding a stray sock at the back of the laundry cabinet - unexpected but undeniably impactful.

Our results suggest a noteworthy association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if a breath taken in one part of the world can influence the well-being of trees in another – the kind of interconnectedness that even a dad joke enthusiast can appreciate. This link emphasizes the importance of global environmental consciousness and the impact of seemingly unrelated phenomena on a broader scale.

In conclusion, we hope this study contributes to a deeper understanding of the intricate and quirky connections that exist in our global ecosystem. Let's remember, sometimes the punchline to a good dad joke is as unexpected and far-reaching as the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The world of environmental science has long been a treasure trove of surprises, much like finding a hidden stash of chocolate in the pantry after a long day. In this vein, our study sets out to unravel a conundrum that is as unexpected as it is compelling: the potential relationship between air quality in the desert metropolis of Phoenix and the remaining forest cover in the luscious expanse of the Brazilian Amazon. It's like discovering a dad joke in a scientific journal – surprising, yet oddly fitting.
Now, you might be wondering – what does the dry, arid climate of Phoenix have to do with the verdant, rain-drenched Amazon? Well, hold onto your hats (and maybe your lab coats too) – because the results of our research may just leave you as wide-eyed as a dad who just realized he's been wearing mismatched socks all day.
Armed with data from the Environmental Protection Agency and Mongabay, we embarked on this scientific expedition with the same gusto as a dad armed with a barbecue on a sunny holiday weekend. We dove headfirst into the numbers, the statistics, and the graphs, and what we found was nothing short of astonishing, like finally understanding a complicated dad joke that's been eluding you for years.
The statistical analysis revealed a correlation coefficient of 0.7052788 and a p-value of less than 0.01 for the period from 1987 to 2022. This may sound like a string of random numbers to the uninitiated, but to us, it was as thrilling as deciphering the punchline of a particularly cunning dad joke – unexpected, but undeniably significant.
Our findings suggest a tangible association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if the winds of Phoenix carry with them the subtle whispers of influence that dance through the amplitudes of the Amazonian rainforest – a notion that tickles the imagination much like a well-crafted dad joke.
In closing, we hope our study not only sheds light on this extraordinary connection but also underscores the importance of recognizing the unexpected ways in which our world is interconnected. Just like a dad joke that transcends generations, the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon is a testament to the wondrous and often whimsical nature of our planet's ecosystems.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The results of our analysis brought forth a correlation coefficient of 0.7052788, indicating a moderately strong positive relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. This association was as clear as a dad joke delivered with impeccable timing, leaving no room for doubt or skepticism.

Additionally, the r-squared value of 0.4974182 revealed that approximately 49.74% of the variability in the remaining forest cover in the Brazilian Amazon could be explained by the air quality in Phoenix. It's like finding out that almost half of the secret to telling a good dad joke lies in the delivery – a revelation that brings both awe and understanding.

Furthermore, the p-value of less than 0.01 indicated that the observed correlation was statistically significant. This level of significance was as unmistakable as a classic dad joke – it was impossible to overlook, and you couldn’t help but smile at its impact.

Behold, the scatterplot in Figure 1 depicts the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. The plot is a testament to the strength of the correlation, much like a well-timed dad joke that elicits laughter from the entire room.

In conclusion, our findings highlight a surprising and substantial connection between the air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. This unexpected relationship serves as a reminder that in the vast theater of environmental science, even the most unlikely characters can share the spotlight – much like a dad joke that unexpectedly steals the show.

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 Air quality in Phoenix 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. 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]]
A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green

[[ABSTRACT]]
In this study, we examine the unlikely connection between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. Our research aimed to shed light on whether the air in the desert oasis of Phoenix could have any influence, direct or indirect, on the lush green canopy of the Amazon. We dived into the data with an eagerness reminiscent of a dad eagerly awaiting the punchline to a joke, and the findings were both insightful and humorous.

Utilizing data from the Environmental Protection Agency and Mongabay, we set out on a mission to unravel this mystery. The correlation coefficient of 0.7052788 and p < 0.01 for the period from 1987 to 2022 emerged as a beacon of statistical significance, shining through the clouds of uncertainty like the sun through the leaves of the rainforest. It was as though we stumbled upon a hidden punchline, much like a dad finding a stray sock at the back of the laundry cabinet - unexpected but undeniably impactful.

Our results suggest a noteworthy association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if a breath taken in one part of the world can influence the well-being of trees in another – the kind of interconnectedness that even a dad joke enthusiast can appreciate. This link emphasizes the importance of global environmental consciousness and the impact of seemingly unrelated phenomena on a broader scale.

In conclusion, we hope this study contributes to a deeper understanding of the intricate and quirky connections that exist in our global ecosystem. Let's remember, sometimes the punchline to a good dad joke is as unexpected and far-reaching as the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon.

[[LITERATURE REVIEW]]
The connection between air quality in urban areas and its impact on global environmental phenomena has been a topic of growing interest in recent years. Smith et al. (2018) conducted a comprehensive study on the influence of urban air pollution on distant ecosystems, highlighting the unforeseen ripple effects of human activity on the natural world. Similarly, Doe and Jones (2017) explored the relationship between atmospheric conditions in densely populated areas and their potential repercussions on remote ecological systems. These studies, much like a dad's one-liner, shed light on the unexpected connections that underpin the complex web of our planet's environmental dynamics.
But now, let's take a detour from the serious to the surreal. In "The Hidden Life of Trees" by Peter Wohlleben, the author uncovers the fascinating and often surprising ways in which trees communicate and interact with their surroundings, almost as if they're sharing the best dad jokes of the forest. Meanwhile, "The Lorax" by Dr. Seuss is a whimsical yet poignant tale that implores us to consider the far-reaching consequences of environmental degradation, albeit without the inclusion of any actual dad jokes.
On a cinematic note, "FernGully: The Last Rainforest" offers a visually captivating portrayal of a lush and vibrant Amazonian setting, prompting viewers to marvel at the awe-inspiring beauty of nature in a manner that is both engaging and informative. Much like a well-timed dad joke, this film strikes a balance between levity and solemnity, merging entertainment with a profound message about the fragility of our planet's ecosystems.
As we venture into the realm of literature and film, it becomes evident that the interconnectedness of seemingly disparate elements forms the crux of our understanding of environmental phenomena. Well, much like a punchline delivered by a dad, the unexpected ironies of our world continue to reveal themselves, reminding us of the delightful absurdity and complexity of existence. So, let's embrace these quirks and dive deeper into the link between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon with a sense of curiosity and, of course, humor.

[[RESULTS]]
The results of our analysis brought forth a correlation coefficient of 0.7052788, indicating a moderately strong positive relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. This association was as clear as a dad joke delivered with impeccable timing, leaving no room for doubt or skepticism.
Additionally, the r-squared value of 0.4974182 revealed that approximately 49.74% of the variability in the remaining forest cover in the Brazilian Amazon could be explained by the air quality in Phoenix. It's like finding out that almost half of the secret to telling a good dad joke lies in the delivery – a revelation that brings both awe and understanding.
Furthermore, the p-value of less than 0.01 indicated that the observed correlation was statistically significant. This level of significance was as unmistakable as a classic dad joke – it was impossible to overlook, and you couldn’t help but smile at its impact.
Behold, the scatterplot in Figure 1 depicts the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. The plot is a testament to the strength of the correlation, much like a well-timed dad joke that elicits laughter from the entire room.
In conclusion, our findings highlight a surprising and substantial connection between the air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. This unexpected relationship serves as a reminder that in the vast theater of environmental science, even the most unlikely characters can share the spotlight – much like a dad joke that unexpectedly steals the show.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

Building upon the foundations laid by previous research, our study verified and expanded upon the surprising link between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. Much like a dad joke that gets funnier with repetition, our findings echo and reinforce the notion that environmental factors in one part of the world can reverberate across the globe, affecting ecosystems in distant locations.

Our results align with the work of Smith et al. (2018) and Doe and Jones (2017), affirming the interconnectedness of urban air quality and remote ecosystems. It's like discovering a well-crafted dad joke – once you hear it from multiple sources, it only gets better. Furthermore, the insights from "The Hidden Life of Trees" and "The Lorax" underscore the complex and far-reaching implications of human activity on natural environments, akin to the wide-reaching impact of a dad joke on an entire room.

The moderately strong positive correlation we discovered is reminiscent of a well-scripted dad joke - clear, impactful, and undeniable. It reinforces the notion that the air quality in one location can play a role in shaping the ecological landscape in another, much like a dad's lighthearted quip can brighten someone's day.

Moreover, the r-squared value indicates that nearly half of the variability in the remaining forest cover in the Brazilian Amazon can be attributed to the air quality in Phoenix. This revelation is akin to realizing that almost half of the success of a dad joke lies in its delivery - a powerful insight that deepens our appreciation for the intricacies of this unexpected connection.

The statistical significance of our findings, with a p-value of less than 0.01, parallels the impact of a timeless dad joke – impossible to ignore and undeniably influential. It highlights the substantial nature of the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon, much like a classic dad joke that never fails to elicit a chuckle.

In essence, our study not only affirms the unanticipated bond between air quality in Phoenix and the forest cover in the Brazilian Amazon, but also underscores the wider implications of seemingly unrelated environmental factors. Just like a well-placed dad joke, this unexpected connection brings a touch of humor and whimsy to the serious landscape of environmental science, reminding us of the delightful and unexpected facets of our planet's interconnected ecosystem.

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 Air quality in Phoenix 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. 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]]
A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green

[[ABSTRACT]]
In this study, we examine the unlikely connection between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. Our research aimed to shed light on whether the air in the desert oasis of Phoenix could have any influence, direct or indirect, on the lush green canopy of the Amazon. We dived into the data with an eagerness reminiscent of a dad eagerly awaiting the punchline to a joke, and the findings were both insightful and humorous.

Utilizing data from the Environmental Protection Agency and Mongabay, we set out on a mission to unravel this mystery. The correlation coefficient of 0.7052788 and p < 0.01 for the period from 1987 to 2022 emerged as a beacon of statistical significance, shining through the clouds of uncertainty like the sun through the leaves of the rainforest. It was as though we stumbled upon a hidden punchline, much like a dad finding a stray sock at the back of the laundry cabinet - unexpected but undeniably impactful.

Our results suggest a noteworthy association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if a breath taken in one part of the world can influence the well-being of trees in another – the kind of interconnectedness that even a dad joke enthusiast can appreciate. This link emphasizes the importance of global environmental consciousness and the impact of seemingly unrelated phenomena on a broader scale.

In conclusion, we hope this study contributes to a deeper understanding of the intricate and quirky connections that exist in our global ecosystem. Let's remember, sometimes the punchline to a good dad joke is as unexpected and far-reaching as the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon.

[[INTRDUCTION]]
The world of environmental science has long been a treasure trove of surprises, much like finding a hidden stash of chocolate in the pantry after a long day. In this vein, our study sets out to unravel a conundrum that is as unexpected as it is compelling: the potential relationship between air quality in the desert metropolis of Phoenix and the remaining forest cover in the luscious expanse of the Brazilian Amazon. It's like discovering a dad joke in a scientific journal – surprising, yet oddly fitting.
Now, you might be wondering – what does the dry, arid climate of Phoenix have to do with the verdant, rain-drenched Amazon? Well, hold onto your hats (and maybe your lab coats too) – because the results of our research may just leave you as wide-eyed as a dad who just realized he's been wearing mismatched socks all day.
Armed with data from the Environmental Protection Agency and Mongabay, we embarked on this scientific expedition with the same gusto as a dad armed with a barbecue on a sunny holiday weekend. We dove headfirst into the numbers, the statistics, and the graphs, and what we found was nothing short of astonishing, like finally understanding a complicated dad joke that's been eluding you for years.
The statistical analysis revealed a correlation coefficient of 0.7052788 and a p-value of less than 0.01 for the period from 1987 to 2022. This may sound like a string of random numbers to the uninitiated, but to us, it was as thrilling as deciphering the punchline of a particularly cunning dad joke – unexpected, but undeniably significant.
Our findings suggest a tangible association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if the winds of Phoenix carry with them the subtle whispers of influence that dance through the amplitudes of the Amazonian rainforest – a notion that tickles the imagination much like a well-crafted dad joke.
In closing, we hope our study not only sheds light on this extraordinary connection but also underscores the importance of recognizing the unexpected ways in which our world is interconnected. Just like a dad joke that transcends generations, the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon is a testament to the wondrous and often whimsical nature of our planet's ecosystems.

[[RESULTS]]
The results of our analysis brought forth a correlation coefficient of 0.7052788, indicating a moderately strong positive relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. This association was as clear as a dad joke delivered with impeccable timing, leaving no room for doubt or skepticism.
Additionally, the r-squared value of 0.4974182 revealed that approximately 49.74% of the variability in the remaining forest cover in the Brazilian Amazon could be explained by the air quality in Phoenix. It's like finding out that almost half of the secret to telling a good dad joke lies in the delivery – a revelation that brings both awe and understanding.
Furthermore, the p-value of less than 0.01 indicated that the observed correlation was statistically significant. This level of significance was as unmistakable as a classic dad joke – it was impossible to overlook, and you couldn’t help but smile at its impact.
Behold, the scatterplot in Figure 1 depicts the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. The plot is a testament to the strength of the correlation, much like a well-timed dad joke that elicits laughter from the entire room.
In conclusion, our findings highlight a surprising and substantial connection between the air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. This unexpected relationship serves as a reminder that in the vast theater of environmental science, even the most unlikely characters can share the spotlight – much like a dad joke that unexpectedly steals the show.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In wrapping up our study, we've unraveled a relationship between air quality in Phoenix and the forest cover in the Brazilian Amazon that's as surprising as a dad joke with impeccable timing. It seems that the winds of Phoenix could whisper a message all the way to the lush greenery of the Amazon – it's like a global game of telephone but with trees.

Our findings reveal a correlation coefficient as robust as a dad joke enthusiast's corny repertoire, with approximately 49.74% of the variability in the Amazonian forest cover being explained by the air quality in Phoenix. We didn't expect this connection to be so "air-resistible"!

Furthermore, the statistically significant p-value of less than 0.01 highlights a link that's as clear as a perfectly delivered dad joke – you can't help but appreciate its impact.

In the grand scheme of environmental science, this connection serves as a reminder that even seemingly disparate phenomena can influence each other. It's as unexpected and interconnected as realizing the punchline to a dad joke you've been scratching your head over.

In conclusion, it seems that no more research is needed in this area. Our findings have left us as satisfied as a dad who's just found the perfect spot for a barbecue – and we can rest assured that our study has earned its place in the hallowed halls of scientific inquiry.

But hey, speaking of hallowed halls, have you heard the rumor about the tree who couldn't find a date to the dance? It's all because it couldn't "twig" its way around the forest – talk about rough "bark"!

Ah, folks, I'll be here all week. And with that, our study bids a fond farewell, much like a dad joke that's endured the test of time.

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 A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Ecological Engineering and Sustainable Solutions

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 A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green. Respond only with the name of a fictional organization.

ChatGPT:

The Ecological Restoration and Sustainable Development Society

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 A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green with an abstract of In this study, we examine the unlikely connection between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon. Our research aimed to shed light on whether the air in the desert oasis of Phoenix could have any influence, direct or indirect, on the lush green canopy of the Amazon. We dived into the data with an eagerness reminiscent of a dad eagerly awaiting the punchline to a joke, and the findings were both insightful and humorous.
Utilizing data from the Environmental Protection Agency and Mongabay, we set out on a mission to unravel this mystery. The correlation coefficient of 0.7052788 and p < 0.01 for the period from 1987 to 2022 emerged as a beacon of statistical significance, shining through the clouds of uncertainty like the sun through the leaves of the rainforest. It was as though we stumbled upon a hidden punchline, much like a dad finding a stray sock at the back of the laundry cabinet - unexpected but undeniably impactful.
Our results suggest a noteworthy association between the air quality in Phoenix and the extent of forest cover in the Brazilian Amazon. It's almost as if a breath taken in one part of the world can influence the well-being of trees in another – the kind of interconnectedness that even a dad joke enthusiast can appreciate. This link emphasizes the importance of global environmental consciousness and the impact of seemingly unrelated phenomena on a broader scale.
In conclusion, we hope this study contributes to a deeper understanding of the intricate and quirky connections that exist in our global ecosystem. Let's remember, sometimes the punchline to a good dad joke is as unexpected and far-reaching as the relationship between air quality in Phoenix and the remaining forest cover in the Brazilian Amazon.

ChatGPT:

Phoenix air quality, Brazilian Amazon forest cover, air pollution correlation, environmental impact, global ecosystem connectivity, air quality influence on rainforest, environmental data analysis, EPA air quality data, Mongabay forest cover data, global environmental consciousness, interconnected phenomena, ecosystem relationships

*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 quality in Phoenix
Detailed data title: Percentage of days with good air quality in Phoenix-Mesa-Scottsdale, AZ
Source: Environmental Protection Agency
See what else correlates with Air quality in Phoenix

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 = 0.7052788 (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 = 0.4974182 (Coefficient of determination)
This means 49.7% 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 quality in Phoenix) over the 36 years from 1987 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.6E-6.^Show 0.0000015620297547884950000000
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 0.71 in 0.00016% of random cases. Said differently, if you correlated 640,193 random variables^Note You don't actually need 640 thousand variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

p-value calculations are useful for understanding the probability of a result happening by chance. They are most useful when used to highlight the risk of a fluke outcome. For example, if you calculate a p-value of 0.30, the risk that the result is a fluke is high. It is good to know that! But there are lots of ways to get a p-value of less than 0.01, as evidenced by this project.

In this particular case, the values are so extreme as to be meaningless. That's why no one reports p-values with specificity after they drop below 0.01.

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 35 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 35 because we have two variables measured over a period of 36 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.

[ 0.49, 0.84 ] 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.

	1987	1988	1989	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	2022
Air quality in Phoenix (Good air quality)	18.1818	24.0437	24.3836	27.9452	26.5753	21.8579	27.6712	20.8219	14.2466	15.847	8.49315	9.31507	1.36986	5.7377	8.21918	8.49315	11.7808	16.3934	13.4247	3.0137	6.0274	11.7486	6.84932	16.1644	5.47945	6.28415	8.21918	6.0274	13.9726	7.10383	8.76712	11.5068	13.6986	3.00546	3.0137	9.31507
Remaining Forest Cover in the Brazilian Amazon (Sq. KM)	3744570	3723520	3705750	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

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([18.1818,24.0437,24.3836,27.9452,26.5753,21.8579,27.6712,20.8219,14.2466,15.847,8.49315,9.31507,1.36986,5.7377,8.21918,8.49315,11.7808,16.3934,13.4247,3.0137,6.0274,11.7486,6.84932,16.1644,5.47945,6.28415,8.21918,6.0274,13.9726,7.10383,8.76712,11.5068,13.6986,3.00546,3.0137,9.31507,])
array_2 = np.array([3744570,3723520,3705750,3692020,3680990,3667200,3652310,3637410,3608350,3590190,3576960,3559580,3542320,3524100,3505930,3484280,3458880,3431110,3412100,3397810,3386160,3373250,3365790,3358790,3352370,3347800,3341910,3336900,3330690,3322800,3315850,3308310,3298550,3290120,3279650,3268050,])
array_1_name = "Air quality in Phoenix"
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. ^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 Air quality in Phoenix
Line chart for only Remaining Forest Cover in the Brazilian Amazon
AI-generated correlation image
The spurious research paper: A Breath of Fresh Air: The Pair Between Phoenix Air and Amazon Green

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Correlation ID: 1942 · Black Variable ID: 21062 · Red Variable ID: 372


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