Spurious correlation #5,407 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is US household spending on postage and stationery and the second variable is Air pollution in Olympia, Washington. The chart goes from 2000 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 US household spending on postage and stationery and the second variable is Air pollution in Olympia, Washington. The chart goes from 2000 to 2022, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As households spent less on postage and stationery, there was a lower demand for sending physical letters and cards. This led to a decrease in the transportation of mail by planes and trucks, resulting in reduced air pollution in Olympia, Washington. It's as if Mother Nature said, "Hey, less mail, less smog! Keep those letters virtual, and let's clear the air!"

^{Show image generation prompt} Model: dalle-3
Prompt: Prompt: Create a serene cyber art piece showing a neighborhood in Olympia, Washington, with clear blue skies and a lack of postal vehicles. Depict the subtle integration of virtual communication over physical mail, leading to a reduction in air pollution and a fresher environment for the residents. The scene should exhibit a tranquil, futuristic ambiance, where the absence of traditional mail transport is key to the city's clean, smog-free atmosphere. 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: US household spending on postage and stationery and Air pollution in Olympia, Washington. 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: An image that looks like it is a scene from A Disney Movie Cyber folk Cyber folk inspired by bauhaus Data cyber art
ChatGPT: Data cyber art

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 US household spending on postage and stationery and Air pollution in Olympia, Washington, in the following situation: As households spent less on postage and stationery, there was a lower demand for sending physical letters and cards. This led to a decrease in the transportation of mail by planes and trucks, resulting in reduced air pollution in Olympia, Washington. It's as if Mother Nature said, "Hey, less mail, less smog! Keep those letters virtual, and let's clear the air!". Keep the description simple.
ChatGPT: Picture a serene neighborhood in Olympia, Washington, where the air is free of smog. As people opt for sending virtual messages and emails instead of physical letters and cards, a picturesque scene of clear blue skies takes over the city. The absence of postal trucks and planes carrying mail contributes to the reduced air pollution, creating a cleaner and fresher environment for the inhabitants of Olympia to enjoy.

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: [ Data cyber art ] and depicting this scene: Picture a serene neighborhood in Olympia, Washington, where the air is free of smog. As people opt for sending virtual messages and emails instead of physical letters and cards, a picturesque scene of clear blue skies takes over the city. The absence of postal trucks and planes carrying mail contributes to the reduced air pollution, creating a cleaner and fresher environment for the inhabitants of Olympia to enjoy. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Prompt: Create a serene cyber art piece showing a neighborhood in Olympia, Washington, with clear blue skies and a lack of postal vehicles. Depict the subtle integration of virtual communication over physical mail, leading to a reduction in air pollution and a fresher environment for the residents. The scene should exhibit a tranquil, futuristic ambiance, where the absence of traditional mail transport is key to the city's clean, smog-free atmosphere.

*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 US household spending on postage and stationery caused Air pollution in Olympia, Washington to decrease. Make it feel plausible.

AI academic paper

(Because p < 0.01)

Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington

Journal of Quirky Environmental Studies

Jan 2024

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

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

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

Please make up a literature review section of an academic research paper presenting the findings of the connection between US household spending on postage and stationery and Air pollution in Olympia, Washington. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then devolve ever further, and mention something completely ridiculous, like you conducted literature review by reading the backs of shampoo bottles.

Here is the title and abstract of the paper:
[[TITLE]]
Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington

[[ABSTRACT]]
In this study, we delved into the intriguing connection between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic may seem as uninspiring as finding a misplaced penny in the bureaucratic maze, our findings shed a humorous light on the unsuspected relationship between these seemingly unrelated factors.

Utilizing data from the Bureau of Labor Statistics and the Environmental Protection Agency, we embarked on an adventure akin to navigating through endless folders of paperwork in search of a lost document, to investigate whether there existed any correlation between US household spending on postage and stationery and the levels of air pollution in Olympia, Washington. Remarkably, our analysis revealed a correlation coefficient of 0.8636410 and an eye-catching p-value of less than 0.01 for the timeframe spanning 2000 to 2022.

The association we unearthed between the whimsical act of mailing letters and the environmental quality in Olympia, Washington, is no mere triviality; it highlights the interconnectedness of seemingly unrelated spheres of human activity. Indeed, one might say that the pen really is mightier than the smog; a thought as whimsical as a balloon losing air! Our findings may serve as a breath of fresh air in the world of academic research, proving that every envelope and sheet of stationery carries a story, even if it's one about air pollution.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The pursuit of understanding the intricate relationships within socioeconomic and environmental realms has led researchers to explore curious and unexpected connections. In the vein of these endeavors, our study delves into the correlation between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic at first glance may seem as predictable as finding a paperclip in an office, our investigation has unwrapped a surprise package of insights, demonstrating that even the most mundane activities can have unexpected implications for environmental quality.
The act of sending letters and purchasing stationery may appear as simple as pie at first glance, yet these seemingly innocuous behaviors have captured our attention due to their potentially indirect consequences on the air quality in Washington’s capital. It is akin to discovering an Easter egg in the most unexpected spot – a delightful surprise that sparks curiosity and intrigue.
Our decision to embark on this research journey stemmed from an appreciation of the interconnectedness of human actions and their ecological ramifications. Just as a postage stamp adheres to an envelope, our examination sought to uncover the bond between household spending habits and the air we breathe in Olympia. Through meticulous analysis of data from the Bureau of Labor Statistics and the Environmental Protection Agency, we undertook a quest comparable to embarking on a treasure hunt amidst the paperwork labyrinth, seeking to unveil the hidden connections between these facets of modern life.
Indeed, the findings that emerged from our rigorous inquiry brought to light a correlation coefficient of 0.8636410, signaling a significant relationship between household spending on postage and stationery and the levels of air pollution in Olympia, Washington. This discovery is as striking as finding a mint-condition collectible in a dusty attic – a testament to the unforeseen connections that lie beneath the surface of everyday activities.
As we proceed to unravel these findings and their implications, we invite fellow scholars and enthusiasts of peculiar consequentialities to explore with us the unforeseen repercussions of something as seemingly innocuous as postage and stationery spending. The knowledge gleaned from this study may not only benefit scholarly dialogues but also evoke a chuckle at the whimsical nature of these unsuspected connections. After all, who would have thought that the humble act of mailing a letter could leave such an indelible mark on the atmosphere? It's almost as surprising as finding a typo in a dictionary!

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The study of the correspondence between US household spending on postage and stationery and air pollution in Olympia, Washington has sparked an array of investigations into the peculiar and unexpected connections that underlie seemingly mundane activities. Our exploration led us to uncover a trove of literature that shed light on this whimsical relationship, akin to stumbling upon a hidden punchline in a sea of serious discourse.

In "Letters, Postage, and the Environment" by Smith, the authors find a modest correlation between letter sending and air quality in urban areas, laying the groundwork for our investigation. Following this serious line of inquiry, "The Economics of Stationery" by Doe delves into the expenditure patterns related to stationery purchases, no doubt an essential foundation for our analysis, as we ponder the potential ramifications of paper and pen on environmental factors.

Turning our attention to non-fiction literature, "The Air We Breathe" by Jones provides thought-provoking insights into the intricacies of air pollution, offering a serious perspective that forms the backdrop of our study. Furthermore, "Environmental Impacts: Uncovering the Inconspicuous" by Green speaks to the interconnectedness of human behaviors and environmental consequences, providing a tantalizing hint at the unexpected relationship we are elucidating.

On the fictional front, "Air Mail Mysteries" by Brown, although a work of fiction, has captivated readers with its imaginative exploration of the mystique and intrigue behind mailing letters, an example of the allure that surrounds the postal universe. Similarly, the classic "Stationery Sorcery" by Black weaves a tale of enchantment and wonder within the realm of office supplies, bearing a certain resemblance to the enchanting allure of our unearthing of this relationship.

As we delved further into our rigorous literature review, we found ourselves venturing into unexpected territories, with sources such as "The Secret Life of Envelopes" by Purple, that, while lacking in scholarly rigor, provided unexpected inspiration. Furthermore, we stumbled upon "Air Pollution for Dummies," admittedly not the most erudite source, but, nevertheless, a gateway to understanding the basics of the atmospheric conundrum we were probing.

In a turn of unconventional rigor, our comprehensive literature review also encompassed unconventional sources, including the backs of shampoo bottles found in the office break room – for even in the unlikeliest of places, knowledge may hide. While these sources may not rival the academic standards to which we aspire, they nevertheless serve as a testament to the lengths we went to in uncovering the unexpected relationship between household spending on postage and stationery and air pollution in Olympia, Washington. Such is the nature of academic inquiry – one must sometimes unearth treasure in the most unlikely of forms!

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 US household spending on postage and stationery and Air pollution in Olympia, Washington. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Bureau of Labor Statistics and Environmental Protection Agency . You used data from 2000 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]]
Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington

[[ABSTRACT]]
In this study, we delved into the intriguing connection between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic may seem as uninspiring as finding a misplaced penny in the bureaucratic maze, our findings shed a humorous light on the unsuspected relationship between these seemingly unrelated factors.

Utilizing data from the Bureau of Labor Statistics and the Environmental Protection Agency, we embarked on an adventure akin to navigating through endless folders of paperwork in search of a lost document, to investigate whether there existed any correlation between US household spending on postage and stationery and the levels of air pollution in Olympia, Washington. Remarkably, our analysis revealed a correlation coefficient of 0.8636410 and an eye-catching p-value of less than 0.01 for the timeframe spanning 2000 to 2022.

The association we unearthed between the whimsical act of mailing letters and the environmental quality in Olympia, Washington, is no mere triviality; it highlights the interconnectedness of seemingly unrelated spheres of human activity. Indeed, one might say that the pen really is mightier than the smog; a thought as whimsical as a balloon losing air! Our findings may serve as a breath of fresh air in the world of academic research, proving that every envelope and sheet of stationery carries a story, even if it's one about air pollution.

[[INTRODUCTION]]
The pursuit of understanding the intricate relationships within socioeconomic and environmental realms has led researchers to explore curious and unexpected connections. In the vein of these endeavors, our study delves into the correlation between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic at first glance may seem as predictable as finding a paperclip in an office, our investigation has unwrapped a surprise package of insights, demonstrating that even the most mundane activities can have unexpected implications for environmental quality.
The act of sending letters and purchasing stationery may appear as simple as pie at first glance, yet these seemingly innocuous behaviors have captured our attention due to their potentially indirect consequences on the air quality in Washington’s capital. It is akin to discovering an Easter egg in the most unexpected spot – a delightful surprise that sparks curiosity and intrigue.
Our decision to embark on this research journey stemmed from an appreciation of the interconnectedness of human actions and their ecological ramifications. Just as a postage stamp adheres to an envelope, our examination sought to uncover the bond between household spending habits and the air we breathe in Olympia. Through meticulous analysis of data from the Bureau of Labor Statistics and the Environmental Protection Agency, we undertook a quest comparable to embarking on a treasure hunt amidst the paperwork labyrinth, seeking to unveil the hidden connections between these facets of modern life.
Indeed, the findings that emerged from our rigorous inquiry brought to light a correlation coefficient of 0.8636410, signaling a significant relationship between household spending on postage and stationery and the levels of air pollution in Olympia, Washington. This discovery is as striking as finding a mint-condition collectible in a dusty attic – a testament to the unforeseen connections that lie beneath the surface of everyday activities.
As we proceed to unravel these findings and their implications, we invite fellow scholars and enthusiasts of peculiar consequentialities to explore with us the unforeseen repercussions of something as seemingly innocuous as postage and stationery spending. The knowledge gleaned from this study may not only benefit scholarly dialogues but also evoke a chuckle at the whimsical nature of these unsuspected connections. After all, who would have thought that the humble act of mailing a letter could leave such an indelible mark on the atmosphere? It's almost as surprising as finding a typo in a dictionary!

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

To conduct this stu- and by "stu-" I mean studying, not a mistake; I don't want anyone to think that kind of behavior is okay - we employed an assortment of research methods that were as diverse as a pack of crayons in a kindergarten classroom. Our data collection, akin to catching a swarm of bees in a net, involved extracting information from a variety of sources, although we spent the majority of our time scrolling through the Bureau of Labor Statistics and the Environmental Protection Agency websites.

We gathered data on household expenditures on postage and stationery from the Bureau of Labor Statistics, sifting through their reports and tables like one would sift through a stack of junk mail to find a hidden gem. Meanwhile, we acquired data on air pollution levels from the Environmental Protection Agency, navigating their website as if we were trying to find a rare postage stamp in a cluttered attic.

In order to establish a time frame for our analysis, we selected data spanning from 2000 to 2022, much like selecting the best vintage wine from the cellar – each year offering a different aroma and character. This timeframe allowed us to capture a comprehensive overview of household spending habits and air pollution levels over the years, providing a canvas as colorful as a box of brand-new markers.

Our data analysis was as thorough as a librarian alphabetizing a vast assortment of library books. We employed statistical techniques, including correlation analysis, linear regression models, and time series analysis, to uncover any potential connections between household spending on postage and stationery and air pollution levels in Olympia, Washington. These techniques were as essential to our research as a ruler is to drawing a straight line – without them, our conclusions would be as haphazard as a doodle on a napkin.

Furthermore, we checked and re-checked our data for accuracy, conducting sensitivity analyses and cross-referencing with other relevant studies. This process was as meticulous as trying to untangle a knot in a ball of yarn, ensuring that our findings were as precise as a calligrapher's script.

In summary, our methodology was as comprehensive as an encyclopedia, delving into the depths of household spending and air pollution data to unveil the unexpected relationship between these seemingly disparate aspects of modern life. Our approach was as methodical as a scientist in a laboratory, aiming to shed light on a connection that is as surprising as receiving a love letter from a stranger. Who knew that studying postage and stationery could be so exhilarating?

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 US household spending on postage and stationery and Air pollution in Olympia, Washington. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

For the time period 2000 to 2022, you found a correlation 0.8636410, r-squared of 0.7458758, 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]]
Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington

[[ABSTRACT]]
In this study, we delved into the intriguing connection between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic may seem as uninspiring as finding a misplaced penny in the bureaucratic maze, our findings shed a humorous light on the unsuspected relationship between these seemingly unrelated factors.

Utilizing data from the Bureau of Labor Statistics and the Environmental Protection Agency, we embarked on an adventure akin to navigating through endless folders of paperwork in search of a lost document, to investigate whether there existed any correlation between US household spending on postage and stationery and the levels of air pollution in Olympia, Washington. Remarkably, our analysis revealed a correlation coefficient of 0.8636410 and an eye-catching p-value of less than 0.01 for the timeframe spanning 2000 to 2022.

The association we unearthed between the whimsical act of mailing letters and the environmental quality in Olympia, Washington, is no mere triviality; it highlights the interconnectedness of seemingly unrelated spheres of human activity. Indeed, one might say that the pen really is mightier than the smog; a thought as whimsical as a balloon losing air! Our findings may serve as a breath of fresh air in the world of academic research, proving that every envelope and sheet of stationery carries a story, even if it's one about air pollution.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The pursuit of understanding the intricate relationships within socioeconomic and environmental realms has led researchers to explore curious and unexpected connections. In the vein of these endeavors, our study delves into the correlation between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic at first glance may seem as predictable as finding a paperclip in an office, our investigation has unwrapped a surprise package of insights, demonstrating that even the most mundane activities can have unexpected implications for environmental quality.
The act of sending letters and purchasing stationery may appear as simple as pie at first glance, yet these seemingly innocuous behaviors have captured our attention due to their potentially indirect consequences on the air quality in Washington’s capital. It is akin to discovering an Easter egg in the most unexpected spot – a delightful surprise that sparks curiosity and intrigue.
Our decision to embark on this research journey stemmed from an appreciation of the interconnectedness of human actions and their ecological ramifications. Just as a postage stamp adheres to an envelope, our examination sought to uncover the bond between household spending habits and the air we breathe in Olympia. Through meticulous analysis of data from the Bureau of Labor Statistics and the Environmental Protection Agency, we undertook a quest comparable to embarking on a treasure hunt amidst the paperwork labyrinth, seeking to unveil the hidden connections between these facets of modern life.
Indeed, the findings that emerged from our rigorous inquiry brought to light a correlation coefficient of 0.8636410, signaling a significant relationship between household spending on postage and stationery and the levels of air pollution in Olympia, Washington. This discovery is as striking as finding a mint-condition collectible in a dusty attic – a testament to the unforeseen connections that lie beneath the surface of everyday activities.
As we proceed to unravel these findings and their implications, we invite fellow scholars and enthusiasts of peculiar consequentialities to explore with us the unforeseen repercussions of something as seemingly innocuous as postage and stationery spending. The knowledge gleaned from this study may not only benefit scholarly dialogues but also evoke a chuckle at the whimsical nature of these unsuspected connections. After all, who would have thought that the humble act of mailing a letter could leave such an indelible mark on the atmosphere? It's almost as surprising as finding a typo in a dictionary!

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The results of our investigation revealed a remarkably strong positive correlation between US household spending on postage and stationery and air pollution in Olympia, Washington. The correlation coefficient of 0.8636410 indicated a robust relationship, and the R-squared value of 0.7458758 demonstrated that approximately 74.6% of the variability in air pollution levels could be explained by changes in household spending on postage and stationery. The p-value of less than 0.01 further underscored the statistical significance of this connection, validating our findings beyond a reasonable doubt.

Upon visual inspection of the data, depicted in Fig. 1, the scatterplot affirmed the strength of the correlation, resembling a constellation of points that align with mathematical precision. This visualization serves as a stark reminder that even in the realm of research, truth can be stranger than fiction, rendering our initial reflection on the topic akin to discovering a pun in a serious conversation.

The robustness of the correlation discovered is as astonishing as finding a needle in a haystack, underlining the unexpected nature of the relationship between household spending on postage and stationery and air pollution levels. Who would have thought that the seemingly innocuous act of purchasing stationery and stamps could be intertwined with the quality of the air we breathe? It's a revelation as surprising as receiving a letter from a long-lost pen pal.

Our findings point to the significance of considering the broader societal and environmental implications of everyday activities. In a world where the interconnectedness of human behavior and environmental outcomes is increasingly recognized, our results provide a whimsical yet insightful addition to the ongoing discourse. Indeed, the connection between US household spending on postage and stationery and air pollution in Olympia, Washington, may just be the stamp of approval on the idea that even the most unexpected relationships can hold weight, much like a letter in the mail.

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 US household spending on postage and stationery and Air pollution in Olympia, Washington. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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]]
Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington

[[ABSTRACT]]
In this study, we delved into the intriguing connection between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic may seem as uninspiring as finding a misplaced penny in the bureaucratic maze, our findings shed a humorous light on the unsuspected relationship between these seemingly unrelated factors.

Utilizing data from the Bureau of Labor Statistics and the Environmental Protection Agency, we embarked on an adventure akin to navigating through endless folders of paperwork in search of a lost document, to investigate whether there existed any correlation between US household spending on postage and stationery and the levels of air pollution in Olympia, Washington. Remarkably, our analysis revealed a correlation coefficient of 0.8636410 and an eye-catching p-value of less than 0.01 for the timeframe spanning 2000 to 2022.

The association we unearthed between the whimsical act of mailing letters and the environmental quality in Olympia, Washington, is no mere triviality; it highlights the interconnectedness of seemingly unrelated spheres of human activity. Indeed, one might say that the pen really is mightier than the smog; a thought as whimsical as a balloon losing air! Our findings may serve as a breath of fresh air in the world of academic research, proving that every envelope and sheet of stationery carries a story, even if it's one about air pollution.

[[LITERATURE REVIEW]]
The study of the correspondence between US household spending on postage and stationery and air pollution in Olympia, Washington has sparked an array of investigations into the peculiar and unexpected connections that underlie seemingly mundane activities. Our exploration led us to uncover a trove of literature that shed light on this whimsical relationship, akin to stumbling upon a hidden punchline in a sea of serious discourse.
In "Letters, Postage, and the Environment" by Smith, the authors find a modest correlation between letter sending and air quality in urban areas, laying the groundwork for our investigation. Following this serious line of inquiry, "The Economics of Stationery" by Doe delves into the expenditure patterns related to stationery purchases, no doubt an essential foundation for our analysis, as we ponder the potential ramifications of paper and pen on environmental factors.
Turning our attention to non-fiction literature, "The Air We Breathe" by Jones provides thought-provoking insights into the intricacies of air pollution, offering a serious perspective that forms the backdrop of our study. Furthermore, "Environmental Impacts: Uncovering the Inconspicuous" by Green speaks to the interconnectedness of human behaviors and environmental consequences, providing a tantalizing hint at the unexpected relationship we are elucidating.
On the fictional front, "Air Mail Mysteries" by Brown, although a work of fiction, has captivated readers with its imaginative exploration of the mystique and intrigue behind mailing letters, an example of the allure that surrounds the postal universe. Similarly, the classic "Stationery Sorcery" by Black weaves a tale of enchantment and wonder within the realm of office supplies, bearing a certain resemblance to the enchanting allure of our unearthing of this relationship.
As we delved further into our rigorous literature review, we found ourselves venturing into unexpected territories, with sources such as "The Secret Life of Envelopes" by Purple, that, while lacking in scholarly rigor, provided unexpected inspiration. Furthermore, we stumbled upon "Air Pollution for Dummies," admittedly not the most erudite source, but, nevertheless, a gateway to understanding the basics of the atmospheric conundrum we were probing.
In a turn of unconventional rigor, our comprehensive literature review also encompassed unconventional sources, including the backs of shampoo bottles found in the office break room – for even in the unlikeliest of places, knowledge may hide. While these sources may not rival the academic standards to which we aspire, they nevertheless serve as a testament to the lengths we went to in uncovering the unexpected relationship between household spending on postage and stationery and air pollution in Olympia, Washington. Such is the nature of academic inquiry – one must sometimes unearth treasure in the most unlikely of forms!

[[RESULTS]]
The results of our investigation revealed a remarkably strong positive correlation between US household spending on postage and stationery and air pollution in Olympia, Washington. The correlation coefficient of 0.8636410 indicated a robust relationship, and the R-squared value of 0.7458758 demonstrated that approximately 74.6% of the variability in air pollution levels could be explained by changes in household spending on postage and stationery. The p-value of less than 0.01 further underscored the statistical significance of this connection, validating our findings beyond a reasonable doubt.
Upon visual inspection of the data, depicted in Fig. 1, the scatterplot affirmed the strength of the correlation, resembling a constellation of points that align with mathematical precision. This visualization serves as a stark reminder that even in the realm of research, truth can be stranger than fiction, rendering our initial reflection on the topic akin to discovering a pun in a serious conversation.
The robustness of the correlation discovered is as astonishing as finding a needle in a haystack, underlining the unexpected nature of the relationship between household spending on postage and stationery and air pollution levels. Who would have thought that the seemingly innocuous act of purchasing stationery and stamps could be intertwined with the quality of the air we breathe? It's a revelation as surprising as receiving a letter from a long-lost pen pal.
Our findings point to the significance of considering the broader societal and environmental implications of everyday activities. In a world where the interconnectedness of human behavior and environmental outcomes is increasingly recognized, our results provide a whimsical yet insightful addition to the ongoing discourse. Indeed, the connection between US household spending on postage and stationery and air pollution in Olympia, Washington, may just be the stamp of approval on the idea that even the most unexpected relationships can hold weight, much like a letter in the mail.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The robust correlation we identified between US household spending on postage and stationery and air pollution levels in Olympia, Washington raises some eyebrow-raising questions about the hidden connections within our daily activities and their impact on the environment. It's as if each stamp and envelope whispers a tale into the ambient air, contributing, puzzlingly, to the atmospheric composition. Our findings provide a compelling case for the consideration of seemingly tangential consumer behaviors in the broader context of environmental quality.

The literature review, as surprisingly varied as a box of assorted chocolates, painted a vivid picture of the unconventional paths we traversed in pursuit of scholarly enlightenment. While the economic analyses and environmental treatises formed the bedrock of our study, the whimsical sources, such as "Air Mail Mysteries" and "Stationery Sorcery," bore an uncanny resemblance to the improbable correspondence we ultimately unveiled. Who would have guessed that literature devoted to the enchantment of mailing letters and the wonder of office supplies would foreshadow our revelatory results?

Our investigation not only supported the existing research but also added a whimsical twist to the ongoing discourse. Much like coming across a magic trick just when the academic dinner party was lulling, our findings injected a sense of astonishment into the serious scholarly conversation on environmental economics. The robust correlation coefficient and the p-value resembling a well-kept secret underscored the gravity of our discovery, akin to uncovering a punchline in a statistical analysis.

Our results, akin to a vending machine unexpectedly dispensing two snacks instead of one, allude to the captivating mystery of the unexplored connections within seemingly ordinary activities. The correlation between household spending on postage and stationery and air pollution levels, as confounding as a riddle wrapped in an enigma, compels a rethinking of the broader impact of consumer behavior on environmental outcomes.

This unconventional relationship is reminiscent of a comedy of errors, wherein the seemingly unrelated orchestrations of daily life intermingle with the solemnity of environmental consequences. As we continue to uncover the hidden absurdity within the ordinary, our findings inspire a whimsical perspective on the profound interconnectedness of human actions and environmental outcomes. Our study may serve as an encouraging nudge to peer beyond the confines of conventionality, inviting researchers to embrace the surprising and unexpected in their scholarly pursuits.

In essence, our research emphasizes the importance of maintaining an open mind in the scholarly pursuit of knowledge. Just as an unexpected quip can enliven a mundane conversation, our unexpected results have injected a touch of whimsy into the analytical dialogue surrounding the intersection of household spending and environmental quality. Much like a well-timed joke, our findings remind us of the possibility of discovering delightful surprises amidst the rigorous pursuit of academic inquiry.

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the 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 US household spending on postage and stationery and Air pollution in Olympia, Washington. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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]]
Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington

[[ABSTRACT]]
In this study, we delved into the intriguing connection between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic may seem as uninspiring as finding a misplaced penny in the bureaucratic maze, our findings shed a humorous light on the unsuspected relationship between these seemingly unrelated factors.

Utilizing data from the Bureau of Labor Statistics and the Environmental Protection Agency, we embarked on an adventure akin to navigating through endless folders of paperwork in search of a lost document, to investigate whether there existed any correlation between US household spending on postage and stationery and the levels of air pollution in Olympia, Washington. Remarkably, our analysis revealed a correlation coefficient of 0.8636410 and an eye-catching p-value of less than 0.01 for the timeframe spanning 2000 to 2022.

The association we unearthed between the whimsical act of mailing letters and the environmental quality in Olympia, Washington, is no mere triviality; it highlights the interconnectedness of seemingly unrelated spheres of human activity. Indeed, one might say that the pen really is mightier than the smog; a thought as whimsical as a balloon losing air! Our findings may serve as a breath of fresh air in the world of academic research, proving that every envelope and sheet of stationery carries a story, even if it's one about air pollution.

[[INTRDUCTION]]
The pursuit of understanding the intricate relationships within socioeconomic and environmental realms has led researchers to explore curious and unexpected connections. In the vein of these endeavors, our study delves into the correlation between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic at first glance may seem as predictable as finding a paperclip in an office, our investigation has unwrapped a surprise package of insights, demonstrating that even the most mundane activities can have unexpected implications for environmental quality.
The act of sending letters and purchasing stationery may appear as simple as pie at first glance, yet these seemingly innocuous behaviors have captured our attention due to their potentially indirect consequences on the air quality in Washington’s capital. It is akin to discovering an Easter egg in the most unexpected spot – a delightful surprise that sparks curiosity and intrigue.
Our decision to embark on this research journey stemmed from an appreciation of the interconnectedness of human actions and their ecological ramifications. Just as a postage stamp adheres to an envelope, our examination sought to uncover the bond between household spending habits and the air we breathe in Olympia. Through meticulous analysis of data from the Bureau of Labor Statistics and the Environmental Protection Agency, we undertook a quest comparable to embarking on a treasure hunt amidst the paperwork labyrinth, seeking to unveil the hidden connections between these facets of modern life.
Indeed, the findings that emerged from our rigorous inquiry brought to light a correlation coefficient of 0.8636410, signaling a significant relationship between household spending on postage and stationery and the levels of air pollution in Olympia, Washington. This discovery is as striking as finding a mint-condition collectible in a dusty attic – a testament to the unforeseen connections that lie beneath the surface of everyday activities.
As we proceed to unravel these findings and their implications, we invite fellow scholars and enthusiasts of peculiar consequentialities to explore with us the unforeseen repercussions of something as seemingly innocuous as postage and stationery spending. The knowledge gleaned from this study may not only benefit scholarly dialogues but also evoke a chuckle at the whimsical nature of these unsuspected connections. After all, who would have thought that the humble act of mailing a letter could leave such an indelible mark on the atmosphere? It's almost as surprising as finding a typo in a dictionary!

[[RESULTS]]
The results of our investigation revealed a remarkably strong positive correlation between US household spending on postage and stationery and air pollution in Olympia, Washington. The correlation coefficient of 0.8636410 indicated a robust relationship, and the R-squared value of 0.7458758 demonstrated that approximately 74.6% of the variability in air pollution levels could be explained by changes in household spending on postage and stationery. The p-value of less than 0.01 further underscored the statistical significance of this connection, validating our findings beyond a reasonable doubt.
Upon visual inspection of the data, depicted in Fig. 1, the scatterplot affirmed the strength of the correlation, resembling a constellation of points that align with mathematical precision. This visualization serves as a stark reminder that even in the realm of research, truth can be stranger than fiction, rendering our initial reflection on the topic akin to discovering a pun in a serious conversation.
The robustness of the correlation discovered is as astonishing as finding a needle in a haystack, underlining the unexpected nature of the relationship between household spending on postage and stationery and air pollution levels. Who would have thought that the seemingly innocuous act of purchasing stationery and stamps could be intertwined with the quality of the air we breathe? It's a revelation as surprising as receiving a letter from a long-lost pen pal.
Our findings point to the significance of considering the broader societal and environmental implications of everyday activities. In a world where the interconnectedness of human behavior and environmental outcomes is increasingly recognized, our results provide a whimsical yet insightful addition to the ongoing discourse. Indeed, the connection between US household spending on postage and stationery and air pollution in Olympia, Washington, may just be the stamp of approval on the idea that even the most unexpected relationships can hold weight, much like a letter in the mail.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our study has unearthed a correlation between US household spending on postage and stationery and air pollution levels in Olympia, Washington, akin to finding a hidden treasure map in a stationery store. The robust correlation coefficient of 0.8636410 and the eye-catching p-value of less than 0.01 provide compelling evidence of this unexpected relationship, leaving us as pleasantly surprised as stumbling upon a funny typo in a research paper.

Our findings elucidate the interconnectedness between seemingly mundane activities and environmental repercussions, illuminating a relationship as quirky as finding a paperclip in a bag of confetti. The visual representation of the data in our scatterplot resembles a constellation of points aligning with meticulous precision, as if the universe itself were sending a message through the art of postage and stationery spending.

One cannot help but ponder the far-reaching implications of our discovery, as vast as the winds carrying the letters we send and receive. The whimsical nature of our findings serves as a reminder that even the most unassuming actions can leave an imprint on the environment, much like a quirky signature at the end of a letter.

In light of these revelations, it is clear that further research in this area is unnecessary, as we have already uncovered a marvel as unexpected as a clown at a board meeting. Thus, we confidently assert that the investigation into the connection between household spending on postage and stationery and air pollution levels in Olympia, Washington, has been satisfactorily stamped and sealed. Time to address other pressing matters - like uncovering the mystery of why pens always seem to go missing!

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 Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington. Respond only with the name of a fictional academic journal.

ChatGPT:

Journal of Quirky Environmental Studies

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of nonprofit research organizations and associations. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding nonprofit, academic, or scientific association or organization that would sponsor research that resulted in a paper entited Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Sustainable Stationery and Air Quality Research

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 Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington with an abstract of In this study, we delved into the intriguing connection between US household spending on postage and stationery and air pollution in Olympia, Washington. While the topic may seem as uninspiring as finding a misplaced penny in the bureaucratic maze, our findings shed a humorous light on the unsuspected relationship between these seemingly unrelated factors.
Utilizing data from the Bureau of Labor Statistics and the Environmental Protection Agency, we embarked on an adventure akin to navigating through endless folders of paperwork in search of a lost document, to investigate whether there existed any correlation between US household spending on postage and stationery and the levels of air pollution in Olympia, Washington. Remarkably, our analysis revealed a correlation coefficient of 0.8636410 and an eye-catching p-value of less than 0.01 for the timeframe spanning 2000 to 2022.
The association we unearthed between the whimsical act of mailing letters and the environmental quality in Olympia, Washington, is no mere triviality; it highlights the interconnectedness of seemingly unrelated spheres of human activity. Indeed, one might say that the pen really is mightier than the smog; a thought as whimsical as a balloon losing air! Our findings may serve as a breath of fresh air in the world of academic research, proving that every envelope and sheet of stationery carries a story, even if it's one about air pollution.

ChatGPT:

US household spending, postage and stationery, air pollution, Olympia Washington, Bureau of Labor Statistics, Environmental Protection Agency, correlation coefficient, p-value, data analysis, interconnectedness, human activity, academic research

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

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Data details

US household spending on postage and stationery
Detailed data title: Annual US household spend on postage and stationery, as a percentage of total household spend
Source: Bureau of Labor Statistics
See what else correlates with US household spending on postage and stationery

Air pollution in Olympia, Washington
Detailed data title: Percentage of days with moderate or worse air quality in Olympia-Tumwater, WA
Source: Environmental Protection Agency
See what else correlates with Air pollution in Olympia, Washington

Correlation r = 0.8636410 (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 = 0.7458758 (Coefficient of determination)
This means 74.6% of the change in the one variable (i.e., Air pollution in Olympia, Washington) is predictable based on the change in the other (i.e., US household spending on postage and stationery) over the 23 years from 2000 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.1E-7.^Show 0.0000001111940830332926800000
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 0.86 in 1.1E-5% of random cases. Said differently, if you correlated 8,993,284 random variables^Note You don't actually need 8 million 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 22 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 22 because we have two variables measured over a period of 23 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.

[ 0.7, 0.94 ] 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.

	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
US household spending on postage and stationery (Household spend)	0.331187	0.30872	0.322049	0.325845	0.357184	0.338296	0.328512	0.306217	0.308997	0.291438	0.274377	0.261543	0.264375	0.273973	0.244883	0.234021	0.239047	0.24975	0.215602	0.19354	0.211954	0.16585	0.175422
Air pollution in Olympia, Washington (Bad air quality days)	0.218579	0.224658	0.252055	0.271978	0.260989	0.238356	0.194521	0.180556	0.198895	0.17033	0.0422535	0.112948	0.166205	0.206044	0.121212	0.12605	0.0601719	0.151515	0.110787	0.115068	0.0710383	0.0151976	0.0603448

Why this works

Data dredging: I have 25,237 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 636,906,169 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.
Outlandish outliers: There are "outliers" in this data.^Note 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. ^{Show the steps to do this.} Step 1: Download and install Python on your computer.

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([0.331187,0.30872,0.322049,0.325845,0.357184,0.338296,0.328512,0.306217,0.308997,0.291438,0.274377,0.261543,0.264375,0.273973,0.244883,0.234021,0.239047,0.24975,0.215602,0.19354,0.211954,0.16585,0.175422,])
array_2 = np.array([0.218579,0.224658,0.252055,0.271978,0.260989,0.238356,0.194521,0.180556,0.198895,0.17033,0.0422535,0.112948,0.166205,0.206044,0.121212,0.12605,0.0601719,0.151515,0.110787,0.115068,0.0710383,0.0151976,0.0603448,])
array_1_name = "US household spending on postage and stationery"
array_2_name = "Air pollution in Olympia, Washington"

# 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 US household spending on postage and stationery
Line chart for only Air pollution in Olympia, Washington
AI-generated correlation image
The spurious research paper: Stamping Out Air Pollution: The Correspondence between US Household Spending on Postage and Stationery and Air Pollution in Olympia, Washington

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Correlation ID: 5407 · Black Variable ID: 19974 · Red Variable ID: 21860


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