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Spurious correlation #3,395 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Prineville, Oregon and the second variable is Global plane crashes.  The chart goes from 1980 to 2022, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

The higher pollution levels created a smokescreen effect, making it harder for pilots to see the ground. This led to an increase in surprise landings and a spike in mid-air collisions, as the planes couldn't spot each other through the hazy skies. It was like a real-life game of aviation hide-and-seek, with the pollution playing the role of the ultimate prankster.

Model: dalle-3
Prompt: A TIME magazine cover image Depicting this scene: In Prineville, Oregon, thick smog hung in the air, obscuring the view of the nearby runway. As planes attempted to take off and land, the pollution particles entered their engines, causing turbulence. A plane struggled to climb, then suddenly nosedived due to poor visibility. This scene mirrored the global trend, as the increasing air pollution led to an uptick in plane crashes worldwide. Enhanced image generation prompt: Create an illustration resembling a TIME magazine cover image. The scene depicts Prineville, Oregon, with the skyline dimly visible through thick, ominous smog. In the foreground, a commercial jet is depicted struggling to ascend, its engines visibly strained by the polluted atmosphere. Another aircraft is shown in a nosedive, symbolizing the perilous impact of the pollution. The image should convey the alarming implications of the global rise in air pollution on air travel. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.
This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: Air pollution in Prineville, Oregon and Global plane crashes. 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 TIME magazine cover image Futuristic An image that looks like it is a scene from a Pixar movie Steampunk a funny image you would see on reddit
ChatGPT: A TIME magazine cover image

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Air pollution in Prineville, Oregon and Global plane crashes, in the following situation: As air pollution in Prineville, Oregon increased, it caused planes to "nose dive" due to decreased visibility. The pollution particles also made their way into the engines, clogging them up and causing "turbulence." The pilots just couldn't "wing it" anymore, leading to an increase in global plane crashes.. Keep the description simple.
ChatGPT: In Prineville, Oregon, thick smog hung in the air, obscuring the view of the nearby runway. As planes attempted to take off and land, the pollution particles entered their engines, causing turbulence. A plane struggled to climb, then suddenly nosedived due to poor visibility. This scene mirrored the global trend, as the increasing air pollution led to an uptick in plane crashes worldwide.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ A TIME magazine cover image ] and depicting this scene: In Prineville, Oregon, thick smog hung in the air, obscuring the view of the nearby runway. As planes attempted to take off and land, the pollution particles entered their engines, causing turbulence. A plane struggled to climb, then suddenly nosedived due to poor visibility. This scene mirrored the global trend, as the increasing air pollution led to an uptick in plane crashes worldwide. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: A TIME magazine cover image Depicting this scene: In Prineville, Oregon, thick smog hung in the air, obscuring the view of the nearby runway. As planes attempted to take off and land, the pollution particles entered their engines, causing turbulence. A plane struggled to climb, then suddenly nosedived due to poor visibility. This scene mirrored the global trend, as the increasing air pollution led to an uptick in plane crashes worldwide. Enhanced image generation prompt: Create an illustration resembling a TIME magazine cover image. The scene depicts Prineville, Oregon, with the skyline dimly visible through thick, ominous smog. In the foreground, a commercial jet is depicted struggling to ascend, its engines visibly strained by the polluted atmosphere. Another aircraft is shown in a nosedive, symbolizing the perilous impact of the pollution. The image should convey the alarming implications of the global rise in air pollution on air travel.

*Variations in the User Prompts from chart to chart are just the result of random number generation in Python. I wrote a few arrays of various styles and methods to ask questions to change up the results. Every time this site writes an explanation or generates an image, the script picks from each at random.

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.

Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how increases in Air pollution in Prineville, Oregon positively influenced Global plane crashes.

AI academic paper

(Because p < 0.01)
Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes

The Journal of Zany Zoological Zoology

Jan 2024

Reminder: This paper is AI-generated. Not real!
Quick note: This sequence is long and repetitive. That's how the prompt engineering works for this one. I manage the output in Python to format it into this PDF.




Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.You write titles and abstracts of goofy academic research papers.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, and add unexpected twists in your writing.

Please draft the title and abstract of an academic research paper presenting the findings of the connection between Air pollution in Prineville, Oregon and Global plane crashes. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Include a pun in the title.

Your research team used data from Environmental Protection Agency and PlaneCrashInfo to assess this nagging question. You found a correlation coefficient of 0.8516236 and p < 0.01 for 1980 to 2022.

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

[[TITLE]]
Lorem ipsum dolor sit

[[ABSTRACT]]
Lorem ipsum dolor sit



ChatGPT:
[[TITLE]]
Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes

[[ABSTRACT]]
Aviation safety and environmental pollution are often studied in isolation, but our research sought to uncover a potential intersection. Utilizing data from the Environmental Protection Agency and PlaneCrashInfo, we conducted a comprehensive analysis to investigate the connection between air pollution levels in Prineville, Oregon, and the occurrence of global plane crashes from 1980 to 2022. Surprisingly, our findings revealed a notable correlation coefficient of 0.8516236 and a statistically significant p-value of less than 0.01, suggesting a strong association between the two seemingly disparate phenomena. This peculiar correlation opens the door to discussions about the impact of localized environmental factors on global aviation incidents. The unexpected nature of our findings underscores the need for interdisciplinary consideration when examining complex systems, proving that, in the world of research, unexpected connections may just be waiting for us in the sky.


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

Please make up the introduction section of an academic research paper presenting the findings of the connection between Air pollution in Prineville, Oregon and Global plane crashes. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Here is the title and abstract of the paper:
[[TITLE]]
Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes

[[ABSTRACT]]
Aviation safety and environmental pollution are often studied in isolation, but our research sought to uncover a potential intersection. Utilizing data from the Environmental Protection Agency and PlaneCrashInfo, we conducted a comprehensive analysis to investigate the connection between air pollution levels in Prineville, Oregon, and the occurrence of global plane crashes from 1980 to 2022. Surprisingly, our findings revealed a notable correlation coefficient of 0.8516236 and a statistically significant p-value of less than 0.01, suggesting a strong association between the two seemingly disparate phenomena. This peculiar correlation opens the door to discussions about the impact of localized environmental factors on global aviation incidents. The unexpected nature of our findings underscores the need for interdisciplinary consideration when examining complex systems, proving that, in the world of research, unexpected connections may just be waiting for us in the sky.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
[[INTRODUCTION]]

When we think of the pristine skies of Prineville, Oregon, we often conjure up images of clear, unpolluted air and the delightful whiff of freshly baked goods from local bakeries. However, beneath this idyllic facade lies a rather unsuspected and, some might say, turbid connection to an entirely unrelated phenomenon - global plane crashes. While this association may seem about as probable as finding a truffle in a haystack, our research has uncovered a hitherto overlooked correlation between the air pollution levels in Prineville and incidents of aviation mishaps around the world.

As seasoned researchers in the realms of environmental science and aeronautics, we have always been taught to keep our feet firmly on the ground and our heads out of the clouds. Yet, our latest foray into the world of statistical analysis has possibly discovered that sometimes it pays to take a leap of faith and look to the skies for unexpected insights. Our groundbreaking findings defy the conventional wisdom in both environmental and aviation research, signalling that the winds of change are blowing in more ways than one.

While the link between local air quality in Prineville and the occurrence of plane crashes on a global scale may seem as unlikely as a Boeing 747 performing loop-de-loops, our data and analysis have demonstrated a striking correlation. The question then becomes not only how Prineville's pollution may be affecting aircraft safety worldwide but also how to address this issue without causing a tailspin in the local economy.

In the following pages, we will embark on a journey through the clouds of statistical analysis, seeking to demystify this unexpected pairing and shed light on the potential mechanisms behind it. While our findings may seem to resemble something out of a Hollywood script, we assure you that our methods have been as rigorous as an FAA inspection, and our conclusions are as solid as the wings of a Boeing Dreamliner. So fasten your seatbelts, stow your tray tables, and prepare for takeoff as we navigate through the uncharted territory where air pollution meets aviation safety. It's bound to be a turbulence-filled, yet enlightening flight.


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

Please make up a literature review section of an academic research paper presenting the findings of the connection between Air pollution in Prineville, Oregon and Global plane crashes. 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 CVS receipts.

Here is the title and abstract of the paper:
[[TITLE]]
Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes

[[ABSTRACT]]
Aviation safety and environmental pollution are often studied in isolation, but our research sought to uncover a potential intersection. Utilizing data from the Environmental Protection Agency and PlaneCrashInfo, we conducted a comprehensive analysis to investigate the connection between air pollution levels in Prineville, Oregon, and the occurrence of global plane crashes from 1980 to 2022. Surprisingly, our findings revealed a notable correlation coefficient of 0.8516236 and a statistically significant p-value of less than 0.01, suggesting a strong association between the two seemingly disparate phenomena. This peculiar correlation opens the door to discussions about the impact of localized environmental factors on global aviation incidents. The unexpected nature of our findings underscores the need for interdisciplinary consideration when examining complex systems, proving that, in the world of research, unexpected connections may just be waiting for us in the sky.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
When we think of the pristine skies of Prineville, Oregon, we often conjure up images of clear, unpolluted air and the delightful whiff of freshly baked goods from local bakeries. However, beneath this idyllic facade lies a rather unsuspected and, some might say, turbid connection to an entirely unrelated phenomenon - global plane crashes. While this association may seem about as probable as finding a truffle in a haystack, our research has uncovered a hitherto overlooked correlation between the air pollution levels in Prineville and incidents of aviation mishaps around the world.
As seasoned researchers in the realms of environmental science and aeronautics, we have always been taught to keep our feet firmly on the ground and our heads out of the clouds. Yet, our latest foray into the world of statistical analysis has possibly discovered that sometimes it pays to take a leap of faith and look to the skies for unexpected insights. Our groundbreaking findings defy the conventional wisdom in both environmental and aviation research, signalling that the winds of change are blowing in more ways than one.
While the link between local air quality in Prineville and the occurrence of plane crashes on a global scale may seem as unlikely as a Boeing 747 performing loop-de-loops, our data and analysis have demonstrated a striking correlation. The question then becomes not only how Prineville's pollution may be affecting aircraft safety worldwide but also how to address this issue without causing a tailspin in the local economy.
In the following pages, we will embark on a journey through the clouds of statistical analysis, seeking to demystify this unexpected pairing and shed light on the potential mechanisms behind it. While our findings may seem to resemble something out of a Hollywood script, we assure you that our methods have been as rigorous as an FAA inspection, and our conclusions are as solid as the wings of a Boeing Dreamliner. So fasten your seatbelts, stow your tray tables, and prepare for takeoff as we navigate through the uncharted territory where air pollution meets aviation safety. It's bound to be a turbulence-filled, yet enlightening flight.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

In "Air Pollution and Its Impact on Global Health," Smith and Doe delve into the complex relationship between air quality and its effects on various domains. While their work primarily focuses on respiratory health and environmental degradation, the implications of localized pollution on distant phenomena remain underexplored. However, their comprehensive review provides a robust foundation for understanding the potential far-reaching consequences of air pollution.

Building upon this foundation, Jones et al. in "Aeronautical Safety: From Theory to Practice" offer a detailed analysis of factors contributing to aviation incidents, emphasizing mechanical failures, human errors, and weather conditions. Yet, the connection between local environmental factors and global flight safety receives only cursory attention, leaving ample room for further investigation.

Moving from non-fiction works to source inspiration from literary pieces often serves as an unconventional yet surprisingly enriching practice. In "Chasing the Scent of Airborne Tragedy," Doe intricately weaves together the mystery of a small town's peculiar air quality with the inexplicable rash of plane crashes across the globe. While the work is classified as fiction, its striking parallels to our research question cannot be dismissed outright.

Transitioning into more speculative and imaginative sources, the renowned novel "Cloudy with a Chance of Crash-landings" by Weatherfield draws readers into a whimsical world where unpredictable weather patterns lead to an unforeseen series of aviation misfortunes. Though firmly nestled in the realm of fiction, the novel's exploration of airborne chaos serves as an unexpected source of inspiration for our inquiry.

In a departure from conventional research practices, we sought to extract valuable insights from sources that may be deemed unorthodox by traditional standards. Amidst these unconventional sources, we happened upon the most unexpected catalyst for our literature review: a comprehensive analysis of CVS receipts. Surprisingly, amidst the cacophony of discounts and promotions, we stumbled upon a revelation that tied together seemingly disparate threads of air pollution and global plane crashes in a manner that was as unexpected as it was utterly ludicrous.

The amalgamation of these diverse sources compelled us to approach our research with a sense of open-mindedness, recognizing that inspiration and knowledge can emerge from the most unassuming of places. Our literature review, therefore, reflects not only the conventional wisdom of academic scholarship but also the unconventional spirit of exploration and ingenuity that propels our quest for knowledge.


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

Please make up the methodology section of an academic research paper presenting the findings of the connection between Air pollution in Prineville, Oregon and Global plane crashes. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and PlaneCrashInfo . You used data from 1980 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]]
Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes

[[ABSTRACT]]
Aviation safety and environmental pollution are often studied in isolation, but our research sought to uncover a potential intersection. Utilizing data from the Environmental Protection Agency and PlaneCrashInfo, we conducted a comprehensive analysis to investigate the connection between air pollution levels in Prineville, Oregon, and the occurrence of global plane crashes from 1980 to 2022. Surprisingly, our findings revealed a notable correlation coefficient of 0.8516236 and a statistically significant p-value of less than 0.01, suggesting a strong association between the two seemingly disparate phenomena. This peculiar correlation opens the door to discussions about the impact of localized environmental factors on global aviation incidents. The unexpected nature of our findings underscores the need for interdisciplinary consideration when examining complex systems, proving that, in the world of research, unexpected connections may just be waiting for us in the sky.

[[INTRODUCTION]]
When we think of the pristine skies of Prineville, Oregon, we often conjure up images of clear, unpolluted air and the delightful whiff of freshly baked goods from local bakeries. However, beneath this idyllic facade lies a rather unsuspected and, some might say, turbid connection to an entirely unrelated phenomenon - global plane crashes. While this association may seem about as probable as finding a truffle in a haystack, our research has uncovered a hitherto overlooked correlation between the air pollution levels in Prineville and incidents of aviation mishaps around the world.
As seasoned researchers in the realms of environmental science and aeronautics, we have always been taught to keep our feet firmly on the ground and our heads out of the clouds. Yet, our latest foray into the world of statistical analysis has possibly discovered that sometimes it pays to take a leap of faith and look to the skies for unexpected insights. Our groundbreaking findings defy the conventional wisdom in both environmental and aviation research, signalling that the winds of change are blowing in more ways than one.
While the link between local air quality in Prineville and the occurrence of plane crashes on a global scale may seem as unlikely as a Boeing 747 performing loop-de-loops, our data and analysis have demonstrated a striking correlation. The question then becomes not only how Prineville's pollution may be affecting aircraft safety worldwide but also how to address this issue without causing a tailspin in the local economy.
In the following pages, we will embark on a journey through the clouds of statistical analysis, seeking to demystify this unexpected pairing and shed light on the potential mechanisms behind it. While our findings may seem to resemble something out of a Hollywood script, we assure you that our methods have been as rigorous as an FAA inspection, and our conclusions are as solid as the wings of a Boeing Dreamliner. So fasten your seatbelts, stow your tray tables, and prepare for takeoff as we navigate through the uncharted territory where air pollution meets aviation safety. It's bound to be a turbulence-filled, yet enlightening flight.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

To tackle this perplexing riddle of the skies, our research team employed a combination of data collection, statistical analysis, and model building akin to an elaborate airplane construction. First, we swooped down on the internet, gathering air quality data from the Environmental Protection Agency (EPA) like seagulls hunting for fish and aircraft crash records from PlaneCrashInfo like archeologists meticulously excavating ancient artifacts. We meticulously compiled information spanning from 1980 to 2022, ensuring our dataset was as comprehensive as a jumbo jet's cargo hold.

Once we amassed our treasure trove of data, we turned to statistical methods as intricate as aircraft navigation systems. We calculated Pearson correlation coefficients and performed regression analyses, navigating through the complex airspace of statistical significance with the precision of an air traffic controller. Our approach was as thorough as a pre-flight checklist, leaving no stone unturned or no engine unexamined in our quest to unravel the mysterious connection between Prineville's pollution and worldwide plane mishaps.

But wait, we didn't stop there! In a daring move reminiscent of an aerobatic stunt, we applied sophisticated time-series analysis to tease out temporal patterns and trends. Our models were as sophisticated as cockpit instruments, allowing us to soar through the turbulence of historical data and discern subtle relationships between air pollution and plane crashes.

In essence, our methodology was a carefully choreographed aeronautical dance between data collection, statistical analysis, and model building, all aimed at shedding light on this unlikely nexus between Prineville's air quality and global aviation accidents. Just like a well-executed maneuver in flight, our research methods were executed with precision, finesse, and, dare we say, a touch of flair.


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

Please make up the results section of an academic research paper presenting the findings of the connection between Air pollution in Prineville, Oregon and Global plane crashes. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

For the time period 1980 to 2022, you found a correlation 0.8516236, r-squared of 0.7252628, 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]]
Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes

[[ABSTRACT]]
Aviation safety and environmental pollution are often studied in isolation, but our research sought to uncover a potential intersection. Utilizing data from the Environmental Protection Agency and PlaneCrashInfo, we conducted a comprehensive analysis to investigate the connection between air pollution levels in Prineville, Oregon, and the occurrence of global plane crashes from 1980 to 2022. Surprisingly, our findings revealed a notable correlation coefficient of 0.8516236 and a statistically significant p-value of less than 0.01, suggesting a strong association between the two seemingly disparate phenomena. This peculiar correlation opens the door to discussions about the impact of localized environmental factors on global aviation incidents. The unexpected nature of our findings underscores the need for interdisciplinary consideration when examining complex systems, proving that, in the world of research, unexpected connections may just be waiting for us in the sky.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
When we think of the pristine skies of Prineville, Oregon, we often conjure up images of clear, unpolluted air and the delightful whiff of freshly baked goods from local bakeries. However, beneath this idyllic facade lies a rather unsuspected and, some might say, turbid connection to an entirely unrelated phenomenon - global plane crashes. While this association may seem about as probable as finding a truffle in a haystack, our research has uncovered a hitherto overlooked correlation between the air pollution levels in Prineville and incidents of aviation mishaps around the world.
As seasoned researchers in the realms of environmental science and aeronautics, we have always been taught to keep our feet firmly on the ground and our heads out of the clouds. Yet, our latest foray into the world of statistical analysis has possibly discovered that sometimes it pays to take a leap of faith and look to the skies for unexpected insights. Our groundbreaking findings defy the conventional wisdom in both environmental and aviation research, signalling that the winds of change are blowing in more ways than one.
While the link between local air quality in Prineville and the occurrence of plane crashes on a global scale may seem as unlikely as a Boeing 747 performing loop-de-loops, our data and analysis have demonstrated a striking correlation. The question then becomes not only how Prineville's pollution may be affecting aircraft safety worldwide but also how to address this issue without causing a tailspin in the local economy.
In the following pages, we will embark on a journey through the clouds of statistical analysis, seeking to demystify this unexpected pairing and shed light on the potential mechanisms behind it. While our findings may seem to resemble something out of a Hollywood script, we assure you that our methods have been as rigorous as an FAA inspection, and our conclusions are as solid as the wings of a Boeing Dreamliner. So fasten your seatbelts, stow your tray tables, and prepare for takeoff as we navigate through the uncharted territory where air pollution meets aviation safety. It's bound to be a turbulence-filled, yet enlightening flight.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

The statistical analysis revealed a substantial and rather surprising correlation between air pollution levels in Prineville, Oregon, and global plane crashes from 1980 to 2022. The correlation coefficient of 0.8516236 indicates a strong positive association, and the coefficient of determination (r-squared) of 0.7252628 suggests that approximately 72.5% of the variation in plane crashes can be explained by changes in air pollution levels. Furthermore, the p-value of less than 0.01 indicates that the correlation is statistically significant, providing compelling evidence for the relationship between these seemingly disparate phenomena.

Figure 1 (to be inserted) depicts a scatterplot that visually illustrates the robust correlation observed between air pollution in Prineville and global plane crashes. The data points convincingly form a pattern reminiscent of a flight path from Prineville to the farthest corners of the world, albeit a rather turbulent one.

The strength of this correlation implies that as air pollution levels in Prineville fluctuated over the years, so too did the occurrence of plane crashes worldwide. This unexpected connection opens the door to a myriad of questions and implications, prompting further investigation into the impact of local environmental factors on global aviation safety.

The findings from this study serve as a striking reminder that sometimes, the most unlikely pairings yield the most fascinating discoveries. While the initial connection between air pollution in a small town and global plane crashes may appear as improbable as finding a pilot who's afraid of heights, our rigorous analysis leaves little doubt about the strength of this association. This peculiar correlation challenges conventional wisdom and underscores the need for interdisciplinary approaches when examining complex phenomena, reminding us that in the world of research, unexpected connections may just be waiting for us in the most unlikely places.


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

Please make up the discussion section of an academic research paper presenting the findings of the connection between Air pollution in Prineville, Oregon and Global plane crashes. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Limit your response to 500 tokens.

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

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

[[TITLE]]
Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes

[[ABSTRACT]]
Aviation safety and environmental pollution are often studied in isolation, but our research sought to uncover a potential intersection. Utilizing data from the Environmental Protection Agency and PlaneCrashInfo, we conducted a comprehensive analysis to investigate the connection between air pollution levels in Prineville, Oregon, and the occurrence of global plane crashes from 1980 to 2022. Surprisingly, our findings revealed a notable correlation coefficient of 0.8516236 and a statistically significant p-value of less than 0.01, suggesting a strong association between the two seemingly disparate phenomena. This peculiar correlation opens the door to discussions about the impact of localized environmental factors on global aviation incidents. The unexpected nature of our findings underscores the need for interdisciplinary consideration when examining complex systems, proving that, in the world of research, unexpected connections may just be waiting for us in the sky.

[[LITERATURE REVIEW]]
In "Air Pollution and Its Impact on Global Health," Smith and Doe delve into the complex relationship between air quality and its effects on various domains. While their work primarily focuses on respiratory health and environmental degradation, the implications of localized pollution on distant phenomena remain underexplored. However, their comprehensive review provides a robust foundation for understanding the potential far-reaching consequences of air pollution.
Building upon this foundation, Jones et al. in "Aeronautical Safety: From Theory to Practice" offer a detailed analysis of factors contributing to aviation incidents, emphasizing mechanical failures, human errors, and weather conditions. Yet, the connection between local environmental factors and global flight safety receives only cursory attention, leaving ample room for further investigation.
Moving from non-fiction works to source inspiration from literary pieces often serves as an unconventional yet surprisingly enriching practice. In "Chasing the Scent of Airborne Tragedy," Doe intricately weaves together the mystery of a small town's peculiar air quality with the inexplicable rash of plane crashes across the globe. While the work is classified as fiction, its striking parallels to our research question cannot be dismissed outright.
Transitioning into more speculative and imaginative sources, the renowned novel "Cloudy with a Chance of Crash-landings" by Weatherfield draws readers into a whimsical world where unpredictable weather patterns lead to an unforeseen series of aviation misfortunes. Though firmly nestled in the realm of fiction, the novel's exploration of airborne chaos serves as an unexpected source of inspiration for our inquiry.
In a departure from conventional research practices, we sought to extract valuable insights from sources that may be deemed unorthodox by traditional standards. Amidst these unconventional sources, we happened upon the most unexpected catalyst for our literature review: a comprehensive analysis of CVS receipts. Surprisingly, amidst the cacophony of discounts and promotions, we stumbled upon a revelation that tied together seemingly disparate threads of air pollution and global plane crashes in a manner that was as unexpected as it was utterly ludicrous.
The amalgamation of these diverse sources compelled us to approach our research with a sense of open-mindedness, recognizing that inspiration and knowledge can emerge from the most unassuming of places. Our literature review, therefore, reflects not only the conventional wisdom of academic scholarship but also the unconventional spirit of exploration and ingenuity that propels our quest for knowledge.

[[RESULTS]]
The statistical analysis revealed a substantial and rather surprising correlation between air pollution levels in Prineville, Oregon, and global plane crashes from 1980 to 2022. The correlation coefficient of 0.8516236 indicates a strong positive association, and the coefficient of determination (r-squared) of 0.7252628 suggests that approximately 72.5% of the variation in plane crashes can be explained by changes in air pollution levels. Furthermore, the p-value of less than 0.01 indicates that the correlation is statistically significant, providing compelling evidence for the relationship between these seemingly disparate phenomena.
Figure 1 (to be inserted) depicts a scatterplot that visually illustrates the robust correlation observed between air pollution in Prineville and global plane crashes. The data points convincingly form a pattern reminiscent of a flight path from Prineville to the farthest corners of the world, albeit a rather turbulent one.
The strength of this correlation implies that as air pollution levels in Prineville fluctuated over the years, so too did the occurrence of plane crashes worldwide. This unexpected connection opens the door to a myriad of questions and implications, prompting further investigation into the impact of local environmental factors on global aviation safety.
The findings from this study serve as a striking reminder that sometimes, the most unlikely pairings yield the most fascinating discoveries. While the initial connection between air pollution in a small town and global plane crashes may appear as improbable as finding a pilot who's afraid of heights, our rigorous analysis leaves little doubt about the strength of this association. This peculiar correlation challenges conventional wisdom and underscores the need for interdisciplinary approaches when examining complex phenomena, reminding us that in the world of research, unexpected connections may just be waiting for us in the most unlikely places.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

The unexpected correlation between air pollution in Prineville, Oregon, and global plane crashes has implications as far-reaching as the jet stream itself. The substantial association we uncovered seems as improbable as a flightless bird piloting a plane, yet our statistically significant findings corroborate the unorthodox relationships hinted at in our literature review.

Our study builds upon the foundational work of Smith and Doe, delving into the unseen interactions between localized air pollution and its effects on seemingly distant domains. While their focus remains primarily on health implications, our findings plow through the clouds to reveal the surprising impact of air pollution on global aviation incidents. Furthermore, the whimsical yet thought-provoking literary sources we perused, such as "Cloudy with a Chance of Crash-landings," may have sparked our initial curiosity, but our rigorous statistical analysis has given these fanciful notions wings, propelling them into the realm of scientific inquiry.

The statistical significance of our correlation coefficient and the coefficient of determination serves as a testament to the robustness of our findings, standing tall like a jumbo jet in a clear sky. While the connection between Prineville's air pollution and global plane crashes may initially seem as far-fetched as a flying pig, our results certainly give one pause—perhaps as much as a sudden spell of turbulence would—a vivid reminder that sometimes, truth is stranger than fiction.

The implications of our research are as vast as the skies themselves, with potential applications ranging from mitigating local pollution to bolstering global aviation safety measures. However, the unexpected nature of our findings also serves as a poignant reminder that the world of research is not unlike a flight path—with each turn and dip revealing the unexpected. As we navigate this uncharted territory, we must remain open to the possibility of connecting seemingly unrelated phenomena and be prepared for whatever surprising discoveries may be waiting for us, whether hidden in the clouds or the most unexpected locations on the ground.


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

Please make up a short conclusion of an academic research paper presenting the findings of the connection between Air pollution in Prineville, Oregon and Global plane crashes. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes

[[ABSTRACT]]
Aviation safety and environmental pollution are often studied in isolation, but our research sought to uncover a potential intersection. Utilizing data from the Environmental Protection Agency and PlaneCrashInfo, we conducted a comprehensive analysis to investigate the connection between air pollution levels in Prineville, Oregon, and the occurrence of global plane crashes from 1980 to 2022. Surprisingly, our findings revealed a notable correlation coefficient of 0.8516236 and a statistically significant p-value of less than 0.01, suggesting a strong association between the two seemingly disparate phenomena. This peculiar correlation opens the door to discussions about the impact of localized environmental factors on global aviation incidents. The unexpected nature of our findings underscores the need for interdisciplinary consideration when examining complex systems, proving that, in the world of research, unexpected connections may just be waiting for us in the sky.

[[INTRDUCTION]]
When we think of the pristine skies of Prineville, Oregon, we often conjure up images of clear, unpolluted air and the delightful whiff of freshly baked goods from local bakeries. However, beneath this idyllic facade lies a rather unsuspected and, some might say, turbid connection to an entirely unrelated phenomenon - global plane crashes. While this association may seem about as probable as finding a truffle in a haystack, our research has uncovered a hitherto overlooked correlation between the air pollution levels in Prineville and incidents of aviation mishaps around the world.
As seasoned researchers in the realms of environmental science and aeronautics, we have always been taught to keep our feet firmly on the ground and our heads out of the clouds. Yet, our latest foray into the world of statistical analysis has possibly discovered that sometimes it pays to take a leap of faith and look to the skies for unexpected insights. Our groundbreaking findings defy the conventional wisdom in both environmental and aviation research, signalling that the winds of change are blowing in more ways than one.
While the link between local air quality in Prineville and the occurrence of plane crashes on a global scale may seem as unlikely as a Boeing 747 performing loop-de-loops, our data and analysis have demonstrated a striking correlation. The question then becomes not only how Prineville's pollution may be affecting aircraft safety worldwide but also how to address this issue without causing a tailspin in the local economy.
In the following pages, we will embark on a journey through the clouds of statistical analysis, seeking to demystify this unexpected pairing and shed light on the potential mechanisms behind it. While our findings may seem to resemble something out of a Hollywood script, we assure you that our methods have been as rigorous as an FAA inspection, and our conclusions are as solid as the wings of a Boeing Dreamliner. So fasten your seatbelts, stow your tray tables, and prepare for takeoff as we navigate through the uncharted territory where air pollution meets aviation safety. It's bound to be a turbulence-filled, yet enlightening flight.

[[RESULTS]]
The statistical analysis revealed a substantial and rather surprising correlation between air pollution levels in Prineville, Oregon, and global plane crashes from 1980 to 2022. The correlation coefficient of 0.8516236 indicates a strong positive association, and the coefficient of determination (r-squared) of 0.7252628 suggests that approximately 72.5% of the variation in plane crashes can be explained by changes in air pollution levels. Furthermore, the p-value of less than 0.01 indicates that the correlation is statistically significant, providing compelling evidence for the relationship between these seemingly disparate phenomena.
Figure 1 (to be inserted) depicts a scatterplot that visually illustrates the robust correlation observed between air pollution in Prineville and global plane crashes. The data points convincingly form a pattern reminiscent of a flight path from Prineville to the farthest corners of the world, albeit a rather turbulent one.
The strength of this correlation implies that as air pollution levels in Prineville fluctuated over the years, so too did the occurrence of plane crashes worldwide. This unexpected connection opens the door to a myriad of questions and implications, prompting further investigation into the impact of local environmental factors on global aviation safety.
The findings from this study serve as a striking reminder that sometimes, the most unlikely pairings yield the most fascinating discoveries. While the initial connection between air pollution in a small town and global plane crashes may appear as improbable as finding a pilot who's afraid of heights, our rigorous analysis leaves little doubt about the strength of this association. This peculiar correlation challenges conventional wisdom and underscores the need for interdisciplinary approaches when examining complex phenomena, reminding us that in the world of research, unexpected connections may just be waiting for us in the most unlikely places.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In conclusion, the results of our study have unveiled an unexpected and rather dizzying association between the air pollution levels in Prineville, Oregon, and the occurrence of global plane crashes. Our findings demonstrate a striking correlation, akin to finding a lost luggage in the Bermuda Triangle, between these seemingly unrelated phenomena, challenging the conventional wisdom in both environmental and aviation research. It appears that the winds of change are blowing through the skies and, much like turbulence during a flight, our understanding of the interconnectedness of seemingly disparate elements is being rattled.

This peculiar correlation raises a myriad of questions, much like a young child experiencing their first flight, prompting further investigation into the impact of localized environmental factors on global aviation safety. The unexpected nature of our findings serves as a potent reminder that in the world of research, just as in take-off procedures, one must always remain prepared for the unexpected.

While the initial connection may seem as unlikely as a pilot flying a paper plane, our research has proven that sometimes, the most unexpected pairings lead to the most astonishing discoveries. Therefore, as we navigate the uncharted territory where air pollution meets aviation safety, we urge our colleagues to keep their aerial senses sharp and lookout for potential connections in the wildest of places.

In light of these findings, we assert that further research in this area may be as unnecessary as having a parachute in a submarine. The robustness and clarity of our results leave little doubt about the strength of the association uncovered in this study, and we believe it is time to steer the focus of our research towards other unexplored territories. As we close the chapter on the air pollution-aviation safety nexus, we can say with confidence that sometimes, the most unexpected pairings lead to the most exhilarating journeys.

In summary, our research has highlighted the need for a broader perspective and a willingness to entertain the most improbable connections, showcasing that, in the world of research, there is always more than meets the eye. Therefore, we direct our attention to new horizons, letting our minds soar beyond this peculiar alchemy between the skies of Prineville and the turbulence of global aviation.


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 Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Zany Zoological Zoology


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 Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes. Respond only with the name of a fictional organization.

ChatGPT:

Society for the Advancement of Unusual Atmospheric Phenomena (SAUAP)


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 Air Affliction: The Unlikely Link Between Prineville's Pollution and Global Plane Crashes with an abstract of Aviation safety and environmental pollution are often studied in isolation, but our research sought to uncover a potential intersection. Utilizing data from the Environmental Protection Agency and PlaneCrashInfo, we conducted a comprehensive analysis to investigate the connection between air pollution levels in Prineville, Oregon, and the occurrence of global plane crashes from 1980 to 2022. Surprisingly, our findings revealed a notable correlation coefficient of 0.8516236 and a statistically significant p-value of less than 0.01, suggesting a strong association between the two seemingly disparate phenomena. This peculiar correlation opens the door to discussions about the impact of localized environmental factors on global aviation incidents. The unexpected nature of our findings underscores the need for interdisciplinary consideration when examining complex systems, proving that, in the world of research, unexpected connections may just be waiting for us in the sky.

ChatGPT:

"Air pollution and aviation safety correlation," "Impact of Prineville pollution on global plane crashes," "Environmental factors and aviation safety," "Prineville, Oregon air quality and plane crashes," "Intersection of air pollution and aviation incidents," "Correlation between local pollution and global plane crashes," "Aviation safety and environmental pollution intersection," "Research on air pollution and plane crash occurrences," "Prineville pollution and international aviation incidents analysis."

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



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Data details

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

Global plane crashes
Source: PlaneCrashInfo
See what else correlates with Global plane crashes

Correlation r = 0.8516236 (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 = 0.7252628 (Coefficient of determination)
This means 72.5% of the change in the one variable (i.e., Global plane crashes) is predictable based on the change in the other (i.e., Air pollution in Prineville, Oregon) over the 43 years from 1980 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 4.5E-13. 0.0000000000004536396159955167
The p-value is a measure of how probable it is that we would randomly find a result this extreme. More specifically the p-value is a measure of how probable it is that we would randomly find a result this extreme if we had only tested one pair of variables one time.

But I am a p-villain. I absolutely did not test only one pair of variables one time. I correlated hundreds of millions of pairs of variables. I threw boatloads of data into an industrial-sized blender to find this correlation.

Who is going to stop me? p-value reporting doesn't require me to report how many calculations I had to go through in order to find a low p-value!
On average, you will find a correaltion as strong as 0.85 in 4.5E-11% of random cases. Said differently, if you correlated 2,204,393,013,175 random variables You don't actually need 2 trillion variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

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

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

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 42 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 42 because we have two variables measured over a period of 43 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.

[ 0.74, 0.92 ] 95% correlation confidence interval (using the Fisher z-transformation)
The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

This one is a bit more complciated than the other calculations, but I include it because many people have been pushing for confidence intervals instead of p-value calculations (for example: NEJM. However, if you are dredging data, you can reliably find yourself in the 5%. That's my goal!


All values for the years included above: If I were being very sneaky, I could trim years from the beginning or end of the datasets to increase the correlation on some pairs of variables. I don't do that because there are already plenty of correlations in my database without monkeying with the years.

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.
1980198119821983198419851986198719881989199019911992199319941995199619971998199920002001200220032004200520062007200820092010201120122013201420152016201720182019202020212022
Air pollution in Prineville, Oregon (Bad air quality days)8.722741.273893.426791.64474000000000000000000000000023.561615.320324.719121.666732.054821.369919.613318.103427.170920.936618.904118.630115.342510.8635
Global plane crashes (Plane crashes)191420181021181822322016192120161820191316141410111381377121541561381221231021011131259011395




Why this works

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

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

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




Try it yourself

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

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

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

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

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

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

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

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

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


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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([8.72274,1.27389,3.42679,1.64474,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,23.5616,15.3203,24.7191,21.6667,32.0548,21.3699,19.6133,18.1034,27.1709,20.9366,18.9041,18.6301,15.3425,10.8635,])
array_2 = np.array([19,14,20,18,10,21,18,18,22,32,20,16,19,21,20,16,18,20,19,13,16,14,14,10,11,13,8,13,7,7,12,154,156,138,122,123,102,101,113,125,90,113,95,])
array_1_name = "Air pollution in Prineville, Oregon"
array_2_name = "Global plane crashes"

# Perform the calculation
print(f"Calculating the correlation between {array_1_name} and {array_2_name}...")
correlation, r_squared, p_value = calculate_correlation(array_1, array_2)

# Print the results
print("Correlation Coefficient:", correlation)
print("R-squared:", r_squared)
print("P-value:", p_value)



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You do not need to attribute "the spurious correlations website," and you don't even need to link here if you don't want to. I don't gain anything from pageviews. There are no ads on this site, there is nothing for sale, and I am not for hire.

For the record, I am just one person. Tyler Vigen, he/him/his. I do have degrees, but they should not go after my name unless you want to annoy my wife. If that is your goal, then go ahead and cite me as "Tyler Vigen, A.A. A.A.S. B.A. J.D." Otherwise it is just "Tyler Vigen."

When spoken, my last name is pronounced "vegan," like I don't eat meat.

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Correlation ID: 3395 · Black Variable ID: 21090 · Red Variable ID: 513
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