Spurious correlation #5,715 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is The distance between Uranus and the Sun and the second variable is Air quality in Anchorage. The chart goes from 1980 to 2023, 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 The distance between Uranus and the Sun and the second variable is Air quality in Anchorage. The chart goes from 1980 to 2023, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As Uranus moved further away, it let out a cosmic toot of relief, creating a gaseous barrier that somehow purified the air in Anchorage. It's as if the universe was just trying to clear the air for the good folks up in Alaska!

^{Show image generation prompt} Model: dalle-3
Prompt: Certainly! How about an image of Uranus with a soft, ethereal glow emanating from its atmosphere, creating a mesmerizing and otherworldly scene? The shimmering barrier of gas would be depicted as a subtle, iridescent sheen around the planet, with Anchorage visible in the distance, bathed in a gentle, clear light. This would convey the sense of cosmic purification and the intriguing connection between the distant planet and the earthly city. 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: The distance between Uranus and the Sun and Air quality in Anchorage. 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 Polaroid photo A photo-realistic image Realistic Glitch art A scene from Skyrim
ChatGPT: A photo-realistic 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 The distance between Uranus and the Sun and Air quality in Anchorage, in the following situation: As Uranus moved further away, it let out a cosmic toot of relief, creating a gaseous barrier that somehow purified the air in Anchorage. It's as if the universe was just trying to clear the air for the good folks up in Alaska!. Keep the description simple.
ChatGPT: As Uranus drifted further away from the Sun, a gentle cosmic toot released, creating a shimmering barrier of gas around the planet. Down on Earth, in Anchorage, the air seemed to clear magically, as if the universe itself was purifying the atmosphere for the city's residents.

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 photo-realistic image ] and depicting this scene: As Uranus drifted further away from the Sun, a gentle cosmic toot released, creating a shimmering barrier of gas around the planet. Down on Earth, in Anchorage, the air seemed to clear magically, as if the universe itself was purifying the atmosphere for the city's residents. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Certainly! How about an image of Uranus with a soft, ethereal glow emanating from its atmosphere, creating a mesmerizing and otherworldly scene? The shimmering barrier of gas would be depicted as a subtle, iridescent sheen around the planet, with Anchorage visible in the distance, bathed in a gentle, clear light. This would convey the sense of cosmic purification and the intriguing connection between the distant planet and the earthly city.

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

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.
^{Show prompt for explanation} Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how an increase in The distance between Uranus and the Sun caused Air quality in Anchorage to increase.

AI academic paper

(Because p < 0.01)

The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage

The International Journal of Planetary Ecology

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

Please make up a literature review section of an academic research paper presenting the findings of the connection between The distance between Uranus and the Sun and Air quality in Anchorage. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Perhaps you also got inspiration from some board games that are vaugely related.

Here is the title and abstract of the paper:
[[TITLE]]
"The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage"

[[ABSTRACT]]
This paper delves into the often overlooked interplanetary forces influencing air quality in terrestrial cities. Do the celestial bodies beyond the asteroid belt have a say in the air we breathe? Utilizing data from Astropy and the Environmental Protection Agency, we set out to investigate the potential correlation between the distance from Uranus to the Sun and air quality in Anchorage, Alaska. Our findings reveal a surprising link that is sure to turn heads faster than the rotation period of Uranus itself! With a correlation coefficient of 0.8025352 and a p-value < 0.01 covering the years 1980 to 2023, our results suggest that Uranus may indeed have a "gassy" influence on air quality in Anchorage.

Every 30.687 Earth years, Uranus completes an orbit around the Sun, but it seems its influence may extend much farther than its mighty rings. Could it be that the gaseous giant is not content with merely being the butt of planetary jokes, but desires to leave its mark on Earth as well? These findings open up a whole new dimension to understanding interplanetary relationships and their very down-to-earth impacts. So the next time you take a deep breath in Anchorage, remember—Uranus may be farther away, but its presence is unexpectedly close!

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The relationship between celestial bodies and terrestrial phenomena has long been a subject of fascination and speculation. While the gravitational influences of the sun and moon on Earth are well-documented, the potential impact of more distant planets, such as Uranus, on our daily lives has been a topic of much less scientific inquiry. This paper seeks to bridge the gap between outer space and the air we breathe, exploring the relationship between Uranus' distance from the Sun and air quality in Anchorage, Alaska.
It is often said that the position of Uranus is so far from the Sun that it might as well be in a different solar system entirely. However, our findings suggest that this distant gas giant may have a more direct impact on the air quality of a city thousands of miles away than previously thought. This revelation is sure to make even the most serious of astronomers crack a smile wider than the rings of Saturn.
The city of Anchorage, nestled amongst the rugged terrain of Alaska, provides an intriguing location for such a study. Known for its stunning natural beauty, it also faces unique air quality challenges due to its geographic location and climatic conditions. By examining air quality data from Anchorage in relation to the varying distance between Uranus and the Sun, we aim to shed light on a potential connection that is as surprising as finding water on Mars.
The theoretical foundation for this study draws from an understanding of atmospheric dynamics and the complexities of interplanetary gravitational forces. While the distance between Uranus and the Sun may seem remote and inconsequential to life on Earth, our analysis uncovers a statistical relationship that is as strong as the gravitational pull of a massive planet – a correlation coefficient of 0.8025352 that can't be written off as just another cosmic coincidence.
Our investigation harkens back to the age-old question of whether distant celestial bodies hold sway over our terrestrial affairs. It appears that Uranus, with its distant yet impactful presence, may have a more significant role in shaping our daily environment than previously imagined. As Mark Twain once humorously noted, "Everyone is a moon, and has a dark side which he never shows to anybody." Similarly, Uranus may have a hidden influence on our planet, affecting even the air we breathe in unexpected ways.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The possibility of a connection between the distance of Uranus from the Sun and air quality in terrestrial urban environments has been a subject of limited scientific exploration. In "Celestial Bodies and Terrestrial Phenomena" by Smith et al., the authors briefly mention the potential interplanetary influences on atmospheric conditions but do not delve into specific planetary relationships.

Moving further into the literature, in "Planetary Dynamics and Their Terrestrial Implications" by Doe, the concept of planetary distances and their impact on Earth's atmospheric composition is discussed. However, the focus remains primarily on the gravitational effects of closer celestial bodies, such as the sun and moon, with only passing reference to the more remote planets.

However, our search widened to include "The Atmospheric Influence of Outer Space Entities" by Jones, which explores the potential connections between distant celestial bodies and earthly environmental conditions. This study raises the possibility of a broader planetary influence on air quality, hinting at a need for further investigation into the more outer reaches of our solar system.

Diving into more popular literature, "The Fabric of the Cosmos" by Brian Greene, while not directly addressing the Uranus-Sun distance and air quality connection, provides valuable insight into the interplay of celestial bodies and their potential influence on the world we inhabit.

In a rather unusual turn, "The Hitchhiker's Guide to the Galaxy" by Douglas Adams offers a humorous take on the cosmic intricacies, including the comedic potential of planetary nomenclature. While not a scientific source, it does raise the question: could Uranus, with its "gassy" nature, be leaving a far-reaching impact on our terrestrial atmosphere?

It is worth noting that the board game "Cosmic Encounter" provides an interesting perspective on the interactions between alien species, each representing a different planet, and the negotiation of influence and alliances – a concept that may not be entirely dissimilar from the potential interplanetary negotiations influencing Earth's air quality.

Now, let us take a breath and explore the surprising correlations revealed by our investigation into the atmospheric dynamics influenced by the distant yet powerful presence of Uranus.

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

Please make up the methodology section of an academic research paper presenting the findings of the connection between The distance between Uranus and the Sun and Air quality in Anchorage. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. 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 Caclculated using Astropy and Environmental Protection Agency . You used data from 1980 to 2023

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]]
"The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage"

[[ABSTRACT]]
This paper delves into the often overlooked interplanetary forces influencing air quality in terrestrial cities. Do the celestial bodies beyond the asteroid belt have a say in the air we breathe? Utilizing data from Astropy and the Environmental Protection Agency, we set out to investigate the potential correlation between the distance from Uranus to the Sun and air quality in Anchorage, Alaska. Our findings reveal a surprising link that is sure to turn heads faster than the rotation period of Uranus itself! With a correlation coefficient of 0.8025352 and a p-value < 0.01 covering the years 1980 to 2023, our results suggest that Uranus may indeed have a "gassy" influence on air quality in Anchorage.

Every 30.687 Earth years, Uranus completes an orbit around the Sun, but it seems its influence may extend much farther than its mighty rings. Could it be that the gaseous giant is not content with merely being the butt of planetary jokes, but desires to leave its mark on Earth as well? These findings open up a whole new dimension to understanding interplanetary relationships and their very down-to-earth impacts. So the next time you take a deep breath in Anchorage, remember—Uranus may be farther away, but its presence is unexpectedly close!

[[INTRODUCTION]]
The relationship between celestial bodies and terrestrial phenomena has long been a subject of fascination and speculation. While the gravitational influences of the sun and moon on Earth are well-documented, the potential impact of more distant planets, such as Uranus, on our daily lives has been a topic of much less scientific inquiry. This paper seeks to bridge the gap between outer space and the air we breathe, exploring the relationship between Uranus' distance from the Sun and air quality in Anchorage, Alaska.
It is often said that the position of Uranus is so far from the Sun that it might as well be in a different solar system entirely. However, our findings suggest that this distant gas giant may have a more direct impact on the air quality of a city thousands of miles away than previously thought. This revelation is sure to make even the most serious of astronomers crack a smile wider than the rings of Saturn.
The city of Anchorage, nestled amongst the rugged terrain of Alaska, provides an intriguing location for such a study. Known for its stunning natural beauty, it also faces unique air quality challenges due to its geographic location and climatic conditions. By examining air quality data from Anchorage in relation to the varying distance between Uranus and the Sun, we aim to shed light on a potential connection that is as surprising as finding water on Mars.
The theoretical foundation for this study draws from an understanding of atmospheric dynamics and the complexities of interplanetary gravitational forces. While the distance between Uranus and the Sun may seem remote and inconsequential to life on Earth, our analysis uncovers a statistical relationship that is as strong as the gravitational pull of a massive planet – a correlation coefficient of 0.8025352 that can't be written off as just another cosmic coincidence.
Our investigation harkens back to the age-old question of whether distant celestial bodies hold sway over our terrestrial affairs. It appears that Uranus, with its distant yet impactful presence, may have a more significant role in shaping our daily environment than previously imagined. As Mark Twain once humorously noted, "Everyone is a moon, and has a dark side which he never shows to anybody." Similarly, Uranus may have a hidden influence on our planet, affecting even the air we breathe in unexpected ways.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

In order to examine the potential correlation between the distance from Uranus to the Sun and air quality in Anchorage, Alaska, we utilized a multifaceted approach that spanned both astronomical and atmospheric data sources. The distance between Uranus and the Sun was calculated using the Astropy package, which provided precise astronomical data spanning the years from 1980 to 2023. This data was then cross-referenced with air quality measurements obtained from the Environmental Protection Agency's extensive database. Our data collection process was as rigorous as a rocket launch, leaving no stone unturned in our quest for interplanetary insight.

To ensure the reliability and validity of our findings, a meticulously constructed analytical framework was employed. First, we conducted a thorough review of existing literature on planetary influences on Earth's atmosphere, mining through scholarly works with the enthusiasm of a prospector seeking cosmic nuggets of wisdom. Subsequently, the gathered astronomical and atmospheric datasets were subjected to rigorous statistical analyses to uncover any potential correlation between the distance from Uranus to the Sun and air quality in Anchorage.

The statistical analyses encompassed a range of sophisticated techniques, including time series analysis, bivariate correlation tests, and multivariate regression models. These methods were employed with the precision of a telescope, allowing us to carefully examine the relationships between Uranus' distance from the Sun and various air quality parameters in Anchorage. Every statistical test and model was scrutinized with the attentiveness of an astrophysicist searching for a new celestial body, ensuring that our results were not mere statistical flukes.

As the saying goes, "When you're feeling stressed, just remember that you're as statistically significant as a p-value less than 0.01." Accordingly, we set a strict threshold for statistical significance at a p-value < 0.01, maintaining a level of confidence that would make even the most skeptical scientist reconsider their cosmic beliefs. This allowed us to identify meaningful relationships between the distance from Uranus to the Sun and air quality in Anchorage, illuminating a connection that is more tangible than the rings of Saturn.

In addition to purely statistical methods, our research incorporated qualitative assessments of broader environmental patterns and historical fluctuations in air quality. We sought to contextualize our statistical findings within the larger narrative of atmospheric dynamics in the Alaskan region, recognizing that correlations, much like planets, do not exist in isolation.

The comprehensive and interdisciplinary nature of our methodology reflects our commitment to exploring the intersection of celestial mechanics and terrestrial atmospherics with the seriousness of an astronomer and the levity of a cosmic jester.

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

Please make up the results section of an academic research paper presenting the findings of the connection between The distance between Uranus and the Sun and Air quality in Anchorage. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. 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 Caclculated using Astropy and Environmental Protection Agency .

For the time period 1980 to 2023, you found a correlation 0.8025352, r-squared of 0.6440628, 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]]
"The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage"

[[ABSTRACT]]
This paper delves into the often overlooked interplanetary forces influencing air quality in terrestrial cities. Do the celestial bodies beyond the asteroid belt have a say in the air we breathe? Utilizing data from Astropy and the Environmental Protection Agency, we set out to investigate the potential correlation between the distance from Uranus to the Sun and air quality in Anchorage, Alaska. Our findings reveal a surprising link that is sure to turn heads faster than the rotation period of Uranus itself! With a correlation coefficient of 0.8025352 and a p-value < 0.01 covering the years 1980 to 2023, our results suggest that Uranus may indeed have a "gassy" influence on air quality in Anchorage.

Every 30.687 Earth years, Uranus completes an orbit around the Sun, but it seems its influence may extend much farther than its mighty rings. Could it be that the gaseous giant is not content with merely being the butt of planetary jokes, but desires to leave its mark on Earth as well? These findings open up a whole new dimension to understanding interplanetary relationships and their very down-to-earth impacts. So the next time you take a deep breath in Anchorage, remember—Uranus may be farther away, but its presence is unexpectedly close!

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The relationship between celestial bodies and terrestrial phenomena has long been a subject of fascination and speculation. While the gravitational influences of the sun and moon on Earth are well-documented, the potential impact of more distant planets, such as Uranus, on our daily lives has been a topic of much less scientific inquiry. This paper seeks to bridge the gap between outer space and the air we breathe, exploring the relationship between Uranus' distance from the Sun and air quality in Anchorage, Alaska.
It is often said that the position of Uranus is so far from the Sun that it might as well be in a different solar system entirely. However, our findings suggest that this distant gas giant may have a more direct impact on the air quality of a city thousands of miles away than previously thought. This revelation is sure to make even the most serious of astronomers crack a smile wider than the rings of Saturn.
The city of Anchorage, nestled amongst the rugged terrain of Alaska, provides an intriguing location for such a study. Known for its stunning natural beauty, it also faces unique air quality challenges due to its geographic location and climatic conditions. By examining air quality data from Anchorage in relation to the varying distance between Uranus and the Sun, we aim to shed light on a potential connection that is as surprising as finding water on Mars.
The theoretical foundation for this study draws from an understanding of atmospheric dynamics and the complexities of interplanetary gravitational forces. While the distance between Uranus and the Sun may seem remote and inconsequential to life on Earth, our analysis uncovers a statistical relationship that is as strong as the gravitational pull of a massive planet – a correlation coefficient of 0.8025352 that can't be written off as just another cosmic coincidence.
Our investigation harkens back to the age-old question of whether distant celestial bodies hold sway over our terrestrial affairs. It appears that Uranus, with its distant yet impactful presence, may have a more significant role in shaping our daily environment than previously imagined. As Mark Twain once humorously noted, "Everyone is a moon, and has a dark side which he never shows to anybody." Similarly, Uranus may have a hidden influence on our planet, affecting even the air we breathe in unexpected ways.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The analysis of the data revealed a notable correlation between the distance of Uranus from the Sun and air quality in Anchorage, Alaska. The correlation coefficient of 0.8025352 suggests a strong positive relationship between these two variables. This implies that as Uranus moves farther from the Sun, air quality in Anchorage tends to deteriorate. It seems that even on a cosmic scale, distance does indeed make the heart grow faint!

The r-squared value of 0.6440628 indicates that approximately 64.41% of the variability in air quality in Anchorage can be explained by the distance between Uranus and the Sun. This finding further supports the notion of a substantial connection between these seemingly disparate phenomena. It’s as if the gravitational pull of Uranus is not content with merely influencing its moons, but also seeks to extend its ethereal embrace to the distant city of Anchorage.

The p-value of less than 0.01 provides strong evidence against the null hypothesis, bolstering the assertion that there is indeed a significant relationship between Uranus' distance from the Sun and air quality in Anchorage. One could say that the probability of this correlation occurring by chance is about as likely as spotting a shooting star on a cloudy night – highly improbable!

The scatterplot (Fig. 1) visually depicts the strong positive correlation between the distance of Uranus from the Sun and air quality in Anchorage, with the data points clustering in a manner that echoes the gravitational dance between these celestial bodies. It appears that even in the vast expanse of space, the influence of Uranus can be felt in the atmospheric composition of a city thousands of miles away. It's a reminder that when it comes to planetary dynamics, we should never underestimate the far-reaching impact of even the most distant of neighbors.

In summary, our analysis uncovers a hitherto unexplored relationship between the position of Uranus in the solar system and air quality in Anchorage. These findings not only expand our understanding of interplanetary influences on terrestrial phenomena but also provide a cosmic twist to the study of air quality dynamics. As Carl Sagan said, "Somewhere, something incredible is waiting to be known." Indeed, the connection between Uranus and air quality in Anchorage has proven to be an unexpected and noteworthy revelation, shedding light on a celestial influence that is closer than it appears.

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

Please make up the discussion section of an academic research paper presenting the findings of the connection between The distance between Uranus and the Sun and Air quality in Anchorage. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. 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]]
"The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage"

[[ABSTRACT]]
This paper delves into the often overlooked interplanetary forces influencing air quality in terrestrial cities. Do the celestial bodies beyond the asteroid belt have a say in the air we breathe? Utilizing data from Astropy and the Environmental Protection Agency, we set out to investigate the potential correlation between the distance from Uranus to the Sun and air quality in Anchorage, Alaska. Our findings reveal a surprising link that is sure to turn heads faster than the rotation period of Uranus itself! With a correlation coefficient of 0.8025352 and a p-value < 0.01 covering the years 1980 to 2023, our results suggest that Uranus may indeed have a "gassy" influence on air quality in Anchorage.

Every 30.687 Earth years, Uranus completes an orbit around the Sun, but it seems its influence may extend much farther than its mighty rings. Could it be that the gaseous giant is not content with merely being the butt of planetary jokes, but desires to leave its mark on Earth as well? These findings open up a whole new dimension to understanding interplanetary relationships and their very down-to-earth impacts. So the next time you take a deep breath in Anchorage, remember—Uranus may be farther away, but its presence is unexpectedly close!

[[LITERATURE REVIEW]]
The possibility of a connection between the distance of Uranus from the Sun and air quality in terrestrial urban environments has been a subject of limited scientific exploration. In "Celestial Bodies and Terrestrial Phenomena" by Smith et al., the authors briefly mention the potential interplanetary influences on atmospheric conditions but do not delve into specific planetary relationships.
Moving further into the literature, in "Planetary Dynamics and Their Terrestrial Implications" by Doe, the concept of planetary distances and their impact on Earth's atmospheric composition is discussed. However, the focus remains primarily on the gravitational effects of closer celestial bodies, such as the sun and moon, with only passing reference to the more remote planets.
However, our search widened to include "The Atmospheric Influence of Outer Space Entities" by Jones, which explores the potential connections between distant celestial bodies and earthly environmental conditions. This study raises the possibility of a broader planetary influence on air quality, hinting at a need for further investigation into the more outer reaches of our solar system.
Diving into more popular literature, "The Fabric of the Cosmos" by Brian Greene, while not directly addressing the Uranus-Sun distance and air quality connection, provides valuable insight into the interplay of celestial bodies and their potential influence on the world we inhabit.
In a rather unusual turn, "The Hitchhiker's Guide to the Galaxy" by Douglas Adams offers a humorous take on the cosmic intricacies, including the comedic potential of planetary nomenclature. While not a scientific source, it does raise the question: could Uranus, with its "gassy" nature, be leaving a far-reaching impact on our terrestrial atmosphere?
It is worth noting that the board game "Cosmic Encounter" provides an interesting perspective on the interactions between alien species, each representing a different planet, and the negotiation of influence and alliances – a concept that may not be entirely dissimilar from the potential interplanetary negotiations influencing Earth's air quality.
Now, let us take a breath and explore the surprising correlations revealed by our investigation into the atmospheric dynamics influenced by the distant yet powerful presence of Uranus.

[[RESULTS]]
The analysis of the data revealed a notable correlation between the distance of Uranus from the Sun and air quality in Anchorage, Alaska. The correlation coefficient of 0.8025352 suggests a strong positive relationship between these two variables. This implies that as Uranus moves farther from the Sun, air quality in Anchorage tends to deteriorate. It seems that even on a cosmic scale, distance does indeed make the heart grow faint!
The r-squared value of 0.6440628 indicates that approximately 64.41% of the variability in air quality in Anchorage can be explained by the distance between Uranus and the Sun. This finding further supports the notion of a substantial connection between these seemingly disparate phenomena. It’s as if the gravitational pull of Uranus is not content with merely influencing its moons, but also seeks to extend its ethereal embrace to the distant city of Anchorage.
The p-value of less than 0.01 provides strong evidence against the null hypothesis, bolstering the assertion that there is indeed a significant relationship between Uranus' distance from the Sun and air quality in Anchorage. One could say that the probability of this correlation occurring by chance is about as likely as spotting a shooting star on a cloudy night – highly improbable!
The scatterplot (Fig. 1) visually depicts the strong positive correlation between the distance of Uranus from the Sun and air quality in Anchorage, with the data points clustering in a manner that echoes the gravitational dance between these celestial bodies. It appears that even in the vast expanse of space, the influence of Uranus can be felt in the atmospheric composition of a city thousands of miles away. It's a reminder that when it comes to planetary dynamics, we should never underestimate the far-reaching impact of even the most distant of neighbors.
In summary, our analysis uncovers a hitherto unexplored relationship between the position of Uranus in the solar system and air quality in Anchorage. These findings not only expand our understanding of interplanetary influences on terrestrial phenomena but also provide a cosmic twist to the study of air quality dynamics. As Carl Sagan said, "Somewhere, something incredible is waiting to be known." Indeed, the connection between Uranus and air quality in Anchorage has proven to be an unexpected and noteworthy revelation, shedding light on a celestial influence that is closer than it appears.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of our study provide compelling evidence to support the hypothesis that the distance of Uranus from the Sun is indeed correlated with air quality in Anchorage, Alaska. This unexpected relationship sheds light on the broader impact of celestial bodies on terrestrial environmental conditions, highlighting the complexities of interplanetary influences on our own planet. The correlation coefficient of 0.8025352 and the r-squared value of 0.6440628 demonstrate a substantial and meaningful association between these two seemingly divergent phenomena.

The findings of our study align with the previous research on planetary dynamics and their potential effects on terrestrial atmospheric composition. The work of Doe, which primarily focused on the gravitational influences of closer celestial bodies, did not explicitly explore the relationship between distant planets and air quality. However, our study's results suggest that the gaseous giant Uranus may indeed exert a palpable influence on the air composition in Anchorage, inviting a reevaluation of the breadth of planetary impacts on Earth's environment.

It is worth noting the light-hearted yet prescient discussion in "The Hitchhiker's Guide to the Galaxy" by Douglas Adams, which humorously addresses the potential far-reaching effects of Uranus's characteristically gassy nature. While not a scientific treatise, it inadvertently raises a thought-provoking question about the broader planetary influence on terrestrial phenomena. Our findings support the notion that even the most distant of planetary neighbors can have an appreciable impact on the air quality of a city thousands of miles away, echoing Adams's humorously intuitive exploration of cosmic intricacies.

Furthermore, the inclusion of "Cosmic Encounter," a board game that explores the interactions between alien species, each representing a different planet, offers an intriguing parallel to our study's findings. The negotiation of influence and alliances among the alien species in the game may not be entirely dissimilar to the potential interplanetary negotiations influencing Earth's air quality—albeit in a more metaphorical sense. Our results suggest that Uranus, with its "gassy" nature, may indeed be leaving a palpable imprint on the air quality in Anchorage, underscoring the surprising breadth of planetary influence on terrestrial environments.

In conclusion, this study has revealed a compelling correlation between the distance of Uranus from the Sun and air quality in Anchorage, expanding our understanding of the intricate relationships between planetary dynamics and terrestrial phenomena. These findings open up new avenues for research into the far-reaching impact of celestial bodies on our own planet, reaffirming the significance of considering the broader cosmic context in understanding Earth's environmental dynamics. So, the next time you take a deep breath in Anchorage, remember—Uranus may be farther away, but its presence is unexpectedly close!

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

Please make up a short conclusion of an academic research paper presenting the findings of the connection between The distance between Uranus and the Sun and Air quality in Anchorage. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. 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]]
"The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage"

[[ABSTRACT]]
This paper delves into the often overlooked interplanetary forces influencing air quality in terrestrial cities. Do the celestial bodies beyond the asteroid belt have a say in the air we breathe? Utilizing data from Astropy and the Environmental Protection Agency, we set out to investigate the potential correlation between the distance from Uranus to the Sun and air quality in Anchorage, Alaska. Our findings reveal a surprising link that is sure to turn heads faster than the rotation period of Uranus itself! With a correlation coefficient of 0.8025352 and a p-value < 0.01 covering the years 1980 to 2023, our results suggest that Uranus may indeed have a "gassy" influence on air quality in Anchorage.

Every 30.687 Earth years, Uranus completes an orbit around the Sun, but it seems its influence may extend much farther than its mighty rings. Could it be that the gaseous giant is not content with merely being the butt of planetary jokes, but desires to leave its mark on Earth as well? These findings open up a whole new dimension to understanding interplanetary relationships and their very down-to-earth impacts. So the next time you take a deep breath in Anchorage, remember—Uranus may be farther away, but its presence is unexpectedly close!

[[INTRDUCTION]]
The relationship between celestial bodies and terrestrial phenomena has long been a subject of fascination and speculation. While the gravitational influences of the sun and moon on Earth are well-documented, the potential impact of more distant planets, such as Uranus, on our daily lives has been a topic of much less scientific inquiry. This paper seeks to bridge the gap between outer space and the air we breathe, exploring the relationship between Uranus' distance from the Sun and air quality in Anchorage, Alaska.
It is often said that the position of Uranus is so far from the Sun that it might as well be in a different solar system entirely. However, our findings suggest that this distant gas giant may have a more direct impact on the air quality of a city thousands of miles away than previously thought. This revelation is sure to make even the most serious of astronomers crack a smile wider than the rings of Saturn.
The city of Anchorage, nestled amongst the rugged terrain of Alaska, provides an intriguing location for such a study. Known for its stunning natural beauty, it also faces unique air quality challenges due to its geographic location and climatic conditions. By examining air quality data from Anchorage in relation to the varying distance between Uranus and the Sun, we aim to shed light on a potential connection that is as surprising as finding water on Mars.
The theoretical foundation for this study draws from an understanding of atmospheric dynamics and the complexities of interplanetary gravitational forces. While the distance between Uranus and the Sun may seem remote and inconsequential to life on Earth, our analysis uncovers a statistical relationship that is as strong as the gravitational pull of a massive planet – a correlation coefficient of 0.8025352 that can't be written off as just another cosmic coincidence.
Our investigation harkens back to the age-old question of whether distant celestial bodies hold sway over our terrestrial affairs. It appears that Uranus, with its distant yet impactful presence, may have a more significant role in shaping our daily environment than previously imagined. As Mark Twain once humorously noted, "Everyone is a moon, and has a dark side which he never shows to anybody." Similarly, Uranus may have a hidden influence on our planet, affecting even the air we breathe in unexpected ways.

[[RESULTS]]
The analysis of the data revealed a notable correlation between the distance of Uranus from the Sun and air quality in Anchorage, Alaska. The correlation coefficient of 0.8025352 suggests a strong positive relationship between these two variables. This implies that as Uranus moves farther from the Sun, air quality in Anchorage tends to deteriorate. It seems that even on a cosmic scale, distance does indeed make the heart grow faint!
The r-squared value of 0.6440628 indicates that approximately 64.41% of the variability in air quality in Anchorage can be explained by the distance between Uranus and the Sun. This finding further supports the notion of a substantial connection between these seemingly disparate phenomena. It’s as if the gravitational pull of Uranus is not content with merely influencing its moons, but also seeks to extend its ethereal embrace to the distant city of Anchorage.
The p-value of less than 0.01 provides strong evidence against the null hypothesis, bolstering the assertion that there is indeed a significant relationship between Uranus' distance from the Sun and air quality in Anchorage. One could say that the probability of this correlation occurring by chance is about as likely as spotting a shooting star on a cloudy night – highly improbable!
The scatterplot (Fig. 1) visually depicts the strong positive correlation between the distance of Uranus from the Sun and air quality in Anchorage, with the data points clustering in a manner that echoes the gravitational dance between these celestial bodies. It appears that even in the vast expanse of space, the influence of Uranus can be felt in the atmospheric composition of a city thousands of miles away. It's a reminder that when it comes to planetary dynamics, we should never underestimate the far-reaching impact of even the most distant of neighbors.
In summary, our analysis uncovers a hitherto unexplored relationship between the position of Uranus in the solar system and air quality in Anchorage. These findings not only expand our understanding of interplanetary influences on terrestrial phenomena but also provide a cosmic twist to the study of air quality dynamics. As Carl Sagan said, "Somewhere, something incredible is waiting to be known." Indeed, the connection between Uranus and air quality in Anchorage has proven to be an unexpected and noteworthy revelation, shedding light on a celestial influence that is closer than it appears.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our research has unveiled a compelling relationship between the distance of Uranus from the Sun and air quality in Anchorage, Alaska. The robust correlation coefficient of 0.8025352 and the significantly low p-value provide strong evidence of a connection that is as undeniable as the gravitational pull of a massive planet. Much like the gravitational force of Uranus, this correlation exerts a considerable influence on the field of atmospheric dynamics, expanding our knowledge of the interplay between celestial bodies and terrestrial environments.

Furthermore, the scatterplot depicts a visually striking positive correlation, with data points aligning in a manner reminiscent of the elegant dance of the celestial bodies. It's as if Uranus is performing a cosmic waltz, with Anchorage's air quality as its enchanted partner. One might even jest that in the grand celestial ballroom, Uranus is leading the atmosphere of Anchorage in an atmospheric tango!

The r-squared value of 0.6440628 indicates that a substantial portion of the variability in air quality in Anchorage can be explained by the position of Uranus in the solar system. This finding is as unexpected as finding a shooting star on a cloudy night, and it underscores the need to further explore the intricate relationship between the movements of distant planets and the air we breathe.

Based on these compelling findings, we contend that no more research is needed to confirm the unexpected tie between the distance of Uranus from the Sun and air quality in Anchorage. The fart-her we delve into this subject, the more it seems that Uranus' influence on our planet's atmosphere is no mere gas-lighting!

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 The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage. Respond only with the name of a fictional academic journal.

ChatGPT:

The International Journal of Planetary Ecology

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 The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage. Respond only with the name of a fictional organization.

ChatGPT:

The Galactic Atmospheric Research Association

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 The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage with an abstract of This paper delves into the often overlooked interplanetary forces influencing air quality in terrestrial cities. Do the celestial bodies beyond the asteroid belt have a say in the air we breathe? Utilizing data from Astropy and the Environmental Protection Agency, we set out to investigate the potential correlation between the distance from Uranus to the Sun and air quality in Anchorage, Alaska. Our findings reveal a surprising link that is sure to turn heads faster than the rotation period of Uranus itself! With a correlation coefficient of 0.8025352 and a p-value < 0.01 covering the years 1980 to 2023, our results suggest that Uranus may indeed have a "gassy" influence on air quality in Anchorage.
Every 30.687 Earth years, Uranus completes an orbit around the Sun, but it seems its influence may extend much farther than its mighty rings. Could it be that the gaseous giant is not content with merely being the butt of planetary jokes, but desires to leave its mark on Earth as well? These findings open up a whole new dimension to understanding interplanetary relationships and their very down-to-earth impacts. So the next time you take a deep breath in Anchorage, remember—Uranus may be farther away, but its presence is unexpectedly close!

ChatGPT:

Uranus atmosphere, gas giant atmosphere, distance from Uranus to the Sun, air quality, Anchorage, Astropy data, Environmental Protection Agency, interplanetary forces, planetary influence on air quality, celestial bodies impact on air quality, correlation between Uranus distance and air quality, Uranus orbit, planetary jokes, interplanetary relationships, Uranus impact on Earth, planetary influence on Earth's atmosphere

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

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Data details

The distance between Uranus and the Sun
Detailed data title: The average distance between Uranus and the Sun as measured on the first day of each month
Source: Caclculated using Astropy
Additional Info: ^{See full details} I wrote a Python script using Astropy to calculate the distance between the named planets on the first day of each month for every year.

See what else correlates with The distance between Uranus and the Sun

Air quality in Anchorage
Detailed data title: Percentage of days with good or moderate air quality in Anchorage, AK
Source: Environmental Protection Agency
See what else correlates with Air quality in Anchorage

Correlation r = 0.8025352 (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 = 0.6440628 (Coefficient of determination)
This means 64.4% of the change in the one variable (i.e., Air quality in Anchorage) is predictable based on the change in the other (i.e., The distance between Uranus and the Sun) over the 44 years from 1980 through 2023.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 5.7E-11.^Show 0.0000000000571223897627642400
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 0.8 in 5.7E-9% of random cases. Said differently, if you correlated 17,506,270,381 random variables^Note You don't actually need 17 billion variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

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

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

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 43 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 43 because we have two variables measured over a period of 44 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.

[ 0.66, 0.89 ] 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.

	1980	1981	1982	1983	1984	1985	1986	1987	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
The distance between Uranus and the Sun (Planetary distance (AU))	18.7519	18.816	18.8813	18.9473	19.0136	19.0797	19.1456	19.2114	19.2773	19.343	19.4085	19.4735	19.5377	19.6002	19.6602	19.7172	19.7706	19.8197	19.8643	19.9045	19.9405	19.9724	20.0008	20.0257	20.0475	20.0658	20.0804	20.0909	20.0968	20.0975	20.0929	20.0826	20.0668	20.0459	20.0203	19.9907	19.9574	19.9211	19.882	19.8403	19.7956	19.748	19.6971	19.6428
Air quality in Anchorage (Good air quality)	87.1585	90.411	87.3973	81.6438	89.071	94.2466	95.8904	97.4138	96.7123	97.7273	95.5923	98.3516	95.3297	97.2376	97.7901	98.6226	98.2906	100	99.1713	98.0831	99.6721	99.3443	99.3421	98.3871	99.3485	99.0099	98.7013	99.6774	99.6795	99.449	98.6301	99.1781	98.6339	98.6301	96.4384	96.9863	98.9071	98.3562	98.9041	96.7123	99.7268	98.9041	99.726	99.4505

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.
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([18.7519,18.816,18.8813,18.9473,19.0136,19.0797,19.1456,19.2114,19.2773,19.343,19.4085,19.4735,19.5377,19.6002,19.6602,19.7172,19.7706,19.8197,19.8643,19.9045,19.9405,19.9724,20.0008,20.0257,20.0475,20.0658,20.0804,20.0909,20.0968,20.0975,20.0929,20.0826,20.0668,20.0459,20.0203,19.9907,19.9574,19.9211,19.882,19.8403,19.7956,19.748,19.6971,19.6428,])
array_2 = np.array([87.1585,90.411,87.3973,81.6438,89.071,94.2466,95.8904,97.4138,96.7123,97.7273,95.5923,98.3516,95.3297,97.2376,97.7901,98.6226,98.2906,100,99.1713,98.0831,99.6721,99.3443,99.3421,98.3871,99.3485,99.0099,98.7013,99.6774,99.6795,99.449,98.6301,99.1781,98.6339,98.6301,96.4384,96.9863,98.9071,98.3562,98.9041,96.7123,99.7268,98.9041,99.726,99.4505,])
array_1_name = "The distance between Uranus and the Sun"
array_2_name = "Air quality in Anchorage"

# 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 The distance between Uranus and the Sun
Line chart for only Air quality in Anchorage
AI-generated correlation image
The spurious research paper: The Atmospherics of Uranus: Examining the Gas Giant's Distance from the Sun and its Impact on Air Quality in Anchorage

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Correlation ID: 5715 · Black Variable ID: 1934 · Red Variable ID: 20268


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