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Spurious correlation #4,972 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air quality in Baton Rouge and the second variable is Google searches for 'i have the flu'.  The chart goes from 2004 to 2023, and the two variables track closely in value over that time. Small Image

AI explanation

The fresher air must have flu away your symptoms! Or maybe people were just feeling too congested to type.

Model: dalle-3
Prompt: Generate an image of a futuristic cityscape set in Baton Rouge. The sky is a vibrant, clear blue, with sleek, modern architecture reaching towards the horizon. A peaceful, pollutant-free atmosphere is indicated by the absence of smog. In the foreground, individuals are joyfully participating in outdoor activities, such as cycling, jogging, and picnicking, exuding healthy vitality. Meanwhile, inside their homes, individuals are observed seeking relief from flu symptoms by searching for "i have the flu" on their futuristic devices. The scene should convey a balance between the vibrant, active outdoor lifestyle and the need for comfort and care indoors. 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 quality in Baton Rouge and Google searches for 'i have the flu'. 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: Cute cartoon Futuristic Cutsy graphics Cutsy art illustration Oragami
ChatGPT: Futuristic

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 quality in Baton Rouge and Google searches for 'i have the flu', in the following situation: The fresher air must have flu away your symptoms! Or maybe people were just feeling too congested to type.. Keep the description simple.
ChatGPT: A clear blue sky stretches over Baton Rouge, with a gentle breeze carrying away any pollutants. In the distance, a group of people can be seen happily engaged in outdoor activities. Meanwhile, in their homes, individuals are seen typing "i have the flu" into their Google search bar, as they seek relief from their congested symptoms.

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: [ Futuristic ] and depicting this scene: A clear blue sky stretches over Baton Rouge, with a gentle breeze carrying away any pollutants. In the distance, a group of people can be seen happily engaged in outdoor activities. Meanwhile, in their homes, individuals are seen typing "i have the flu" into their Google search bar, as they seek relief from their congested symptoms. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a futuristic cityscape set in Baton Rouge. The sky is a vibrant, clear blue, with sleek, modern architecture reaching towards the horizon. A peaceful, pollutant-free atmosphere is indicated by the absence of smog. In the foreground, individuals are joyfully participating in outdoor activities, such as cycling, jogging, and picnicking, exuding healthy vitality. Meanwhile, inside their homes, individuals are observed seeking relief from flu symptoms by searching for "i have the flu" on their futuristic devices. The scene should convey a balance between the vibrant, active outdoor lifestyle and the need for comfort and care indoors.

*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 quality in Baton Rouge positively influenced i have the flu (Google searches for 'i have the flu'). Include one good pun.

AI academic paper

(Because p < 0.01)
Air We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches

The Journal of Eccentric Environmental Health Studies

Jan 2024
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 silly 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 quality in Baton Rouge and Google searches for 'i have the flu'. Make lots of jokes, goofy observations, and puns.

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

Your research team used data from Environmental Protection Agency and Google Trends to assess this nagging question. You found a correlation coefficient of 0.8196337 and p < 0.01 for 2004 to 2023.

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 We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches

[[ABSTRACT]]
In this research paper, we examine the curious correlation between air quality in Baton Rouge and the number of Google searches for 'i have the flu'. Our study takes a lighthearted approach to a serious topic, exploring the peculiar relationship between environmental factors and public health behavior. We utilized data from the Environmental Protection Agency and Google Trends to analyze a time period stretching from 2004 to 2023, aiming to determine whether there is a definitive linkage between poor air quality and an influx of flu-related web searches.

Our findings revealed a surprisingly strong correlation coefficient of 0.8196337, with a statistically significant p-value of less than 0.01. While the results do not imply causation, they certainly raise some eyebrows and prompt a chuckle or two. We discuss potential implications of these findings for public health awareness campaigns, as well as the need for further investigation into the association between air quality and online symptom-searching behavior. Ultimately, this study offers a whimsical yet thought-provoking exploration of the intersection between respiratory ailments, internet surfing habits, and atmospheric conditions in Baton Rouge.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 quality in Baton Rouge and Google searches for 'i have the flu'. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Here is the title and abstract of the paper:
[[TITLE]]
Air We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches

[[ABSTRACT]]
In this research paper, we examine the curious correlation between air quality in Baton Rouge and the number of Google searches for 'i have the flu'. Our study takes a lighthearted approach to a serious topic, exploring the peculiar relationship between environmental factors and public health behavior. We utilized data from the Environmental Protection Agency and Google Trends to analyze a time period stretching from 2004 to 2023, aiming to determine whether there is a definitive linkage between poor air quality and an influx of flu-related web searches.

Our findings revealed a surprisingly strong correlation coefficient of 0.8196337, with a statistically significant p-value of less than 0.01. While the results do not imply causation, they certainly raise some eyebrows and prompt a chuckle or two. We discuss potential implications of these findings for public health awareness campaigns, as well as the need for further investigation into the association between air quality and online symptom-searching behavior. Ultimately, this study offers a whimsical yet thought-provoking exploration of the intersection between respiratory ailments, internet surfing habits, and atmospheric conditions in Baton Rouge.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
Ah, the ever-entertaining world of research! Delving into the nuances of quirky correlations and unexpected findings is a true delight for any inquisitive mind. In this whimsically crafted research paper, we embark on a journey through the peculiar intersection of environmental factors and public health behavior. Our curious concoction? The relationship between air quality in the charming city of Baton Rouge and the Google searches for 'i have the flu'.

Now, it may seem like an odd pairing at first, but as we plunge into the depths of statistical analysis and data interpretation, we aim to shed some light on this unconventional link. We hope to cultivate a lighthearted yet enlightening atmosphere to explore this quirky correlation. After all, why not inject some levity into the serious world of academia?

We can't help but muse over the comical potential of uncovering a causational link between the air one breathes and the flu symptoms one searches for online. Will the data reveal a flurry of searches coinciding with a surge in pollution levels? Or will we uncover a sneeze-inducing spike in web queries as the air quality takes a nosedive? In the realm of research, the possibilities are as endless as a statistician's supply of probability distributions!

So, don your metaphorical lab coat and buckle up for a delightful romp through the quirky, the peculiar, and the downright unexpected. Our study is certainly not your typical run-of-the-mill investigation. Instead, it's a mischievous dance between empirical observations and the ever-fascinating world of internet browsing habits.

The data we've collected provides a smorgasbord of statistical morsels that have left us both scratching our heads and stifling the occasional guffaw. Join us as we dissect the implications of our findings and revel in the whimsy of this offbeat exploration. After all, in the illustrious words of Albert Einstein, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...'." And oh, how our findings are tickling our statistical funny bone!


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 quality in Baton Rouge and Google searches for 'i have the flu'. Make lots of 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 name a few real TV shows that sound like they might be relevant to the topic that you watched as research.

Here is the title and abstract of the paper:
[[TITLE]]
Air We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches

[[ABSTRACT]]
In this research paper, we examine the curious correlation between air quality in Baton Rouge and the number of Google searches for 'i have the flu'. Our study takes a lighthearted approach to a serious topic, exploring the peculiar relationship between environmental factors and public health behavior. We utilized data from the Environmental Protection Agency and Google Trends to analyze a time period stretching from 2004 to 2023, aiming to determine whether there is a definitive linkage between poor air quality and an influx of flu-related web searches.

Our findings revealed a surprisingly strong correlation coefficient of 0.8196337, with a statistically significant p-value of less than 0.01. While the results do not imply causation, they certainly raise some eyebrows and prompt a chuckle or two. We discuss potential implications of these findings for public health awareness campaigns, as well as the need for further investigation into the association between air quality and online symptom-searching behavior. Ultimately, this study offers a whimsical yet thought-provoking exploration of the intersection between respiratory ailments, internet surfing habits, and atmospheric conditions in Baton Rouge.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Ah, the ever-entertaining world of research! Delving into the nuances of quirky correlations and unexpected findings is a true delight for any inquisitive mind. In this whimsically crafted research paper, we embark on a journey through the peculiar intersection of environmental factors and public health behavior. Our curious concoction? The relationship between air quality in the charming city of Baton Rouge and the Google searches for 'i have the flu'.
Now, it may seem like an odd pairing at first, but as we plunge into the depths of statistical analysis and data interpretation, we aim to shed some light on this unconventional link. We hope to cultivate a lighthearted yet enlightening atmosphere to explore this quirky correlation. After all, why not inject some levity into the serious world of academia?
We can't help but muse over the comical potential of uncovering a causational link between the air one breathes and the flu symptoms one searches for online. Will the data reveal a flurry of searches coinciding with a surge in pollution levels? Or will we uncover a sneeze-inducing spike in web queries as the air quality takes a nosedive? In the realm of research, the possibilities are as endless as a statistician's supply of probability distributions!
So, don your metaphorical lab coat and buckle up for a delightful romp through the quirky, the peculiar, and the downright unexpected. Our study is certainly not your typical run-of-the-mill investigation. Instead, it's a mischievous dance between empirical observations and the ever-fascinating world of internet browsing habits.
The data we've collected provides a smorgasbord of statistical morsels that have left us both scratching our heads and stifling the occasional guffaw. Join us as we dissect the implications of our findings and revel in the whimsy of this offbeat exploration. After all, in the illustrious words of Albert Einstein, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...'." And oh, how our findings are tickling our statistical funny bone!

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

Previous research has delved into the intricate web of relationships between air quality and public health behavior, with a particular focus on environmental factors and their impact on respiratory ailments and overall well-being. Smith et al. (2015) conducted a comprehensive analysis of air quality in urban areas, highlighting the potential health risks associated with heightened levels of air pollution. Meanwhile, Doe and Jones (2018) explored the behavioral patterns of individuals seeking health-related information online, shedding light on the trends and motivations behind internet symptom searches.

Turning to the realm of non-fiction literature, books such as "The Air Pollution Solution" by Clean Air Enthusiasts (2017) and "Digital Diagnosis: Navigating Online Health Information" by Medica S. Expert (2019) have provided valuable insights into the intersection of environmental health and digital information-seeking behavior. These sources offer a robust foundation for understanding the multifaceted dynamics at play in our investigation.

In the realm of fiction, novels such as "The Flu Files" by A. Sweez and "Searchers of the Web: An Online Odyssey" by E. Googler (2016) present imaginative narratives that, while not grounded in empirical data, capture the collective imagination's fascination with the convergence of illness and internet exploration.

On a more light-hearted note, the research team also immersed themselves in the viewing of relevant television programming, including medical dramas such as "Grey's Anatomy" and "House MD," to gain a sense of the public's perception of online health-related searches. While these shows offered drama and intrigue in abundance, they also provided a glimpse into the general population's curiosity about medical symptoms and diagnoses.

As the literature shows, our examination of the correlation between air quality in Baton Rouge and 'i have the flu' Google searches is situated within a broader landscape of research and cultural representation. With this diverse array of sources in mind, we proceed to analyze and interpret our own findings with a high degree of scientific rigor and a healthy dose of whimsy.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 quality in Baton Rouge and Google searches for 'i have the flu'. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Google Trends . You used data from 2004 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]]
Air We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches

[[ABSTRACT]]
In this research paper, we examine the curious correlation between air quality in Baton Rouge and the number of Google searches for 'i have the flu'. Our study takes a lighthearted approach to a serious topic, exploring the peculiar relationship between environmental factors and public health behavior. We utilized data from the Environmental Protection Agency and Google Trends to analyze a time period stretching from 2004 to 2023, aiming to determine whether there is a definitive linkage between poor air quality and an influx of flu-related web searches.

Our findings revealed a surprisingly strong correlation coefficient of 0.8196337, with a statistically significant p-value of less than 0.01. While the results do not imply causation, they certainly raise some eyebrows and prompt a chuckle or two. We discuss potential implications of these findings for public health awareness campaigns, as well as the need for further investigation into the association between air quality and online symptom-searching behavior. Ultimately, this study offers a whimsical yet thought-provoking exploration of the intersection between respiratory ailments, internet surfing habits, and atmospheric conditions in Baton Rouge.

[[INTRODUCTION]]
Ah, the ever-entertaining world of research! Delving into the nuances of quirky correlations and unexpected findings is a true delight for any inquisitive mind. In this whimsically crafted research paper, we embark on a journey through the peculiar intersection of environmental factors and public health behavior. Our curious concoction? The relationship between air quality in the charming city of Baton Rouge and the Google searches for 'i have the flu'.
Now, it may seem like an odd pairing at first, but as we plunge into the depths of statistical analysis and data interpretation, we aim to shed some light on this unconventional link. We hope to cultivate a lighthearted yet enlightening atmosphere to explore this quirky correlation. After all, why not inject some levity into the serious world of academia?
We can't help but muse over the comical potential of uncovering a causational link between the air one breathes and the flu symptoms one searches for online. Will the data reveal a flurry of searches coinciding with a surge in pollution levels? Or will we uncover a sneeze-inducing spike in web queries as the air quality takes a nosedive? In the realm of research, the possibilities are as endless as a statistician's supply of probability distributions!
So, don your metaphorical lab coat and buckle up for a delightful romp through the quirky, the peculiar, and the downright unexpected. Our study is certainly not your typical run-of-the-mill investigation. Instead, it's a mischievous dance between empirical observations and the ever-fascinating world of internet browsing habits.
The data we've collected provides a smorgasbord of statistical morsels that have left us both scratching our heads and stifling the occasional guffaw. Join us as we dissect the implications of our findings and revel in the whimsy of this offbeat exploration. After all, in the illustrious words of Albert Einstein, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...'." And oh, how our findings are tickling our statistical funny bone!

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

To embark on our whimsical journey of uncovering the connection between air quality in Baton Rouge and the number of Google searches for 'i have the flu', we turned to a mosaic of methodologies that would make even the most stoic of statisticians crack a smile. Our research team gathered data from sources as varied as a mad scientist's concoction, primarily relying on the Environmental Protection Agency's air quality measurements and the delightful treasure trove of internet search trends served up by the esteemed Google Trends.

In our pursuit of the holy grail of correlation, we parsed through data spanning from 2004 to 2023, traversing a tapestry of flu seasons and air quality oscillations. Our first step was to curate a comprehensive dataset, ensuring that our statistical stew was simmering with a rich blend of air quality indices and the frequency of 'i have the flu' queries. We embraced the chaos of the internet, allowing Google Trends to guide us through the labyrinthine paths of search patterns, while also keeping a watchful eye on the capricious dance of air pollutants monitored by the Environmental Protection Agency.

Once our data cauldron was brimming with an enchanting blend of variables, we summoned the spirits of statistical analysis to peer into the brew and uncover any hidden connections. Our tools of choice included the trusty correlation coefficient, a magician's wand for revealing mesmerizing patterns in the data, and the almighty p-value, a yardstick wielded to discern the true significance of our findings amidst the statistical noise. With these sorcerous instruments at our disposal, we teased out the strength and significance of the relationship between air quality and flu-related cyber explorations.

But this was no straightforward wizardry – oh no, we ventured into the weeds of regression models and time series analysis to unravel the enigmatic threads binding air quality and flu searches. We wanted to unearth any temporal nuances and seasonal whims that might add an extra dash of peculiarity to our findings. Like intrepid explorers armed with quill and parchment, we chronicled our expeditions through the labyrinth of statistical inference, aiming to capture the essence of this remarkable correlation while reveling in the mischievous antics of our scholarly pursuit.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 quality in Baton Rouge and Google searches for 'i have the flu'. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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

For the time period 2004 to 2023, you found a correlation 0.8196337, r-squared of 0.6717994, 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 We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches

[[ABSTRACT]]
In this research paper, we examine the curious correlation between air quality in Baton Rouge and the number of Google searches for 'i have the flu'. Our study takes a lighthearted approach to a serious topic, exploring the peculiar relationship between environmental factors and public health behavior. We utilized data from the Environmental Protection Agency and Google Trends to analyze a time period stretching from 2004 to 2023, aiming to determine whether there is a definitive linkage between poor air quality and an influx of flu-related web searches.

Our findings revealed a surprisingly strong correlation coefficient of 0.8196337, with a statistically significant p-value of less than 0.01. While the results do not imply causation, they certainly raise some eyebrows and prompt a chuckle or two. We discuss potential implications of these findings for public health awareness campaigns, as well as the need for further investigation into the association between air quality and online symptom-searching behavior. Ultimately, this study offers a whimsical yet thought-provoking exploration of the intersection between respiratory ailments, internet surfing habits, and atmospheric conditions in Baton Rouge.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
Ah, the ever-entertaining world of research! Delving into the nuances of quirky correlations and unexpected findings is a true delight for any inquisitive mind. In this whimsically crafted research paper, we embark on a journey through the peculiar intersection of environmental factors and public health behavior. Our curious concoction? The relationship between air quality in the charming city of Baton Rouge and the Google searches for 'i have the flu'.
Now, it may seem like an odd pairing at first, but as we plunge into the depths of statistical analysis and data interpretation, we aim to shed some light on this unconventional link. We hope to cultivate a lighthearted yet enlightening atmosphere to explore this quirky correlation. After all, why not inject some levity into the serious world of academia?
We can't help but muse over the comical potential of uncovering a causational link between the air one breathes and the flu symptoms one searches for online. Will the data reveal a flurry of searches coinciding with a surge in pollution levels? Or will we uncover a sneeze-inducing spike in web queries as the air quality takes a nosedive? In the realm of research, the possibilities are as endless as a statistician's supply of probability distributions!
So, don your metaphorical lab coat and buckle up for a delightful romp through the quirky, the peculiar, and the downright unexpected. Our study is certainly not your typical run-of-the-mill investigation. Instead, it's a mischievous dance between empirical observations and the ever-fascinating world of internet browsing habits.
The data we've collected provides a smorgasbord of statistical morsels that have left us both scratching our heads and stifling the occasional guffaw. Join us as we dissect the implications of our findings and revel in the whimsy of this offbeat exploration. After all, in the illustrious words of Albert Einstein, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...'." And oh, how our findings are tickling our statistical funny bone!

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

The results of our analysis left us anything but under the weather! After an undoubtedly amusing romp through the statistical landscapes, we uncovered a correlation coefficient of 0.8196337 between air quality in Baton Rouge and the volume of Google searches for 'i have the flu'. This correlation is even stronger than the bond between a scientist and their coffee during a late-night data crunch.

With an r-squared value of 0.6717994, we danced a statistical jig over the substantial amount of variance in 'i have the flu' searches that can be explained by air quality. The p-value of less than 0.01 left us feeling more confident in our findings than a researcher with a meticulously crafted hypothesis.

In the spirit of levity and scientific curiosity, we present Fig. 1, a scatterplot showcasing the robust correlation between air quality and 'i have the flu' Google searches. This visualization had us marveling at the marriage of digital data and environmental indicators, akin to a fusion between art and science that even da Vinci himself would envy.

We can't help but raise a toast to the delightful absurdity of our findings, sparking a sense of scientific wonderment and a few knowing chuckles. While our results do not establish a causational link between air quality and flu-related web searches, they certainly shine a whimsical spotlight on the peculiar connections in our world.

Our findings beckon further investigation, as we ponder the potential implications for public health campaigns and the interdisciplinary fusion of environmental science and digital behavior. This study is a quirky ode to the unanticipated, a comedic twist narrated by the gentle arithmetic hum of statistical computations. After all, the world of research is not without its moments of statistical hilarity!


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 quality in Baton Rouge and Google searches for 'i have the flu'. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Limit your response to 500 tokens.

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

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

[[TITLE]]
Air We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches

[[ABSTRACT]]
In this research paper, we examine the curious correlation between air quality in Baton Rouge and the number of Google searches for 'i have the flu'. Our study takes a lighthearted approach to a serious topic, exploring the peculiar relationship between environmental factors and public health behavior. We utilized data from the Environmental Protection Agency and Google Trends to analyze a time period stretching from 2004 to 2023, aiming to determine whether there is a definitive linkage between poor air quality and an influx of flu-related web searches.

Our findings revealed a surprisingly strong correlation coefficient of 0.8196337, with a statistically significant p-value of less than 0.01. While the results do not imply causation, they certainly raise some eyebrows and prompt a chuckle or two. We discuss potential implications of these findings for public health awareness campaigns, as well as the need for further investigation into the association between air quality and online symptom-searching behavior. Ultimately, this study offers a whimsical yet thought-provoking exploration of the intersection between respiratory ailments, internet surfing habits, and atmospheric conditions in Baton Rouge.

[[LITERATURE REVIEW]]
Previous research has delved into the intricate web of relationships between air quality and public health behavior, with a particular focus on environmental factors and their impact on respiratory ailments and overall well-being. Smith et al. (2015) conducted a comprehensive analysis of air quality in urban areas, highlighting the potential health risks associated with heightened levels of air pollution. Meanwhile, Doe and Jones (2018) explored the behavioral patterns of individuals seeking health-related information online, shedding light on the trends and motivations behind internet symptom searches.
Turning to the realm of non-fiction literature, books such as "The Air Pollution Solution" by Clean Air Enthusiasts (2017) and "Digital Diagnosis: Navigating Online Health Information" by Medica S. Expert (2019) have provided valuable insights into the intersection of environmental health and digital information-seeking behavior. These sources offer a robust foundation for understanding the multifaceted dynamics at play in our investigation.
In the realm of fiction, novels such as "The Flu Files" by A. Sweez and "Searchers of the Web: An Online Odyssey" by E. Googler (2016) present imaginative narratives that, while not grounded in empirical data, capture the collective imagination's fascination with the convergence of illness and internet exploration.
On a more light-hearted note, the research team also immersed themselves in the viewing of relevant television programming, including medical dramas such as "Grey's Anatomy" and "House MD," to gain a sense of the public's perception of online health-related searches. While these shows offered drama and intrigue in abundance, they also provided a glimpse into the general population's curiosity about medical symptoms and diagnoses.
As the literature shows, our examination of the correlation between air quality in Baton Rouge and 'i have the flu' Google searches is situated within a broader landscape of research and cultural representation. With this diverse array of sources in mind, we proceed to analyze and interpret our own findings with a high degree of scientific rigor and a healthy dose of whimsy.

[[RESULTS]]
The results of our analysis left us anything but under the weather! After an undoubtedly amusing romp through the statistical landscapes, we uncovered a correlation coefficient of 0.8196337 between air quality in Baton Rouge and the volume of Google searches for 'i have the flu'. This correlation is even stronger than the bond between a scientist and their coffee during a late-night data crunch.
With an r-squared value of 0.6717994, we danced a statistical jig over the substantial amount of variance in 'i have the flu' searches that can be explained by air quality. The p-value of less than 0.01 left us feeling more confident in our findings than a researcher with a meticulously crafted hypothesis.
In the spirit of levity and scientific curiosity, we present Fig. 1, a scatterplot showcasing the robust correlation between air quality and 'i have the flu' Google searches. This visualization had us marveling at the marriage of digital data and environmental indicators, akin to a fusion between art and science that even da Vinci himself would envy.
We can't help but raise a toast to the delightful absurdity of our findings, sparking a sense of scientific wonderment and a few knowing chuckles. While our results do not establish a causational link between air quality and flu-related web searches, they certainly shine a whimsical spotlight on the peculiar connections in our world.
Our findings beckon further investigation, as we ponder the potential implications for public health campaigns and the interdisciplinary fusion of environmental science and digital behavior. This study is a quirky ode to the unanticipated, a comedic twist narrated by the gentle arithmetic hum of statistical computations. After all, the world of research is not without its moments of statistical hilarity!

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

Our findings align with the current body of literature regarding the intersection of air quality, health-related information-seeking behavior, and the zany world of statistical analysis. The correlation coefficient we unearthed between Baton Rouge air quality and 'i have the flu' Google searches not only raised eyebrows but also lifted our spirits higher than a hot air balloon on a sunny day.

Our results supported the work of Smith et al. (2015) who emphasized the health risks associated with air pollution. In our study, poor air quality seemed to prompt more flu-related searches, similar to how a bad joke prompts eye rolls – with clear cause and effect. Likewise, Doe and Jones (2018) provided insights into the behaviors of online health information seekers, and our findings seem to confirm that when the air quality's questionably fresh, folks are more likely to turn to the internet for hypochondriacal pursuits.

Even our exploration of fiction and television programming proved to be surprisingly relevant. "The Flu Files" by A. Sweez and "Searchers of the Web: An Online Odyssey" by E. Googler presented fictional tales, but our study supports their imaginative blend of illness and online exploration. And while medical dramas like "Grey's Anatomy" and "House MD" might not be rooted in empirical data, they do capture the whimsical public intrigue with health-related searches. Our study underlines the entertaining correlation between atmospheric conditions and online symptom sleuthing, offered with a hefty dose of statistical rigor and a sprinkle of unbridled gumption.

The implications of our findings are as intriguing as a good whodunit, suggesting potential opportunities for targeted public health campaigns during times of poor air quality. Furthermore, the fusion of environmental science and digital behavior is as comical as a chemist trying to tell a joke – unexpected but undeniably delightful.

Our study does have its limitations, and it’s important to approach the results with a level of scientific sobriety amid the revelry. The correlation we observed does not imply causation, much like the presence of a firetruck at a fire does not imply it caused the fire. It merely indicates two factors dancing in statistical harmony, perhaps due to some external influence yet to be uncovered. Future research could delve into the specific reasons behind this correlation, like Sherlock Holmes on a mission to solve a scientific caper.

In conclusion, our study uncovers a quirky link between air quality and 'i have the flu' Google searches, adding a touch of humor and curiosity to the realm of serious scientific inquiry. We hope this research inspires others to embrace the unexpected and pursue their statistical and scientific endeavors with a dash of whimsy. After all, science need not always be serious – a little levity can go a long way in unraveling the mysteries of the world we inhabit.


Model: gpt-3.5-turbo-1106
System prompt: You are a silly 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 quality in Baton Rouge and Google searches for 'i have the flu'. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
Air We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches

[[ABSTRACT]]
In this research paper, we examine the curious correlation between air quality in Baton Rouge and the number of Google searches for 'i have the flu'. Our study takes a lighthearted approach to a serious topic, exploring the peculiar relationship between environmental factors and public health behavior. We utilized data from the Environmental Protection Agency and Google Trends to analyze a time period stretching from 2004 to 2023, aiming to determine whether there is a definitive linkage between poor air quality and an influx of flu-related web searches.

Our findings revealed a surprisingly strong correlation coefficient of 0.8196337, with a statistically significant p-value of less than 0.01. While the results do not imply causation, they certainly raise some eyebrows and prompt a chuckle or two. We discuss potential implications of these findings for public health awareness campaigns, as well as the need for further investigation into the association between air quality and online symptom-searching behavior. Ultimately, this study offers a whimsical yet thought-provoking exploration of the intersection between respiratory ailments, internet surfing habits, and atmospheric conditions in Baton Rouge.

[[INTRDUCTION]]
Ah, the ever-entertaining world of research! Delving into the nuances of quirky correlations and unexpected findings is a true delight for any inquisitive mind. In this whimsically crafted research paper, we embark on a journey through the peculiar intersection of environmental factors and public health behavior. Our curious concoction? The relationship between air quality in the charming city of Baton Rouge and the Google searches for 'i have the flu'.
Now, it may seem like an odd pairing at first, but as we plunge into the depths of statistical analysis and data interpretation, we aim to shed some light on this unconventional link. We hope to cultivate a lighthearted yet enlightening atmosphere to explore this quirky correlation. After all, why not inject some levity into the serious world of academia?
We can't help but muse over the comical potential of uncovering a causational link between the air one breathes and the flu symptoms one searches for online. Will the data reveal a flurry of searches coinciding with a surge in pollution levels? Or will we uncover a sneeze-inducing spike in web queries as the air quality takes a nosedive? In the realm of research, the possibilities are as endless as a statistician's supply of probability distributions!
So, don your metaphorical lab coat and buckle up for a delightful romp through the quirky, the peculiar, and the downright unexpected. Our study is certainly not your typical run-of-the-mill investigation. Instead, it's a mischievous dance between empirical observations and the ever-fascinating world of internet browsing habits.
The data we've collected provides a smorgasbord of statistical morsels that have left us both scratching our heads and stifling the occasional guffaw. Join us as we dissect the implications of our findings and revel in the whimsy of this offbeat exploration. After all, in the illustrious words of Albert Einstein, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...'." And oh, how our findings are tickling our statistical funny bone!

[[RESULTS]]
The results of our analysis left us anything but under the weather! After an undoubtedly amusing romp through the statistical landscapes, we uncovered a correlation coefficient of 0.8196337 between air quality in Baton Rouge and the volume of Google searches for 'i have the flu'. This correlation is even stronger than the bond between a scientist and their coffee during a late-night data crunch.
With an r-squared value of 0.6717994, we danced a statistical jig over the substantial amount of variance in 'i have the flu' searches that can be explained by air quality. The p-value of less than 0.01 left us feeling more confident in our findings than a researcher with a meticulously crafted hypothesis.
In the spirit of levity and scientific curiosity, we present Fig. 1, a scatterplot showcasing the robust correlation between air quality and 'i have the flu' Google searches. This visualization had us marveling at the marriage of digital data and environmental indicators, akin to a fusion between art and science that even da Vinci himself would envy.
We can't help but raise a toast to the delightful absurdity of our findings, sparking a sense of scientific wonderment and a few knowing chuckles. While our results do not establish a causational link between air quality and flu-related web searches, they certainly shine a whimsical spotlight on the peculiar connections in our world.
Our findings beckon further investigation, as we ponder the potential implications for public health campaigns and the interdisciplinary fusion of environmental science and digital behavior. This study is a quirky ode to the unanticipated, a comedic twist narrated by the gentle arithmetic hum of statistical computations. After all, the world of research is not without its moments of statistical hilarity!

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In conclusion, our whimsically crafted journey through the correlation between air quality in Baton Rouge and Google searches for 'i have the flu' has left us feeling more elated than a researcher stumbling upon a significant p-value. The results of our investigation have unveiled a correlation coefficient that's as strong as a lab-grade centrifuge, with a statistically significant p-value that's more rock-solid than a petrified forest.

Our findings, while not establishing a definitive causational link, have certainly tickled our scientific funny bone and sparked gleeful musings about the delightful absurdity of statistical exploration. We suggest that future research takes a similarly lighthearted approach to unraveling the mysteries of public health behavior and environmental influences.

The implications of our findings may prompt public health campaigns to consider the interplay between air quality and digital symptom-searching behavior. As we bid adieu to this whimsical escapade, we assert that no more research is needed in this area. After all, we've certainly had our fill of statistical merriment, and it's time to leave this comical correlation in the capable hands of future jesters of academia.


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 We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Eccentric Environmental Health Studies


Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of nonprofit research organizations and associations. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding nonprofit, academic, or scientific association or organization that would sponsor research that resulted in a paper entited Air We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Zany Air Quality Studies


Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled Air We Feeling Under the Weather: A Quirky Connection Between Air Quality in Baton Rouge and 'I Have the Flu' Google Searches with an abstract of In this research paper, we examine the curious correlation between air quality in Baton Rouge and the number of Google searches for 'i have the flu'. Our study takes a lighthearted approach to a serious topic, exploring the peculiar relationship between environmental factors and public health behavior. We utilized data from the Environmental Protection Agency and Google Trends to analyze a time period stretching from 2004 to 2023, aiming to determine whether there is a definitive linkage between poor air quality and an influx of flu-related web searches.
Our findings revealed a surprisingly strong correlation coefficient of 0.8196337, with a statistically significant p-value of less than 0.01. While the results do not imply causation, they certainly raise some eyebrows and prompt a chuckle or two. We discuss potential implications of these findings for public health awareness campaigns, as well as the need for further investigation into the association between air quality and online symptom-searching behavior. Ultimately, this study offers a whimsical yet thought-provoking exploration of the intersection between respiratory ailments, internet surfing habits, and atmospheric conditions in Baton Rouge.

ChatGPT:

Baton Rouge, air quality, flu, Google searches, correlation, environmental factors, public health behavior, EPA data, Google Trends, respiratory ailments, public health awareness, online symptom-searching behavior

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



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Data details

Air quality in Baton Rouge
Detailed data title: Percentage of days with good air quality in Baton Rouge, LA
Source: Environmental Protection Agency
See what else correlates with Air quality in Baton Rouge

Google searches for 'i have the flu'
Detailed data title: Relative volume of Google searches for 'i have the flu' (Worldwide, without quotes)
Source: Google Trends
Additional Info: Relative search volume (not absolute numbers)

See what else correlates with Google searches for 'i have the flu'

Correlation r = 0.8196337 (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 = 0.6717994 (Coefficient of determination)
This means 67.2% of the change in the one variable (i.e., Google searches for 'i have the flu') is predictable based on the change in the other (i.e., Air quality in Baton Rouge) over the 20 years from 2004 through 2023.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 9.8E-6. 0.0000097685082904068060000000
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 0.82 in 0.00098% of random cases. Said differently, if you correlated 102,370 random variables You don't actually need 102 thousand variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

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

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

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 19 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 19 because we have two variables measured over a period of 20 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.

[ 0.59, 0.93 ] 95% correlation confidence interval (using the Fisher z-transformation)
The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

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


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

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.
20042005200620072008200920102011201220132014201520162017201820192020202120222023
Air quality in Baton Rouge (Good air quality)42.349725.479524.383634.520541.803345.205529.86332.602745.628456.986347.123344.383650.819763.287761.643861.369968.579267.123357.534246.3504
Google searches for 'i have the flu' (Rel. search volume)3.333334.583334.083333.916676.9166728.583311.166715.166716.666723.521.083319.416718.833324.1667343033.2521.333329.333317.6667




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.




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([42.3497,25.4795,24.3836,34.5205,41.8033,45.2055,29.863,32.6027,45.6284,56.9863,47.1233,44.3836,50.8197,63.2877,61.6438,61.3699,68.5792,67.1233,57.5342,46.3504,])
array_2 = np.array([3.33333,4.58333,4.08333,3.91667,6.91667,28.5833,11.1667,15.1667,16.6667,23.5,21.0833,19.4167,18.8333,24.1667,34,30,33.25,21.3333,29.3333,17.6667,])
array_1_name = "Air quality in Baton Rouge"
array_2_name = "Google searches for 'i have the flu'"

# 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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Correlation ID: 4972 · Black Variable ID: 20332 · Red Variable ID: 1528
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